EXPERIMENTAL PSYCHOLOGY ----------------------------------------------------------- EXPERIMENTAL PSYCHOLOGY 4 Manual of Laboratory Practice BY EDWARD BRADFORD TITCHENER VOLUME II QUANTITATIVE EXPERIMENTS PART II. INSTRUCTOR'S MANUAL fe pense, quant a moi, et j' affirme que rant qu' un phnom2ne, quel qtt'zl soil, physiqe au moral, n'a pas bres, zl lazsse dotes l'esprtl toujours quelque chose de myslb- rieux.-- DELB(EUF. THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. x923 All rzx'hls reserved ----------------------------------------------------------- COPYRIGF-T, I9o5, THE MACMILLAIq COMPAIg¾. Set up and electrotyped. Pubhshed October, go5 otmool Barwick & Smith Co , Norwood, Maas., U.S.A o the flemor of JOSEPH REMI LPOPOLD DELBOZUF x83x-t896 ----------------------------------------------------------- PREFACE THs second volume follows the plan of the first, with such modifications (noted in their place) as the difference of subject matter has seemed to make necessary. The major part of the book--in Pt. i., the Introduction, Ch. I., and the expository portions of Ch. II.; in Pt. if., the Introduction, Ch. I., and the historical and critical Sections of Ch. II.--was written in 9ox-9o3. In the autumn of x9o3, I was obliged to turn aside for a time to other occupations, and did not resume my main task until the spring of x9o4 ß In the meanwhile, Pro- fessor G. E. Muller had published his Gesichtspunkte und Tat- sachen der psychophysischet Methodik, a work of practically the same range as my Chs. I. and II. I had been greatly influenced by Mfiller's previous writings, and had shaped my account of the Metric Methods in conformity with his standards; I had also, if it may be said without self-praise, carried psychophysical analysis, in various directions, beyond the point at which he had left it. When, therefore, the Methodik appeared, I found nothing to alter or amend; though, as I had known before, there was much that might be deepened and broadened. I xvas sorely tempted to leave my text as it stood, and to take account of Mhller's book simply in foot-note references. But the better counsel prevailed: I have gone over again the ground covered by Mfiller's researches, and ha:,e sought to make the new results an organic part of my expo- sition. Next after my wife, I owe most, in the preparation of this volume, to Professor E. C. Sanford, of Clark University, and to .my colleague Professor I. M. Bentley. I am also heavily indebted to my former assistant, Dr. J. W. Baird, noxv of the Johns H6p- kins University, and to my present assistants, Mr. H. C. Stevens and Mr. C. E. Ferree. The Sections that deal with physical and mathematical questions have been read and revised by Professors lU ----------------------------------------------------------- iv Pre[ace j. MacMahon, E. L. Nichols and H. J. Ryan, of Cornell Uni- versit 3,: so that, if any errors remain, they have escaped the ex- pert eve. Professor G. E. Mfiller, of Gbttingen, and Dr. G. F. Lipps. of Leipzig, have kindly furnished me with information upon various special points. I must mention, further, Professor J. McK. Cattell, of Columbia University; Mr. W. H. Davis, of Lehigh Universit3-; Professor C. H. Judd, of Yale University; Professor W. B. Pillsbury, of the University of Michigan; Dr. H. F. Stecker, late of Cornell University, now of the Pennsyl- vania State College; Professor G. M. Whipple, of Cornell Uni- versity; and Mr. L. N. Wilson, Librarian of Clark University: all of whom have rendered me substantial aid. There is, indeed, hardly any one of my American colleagues upon whom I have not called for occasional assistance, which has been willingly granted; and if I do not cite more names in this Preface, it is only because the list, to have significance at all, must end somewhere. I desire to express, in general terms, my sincere gratitude to all--named or unnamed--who have given me of their time and knowledge. x I have dedicated this volume to the memory of the late Pro- fessor Delbceuf, first, as the author of the 'Reconstruction' which I trace in õ 6, but secondly and more personally as the friend who, during the last four years of his life, opened to me a treasure-house of erudition and psychological inspiration. CORNELL HEIGHTS, ITHACA, N. Y. Aprd st, 9o5. x Of my own students, my thanks are due in partmular to Mr. B. R. Andrews, Miss G M. Andrus, Professor J. C. Barnes, Mr. W. A. Frayer, Miss F. Gantt, 3,lr. R. H. Gault, Miss A. Jenkins, Dr. M. S. Macdonald, Mss M.A. Martin, Miss E. Murray, Miss M. C Nerney, Miss E. Parry, Mxss J. B. Peirson, Mr. G. H. Sabine, Dr. W. D Scott, Dr. C. R Sqmre, Mr. R. B. ¾Vaugh, Miss F.M. Winger (Mrs. W. C. Bagley), and the late Mr. O. G. Schumard. TABLE OF CONTENTS INTRODUCTION TIIœ I½IS] .4zVD ?If'OGReSS OF QU.42VTITvl TIFE PSYCHOLOGY  I. Weber's Experiments { 2. Fechner's Interpretation . 3. The Reception of the Elemenle { 4. Crnicmm (I) The gven S not a sum of S-units () The equabty of the j. n. d. (3) The ' psychophysical law' . 5. Our Debt to Fechner { 6. Reconstructran { 7. Notes on {{ I-7 of the Text .{ 8. Questions and Essay Subjects { 9. The Problems of Sensiuvty XII1 xx xlwi xlvni Ixvii lxxxlx cwi cxvi cxhv clvii clxv CHAPTER I. PRELIMINARY EXPERIMENTS EXPERIMENT I  20. The Qualitative L for Tones; the Lowest Audible Tone EXPERIMENT II   t. The Qualitative _NZ for Tones; Alternative Experiment  i2. Determinatmns of he Lowest Audfi)le Tone EXPERIMENT III  3. The Quahtative 77? for Tones; the Highest Audible Tone  4 Determinatmns of the Hghest Audible Tone EXPERIMENTS IV-VI  I5. The Intensive Nœ for Pressure v 2I 31 46 ----------------------------------------------------------- EXPERIM'ENTS VII, VIII  I& The Intenst'e Rœ for Sound . 56  r7. Weber's Law 6I EXPERIMENrS IX-XII  I8. Demonstrations of Weber's Law 72 CHAPTER I[. THE METRIC METHODS . 19. The Law of Error . 93  2o. The Method of Limits: Historical 99  2. The Method of Limits: Critical II6 EXPERIMENTS XIII,  22. The lX.lethod of Limits. Notes on  r6 of the Text Ii  23. The Lmens of Cont, nuous Chaage I37 EXPERISIENT XV 24. Fechner's Method of Average Error: Notes on  7 of the Text I43 25. The Method of Average Error. Historycat x6o EXPERIMENTS XVI, XVII  26. The Method of Eqmvalents: Notes on  :8 of the Text 87  27. The Method o Equivalents: Historical i9 I EXPERIMENTS XVIII, XIX 28. The Method of Equal Sense Distances: Notes on  19 of the Text I94 29 Tle Method of Equal Seuse Dmtances: Historical and Cmtical 3o. The Psychophysxcs of Toue . the Tonal Dœ and Judgments of Tonal Distance 232 EXPERIMENT XX 3I. The Method of Constant R: Notes on  2o of the Text . 248 EXPERIMENT XX[ 32 . The Determmauon of Equvalent] bythe Method of Constant ]?: Notes on  2I of the Text . 258 EXPERI3,IENTS XX[I, XXIH 33. The Method of Constant R-chfferences: Notes on  22 of the Text 263 34- The Method of Right and Wrong Cases: Historical and Critical 275 Table v/Contents vii CHAPTER IH. THE REACTION EXPERIMENT  35. Electrical Unitg and Measurements 3r 9  36. The Techmque of the Smple Reaction . 326 EXPERIMENT XX[V  37- The Three Types of Simple Reaction 356 EXPERIMENT XXV  38. Compound Reactions . Dscrlmination, Cognition, Choice 375 EXPERIMENT XXVI  39' Compound Reactions: Association 38I CHAPTER IV. THE PSYCHOLOGY OF TIME EXPERIMENT XXVII  40. The Estimation of Tme 393 CHAPTER V. THE RANGE OF QUANTITATIVE PSYCHOLOGY  4I. Some Typical Experiments m Quantitative Psychology . 4o5 APPENDICES APPENDIX I. EXAMINATION QUESTIONS . 4i 3 .APPENDIX I1-. BOOKS AND PERIODICALS . 4i 7 APPENDIX III. FIRMS AND INSTRUMENTS . 423 LIST OF MATERIALS 425 INDEX OF NAMES 429 INDEX OF SUBJECTS 439 ----------------------------------------------------------- FIG I 2. 3. INDEX OF FIGURES Jr. 5. 6. 7. 8. 9- IO. II. 12. 13. I4. 15. 16. I7. I8. I9 20 21. 22. 23. 2.. 25. 26. 27- 28. 29 3 ¸ 3I. 32 ß Progression of tl/e DL with increasing R (Ament) Diagram tlIustrattveof the nterpretations of Weber's Law Koenig's giant fork . Appunn's wire fork Appunn's series of hgh forks One of Appunn's high forks, with cork attachment Politzer's acoumeter Zoth's acoumeter Seashore's audiometer Massoa's disc Demonstratmn dscs for Webefts Law Lehmann's arrangement for the photomerry of grey glasses Eplscotister Curves of xveight dmcrimmaton Graphic expression of ratio-series Curve of brightness dmcrlmlnaton Curve ot brightness dscnmlnatlon Martius' dmc Hering's discs Appunn's octave tonometer Schema of Method of Limits Jastrow's pressure balance Marbe's colour mixer Stern's tone varlator, first model Stern's tone variator, latest model Schema of Stern's tone varmtor Stern's tone x.arlator with g'asometer Whlpple's double gasometer Stratton's estheslometer . Schema of Stratton's ,esthesometer Mtinsterberg's apparatus for the comparison of visual extents Wundt's grawty phonometer ix 1XXXV XC1 x3 14- 3 33 59 59 60 77 78 79 79 83 84 86 86 87 88 9 r  36 38 t39 39 $9 14o 14-2 14-2 2Io 221 ----------------------------------------------------------- x fndex of Figures _33. Wundt's apparatus for memory of visual distances . .34. Curves illustrating the Method o,1' Rght and Vrong Cases (Fullerton and Cattell) 35. Curves showing the dlstnbutmn off, zv and u cases as deter- miued by Gauss' Law of Error (Kulpe) 36. Weston portable aremeter 37. Arrangement for measuring resistance of Hipp magnets 38. Old-pattern chronoscope-arrangement for break to break 39 Hipp chronoscope, housed, with release key 40. Wunclt's demonstratmn chronoscope 4t. d'Arsonval chronometer 42. Mechamsm of d'Arsonval chronometer 43 Munsterberg's chronoscope 44- W. G. Smth's reaction arrangement 45. Wundt's large control hammer 46. Keys of large control hammer 47. Detail of wheel contacts for noise stimulator 48. Ewald's reactran key 49. Ewald's rocking key 50. Kmsow's electroaesthesiometer ' St. Ranschburg's key , . 52. Bryan's apparatus for precision of movement 53. Muller's apparatus for memory and association 54- %Vundt's ume-sense apparatus 55- Meumann's time-sense apparatus 56. Tme-sense contacts (Meumann, Schumann) 57- Apparatus for brightness contrast (Hess and Pretori) 58. Wundt's comphcatmn pendulum 59- Wundt's comphcatmn clock 60. Whipple's apparatus for the temporal hmen of disparate im- pressions 61. Donders' tooscope 6o_. Hermg's haploscope (H111ebrand) .. 63 Apparatus for quantitauve study of the Miiller~Lyer illusion (Heymans) 64 Apparatus for quanttauve study of the Zollner illusion (Heyroans) 65. Memory apparatus (T. L. Smith) 57 269 0-70 322 .325 .327 .328 33 336 336 337 339 34I 342 344 346 347 347 35o 37 39 395 399 4 ø i 406 4o8 409 409 4o 4to 4II 4II 42 Zzst of A bbrcviatwns xi LIST OF ABBREVIATIONS A.J. The American Journal of Psychology, ed. 1887-1895 by G. S. Hall; 1895 if. by G. S. Hall, E. C. Sanford and E. B. Tltchener. El. G.T. Fechner, Elemente der Psychophyslk. Reprint, 2 vols., i889. Leipzig, Breitkopt und Hartel. G. G.E. Muller, Zur Grundlegung der Psychophysik. 1878. Berlin, T. Grieben. I.S. G. T. Fechner, In Sachen der Psychophysik. 1877. Leipzig, Bretkopf und Hartel. M. G.E. Mfiller, Die Gesichtspunkte und dm Tatsachen der psycho- physischen Methodik. 19o 4 . Wesbaden, J. F. Bergmann. Off-printed from L. Asher and K. Spiro, Ergebnisse der Phy- siologie, 2ter Jahrgang, n. Abt., 266-56. P. P. W. Wundt, Grundzuge der physmlogmchen Psychologie. I vol., 874; 2 vols., I88O, 887, 893; 3 vols., with separate index, 19o2- 3. Leipzig, W. Engelmann. P.S. Philosophmche Studien, ed. by W. Wundt. R. G. T. Fechner, Revision tier Hauptpuncte der Psychophysik. I882. Leipzig, Bretkopf und Hartel. Z. Zeltschnft far Psychologm und Physiologe der Sinnesorgane, ed. I89O-I9OI by H. Ebbinghaus and A. Konig; I9O2 , by H. Ebbnghaus; i9o2 if., by H. Ebbinghaus and W. A. Nagel. ----------------------------------------------------------- INTRODUCTION: THE RISE AND PROGRESS OF QUANTITATIVE PSYCHOLOGY Zu einem Werke, wle den lementen der Psychofiyszk, bedurfte es emer Vertrautheit mxt den Prmzxpieu exakter physikahsch-mathematmcher Methodxk, und zugleich einer Neigung, m die fiefsten Probleme des menschlichen Seins smh zu vertiefen, wm in dxeser Veretmgung nut Fechner sic besass Und dazu brachte er lene Ursprunglichkeit des Denkens, welche die uberkommeuen Hilfsmittel frei nach egenen Bedurfnissen umzugestalten wusste, und keiu Bedenkeu trug, neue und ungewohnte W'ege emzuschlagen . . Die Art, wie er so aus einera zerstreuten und luckenhaften MateriM kiar formuherte und exakt durchgearbeitete Methoden geschaffen hat, ist smherhch eine der grossartisten Leistungeu, welche die Wtssenschaft uflserer Tage aufzuweisen hat --WuNDT Fechner's hook was the starting point of a new department of literature, which it would be perhaps impossible to match for the quahtes of thoroughness and subtlety, but of which, in the humble opinion of the present writer, the proper psychological outcome is lust nothzng' õ I. Weber's ]xperiments.--In the years 829-834, Ernst Heinrich Weber (I795-878), then professor of Anatomy in the University of Leipzig, published by installments a long experi- mental study of cutaneous and kinesthetic sensation. The mono- graph is reprinted, under the general title De tactu, in Weber's Annotationes anatomica et physiologicze: programmata coilecru, Leipzig 85 (fasc. i., 834 , 44 if.). It falls into two parts: the De subtilitate tactus diversa in diversis partibus sensui huic dicatis, and the Summa eorum quae experimentis de tactu didi- cimus. In the first part (83L 9 ø f.), Weber describes experiments which show that, with a given standard weight of 32 oz., "our observations of the magnitude of weights are rendered more than twice as accurate, if for their estimation we employ the coenes- thesis of the muscles as well as touch." The fact is interesting, but would, if it stood alone, possess but little importance; tests must be made with other weights, larger and smaller than 32 oz. Weber therefore proceeds to experiment with two standards, of 32 oz. and of  oz. or 32 dr. respectively (9 , I63). He finds that "a difference of the smaller weights is not less accurately Xlll ----------------------------------------------------------- xiv Introdu chon distinguished by touch than the same difference of the larger weights." The results are as follows: o I MODE OF JUDGMENT Pressure Litlng Pressure Lmg Pressure Lifting Pressure Lifting Pressure Lifting Ldung LEAST PERCEPTIBLE DIFFERENCE 32 -- I7 oz.  15 oz. 32 -- 3o.5 oz. : I 5 oz. 32 --24 dr. - 8 dr. 32- 3o dr. = 2 dr. 32 --22 OZ. = IO OZ. 32 -- 3 ø5 oz. : 1.5 OZ. 32 -- 22 dr. = IO dr. 32 -- 3 ø dr. = 2 dr. 32 -- 20 oz. : 12 oz. 32 -- 26 oz. = 6 oz. 32 --26 dr. = 6 dr. Pressure Lifting Lifting 32 --26 oz. = 6 oz. 32 -- 3 ø oz. = 2 oz. 32--29 dr. = 3 dr. "Now," he says, "if you compare the differences of the heavier ahd lighter weight,s which escape our observation, you will observe that they ar almost the same." For method and sources of error, see 85 f.; for differences of sen- Sltvity, 89 f. Cf. O. Funke, Hermann's Hdbch., iii., 2, I88o, 334 if.; G. E. Miiller, G., I89 if.; Fechner, El., i., t38 f.; Wundt, P. P., I874, 33 f-; i., 19o2, 53 ø f. The values of the Table are exceedingly irregular. If we ' mass ' the four O's, we get the averages: oz. dr. Pressure Io.7 -4- 2.7 9 .0 : I.o Lifting 2.7 + 1.6 3.2 : 1.3 Weber does not seem to have worked with weights heavier than 32 oz. In 833 (32 fl.) Weber published the results of further experiments, made with a standard weight of I5 half-ounces under varying conditions: with simultaneous and successive appli- cation of the weights, with application to the same or to differ- ent hand or finger, with the hand supported and unmoved or held õ . [Vebcr's E.vpert;;tcuts xv free above the table. Under the most favourable circumstances, the weight of t5 was distinguished from that of 4.5 half-ounces: "we perceive correctly a difference between the weights which is expressed by the numbers 29:3 o" (t33, 35). In summmg up the De tactu (x7x), VCebersays that apt and practised O's"½hfferentlam duorum ponderurn successwe una eademque manu hbrantes" can discriminate a weight of 29 from a weight of 3 ø oz. or dr.. whfie 0'sless apt or practiseddscrlmlnate x4 &om 15 . Here weseem, since there s no evidence of any further experlmentaton, to haxe a mixed reference to the two sets of expermen'ts,--those with 32 oz. and dr., and those wth 5 half-oz. Tbls supposition m, indeed, raised pr,tc- tmallyto certainty by a reference on I6O f., where the two sets of exper- nnents are treated together, and where the I5 half-oz. have become, for Weber hlmself, x5 oz It ls equally certain that the .DZ. of Po is ascribed by Weber not to pressure alone, but to pressure plus the muscle sense. The words ,,manu hbrantes," in the passage just quoted, are clear. Moreover, Weber proceeds: "it follows, then, that touch, in hands voluntar1Iy moved (consulto motto), is so subtle" that we get a Z)Z. of _2. And, besides, the words on p. 16o are explicit. Nevertheless, [n the Tastsmn Weber gives the hmen for passive touch as  (559), and refers to hm oIder expenments to support his statement (547)! MuIler, msled by the Tastslnn, ctes both it and the De tactu, I7I, as giwng "den eben merklichen Unterschied zweier allein mittels des Drucksinnes wahrge- nommener Gewchte" (G., I9x ). The primary reason for Weber's confusion lies, probably, in the fact that the De tactu is concerned wth the &fference between skin and skin plus muscles, the Tastsinn with the difference between skin and muscles alone (546 L). He must, by lapse of memory or what not, have attributed to skin--now sharply opposed in his mnd to muscles--what had in reality belonged to skin and muscles together. Hs statement that ,'neuere Versuchsreihen" confirm the previous result, the result, i.e., that wmghtsof29.30 aredscnmlnated ,,nur mt der grossten Mdhe" by the resting hand, suggests the posslbfiity that he had not even referred to his older work, but found the value 2 in hm memory, and (after prac- true wth the muscle sense) made some fresh tests upon passive touch to verify t. In the second part of the study (834). we have the first for- mulation of what is noxv knowPi as Weber's Law. "In obser- vando discrimine rerum inter se comparatarum," writes Weber, ----------------------------------------------------------- xvi Introduction "non differentiam rerum, sed rationem differenti,e ad magni- tudinem rerum inter se comparatarum precipimus" (172). In comparing objects and observing the distinction between them, we perceive, not the difference between the objects, but the ratio of this difference to the magnitude of the objects compared. "If we are comparing by touch two weights, the one of 3 ø and the other of 29 half-ounces, the difference is not more easily perceived than that between weights of 3 ¸ and 29 drachms .... Since the distinction is not perceived more easily in the former case than in the latter, it is clear that not the weights of the differences but their ratios are perceived,... Experience has taught us that apt and practised O's sense the difference between weights, if it is not less than the thirtieth part of the heavier weight, and that the same O's perceive the difference not less easily, if drachms are put in the place of half-ounces. "That which I have set forth with regard to weights com- pared by touch holds also of lines to be compared by sight. For whether you compare longer or shorter lines, you will find that the difference is not sensed by most O's if the second line is less by a hundredth part... The length in which the distinction resides, therefore, although [in the case of lines of 5 ¸ and 50.5 mm.] it is twice as small [as it is in the case of lines of Ioo and lOI mm.], is nevertheless no less easily apprehended, for the reason that in both cases the difference of the compared lib-if2 is one hundredth of the longer line. x "I have made no experiments upon the comparison of tones by the ear. [Delezenne. however. determined the j. n. d. of the b of 24o vs.] As this author does not say that this difference is discriminated less easily in deeper, more easily in higher tones, and as I have never heard that a difference is more easily per- ceived in higher tones .... I imagine that in audition also not the absolute difference between the vibrations of two tones, but the relative, compared with the number of vibrations of the tones, is discriminated. 2 "The observation, confirmed in several departments of sense, I On pp. 142 if-, 72, we read only of experiments with a single standard of xoo mm The line df 5 ø mm appears for the first time on p. 73. .2 Tones are first mentioued on p I72, m a reference to W. Weber and to De- lezemm: for an account of these experiments, see pp. 235 f. below. õ . Weber's Expermeuts xvii that in observing the distinction betveen objects we perceive not the absolute but the relative differences, has again and again impelled me to investigate the cause of this phenomenon; and  hope that, when this cause is sufficiently understood, we shall be able to judge more correctly regarding the nature of the senses" (172 fl.)- So much was written in 1834. In 846 appeared Weber's article Der Tastsinn und das Gemeingeftihl (R. Wagher's Hand- wOrterbuch der Physiologie, iii., 2, 846, 481; published sepa- rarely, 849, 85), which may be considered the foundation stone of experimental psychology. Weber devotes a brief chapter to the "least differences (Verschiedenheiten) of weights which we can distinguish by the sense of touch, of the length of lines, which we can distinguish by sight, and of tones, which we can distin- guish by ear" (559). "I have shown," he writes, "that the result in the determinations of weight is the same, whether one takes ounces or half-ounces; for it is not a question of the num- ber of grains that make up the increment of weight, but of the fact that this increment is the thirtieth or fiftieth [should be. fortieth] part of the weight which we are comparing with a second weight2 The same thing holds of the comparison of the length of two lines and of the pitch of two tones. It makes no difference whether we compare lines that are, say, two inches or one inch long, ... and yet the extent by which the one line exceeds the other is in the former case twice as great as in the latter .... _o "So too in the comparison of the pitch of two tones, it does not matter vhether the two tones are seven tonal steps [i.e., an octave] higher or lower, provided only that they do not lie at the end of the tonal series, where the exact discrimination of small  Weber attempts to reach a pure judgment m terms of the muscle sense by plamng the weights in a cloth, which O lifts wthout touching the weights them- selves. He finds that weights of 78 and 80 oz. are dscrlminated. Hence the 29I. is ½,: not , as he later gxves it (547, 560) - Curiously enough, Weber seems to have worked with only one standard weight, and to have generalised his result in the light of his earlier experiments. The value , has been discussed above. See G. E. Muller, G, 93 ff, Fechner, El, i., 99 ß 2 Weber worked throughout th very short hnes De tactu,/oc c!; Tastsmn, 559, 56x. See G E. Muller, G, 205 , Fechner, El., i, 294. ----------------------------------------------------------- xviii Introduction tonal differences becomes more difficult. Here again, therefore, it is not a question of the number of vibrations by which the one tone exceeds the other, but of the vibration ratio of the two tones which we are comparinõ ....  '" The apprehension of the relation of whole magnitudes, with- out our having measured the magnitudes by a smaller scale-unit, and without our having ascertained the absolute difference between them, is an extremely interesting psychological phenom- enon. In music we apprehend the relations of tones without knowing their vibration rates [i.e., their absolute pitch]; in archi- tecture, the relations of spatial magnitudes, without having deter- mined them by inches; and in the same way we apprehend the magnitudes of sensation or of force in the comparison of weights" (559 if.)' Weber had, then, first-hand evidence for his law in the spheres of pressure, lifted weights-ø and visual distances. In the case of tones, he appealed to Delezenne,--mistakenly, as we shall see later (õ 3o), since Delezenne made no comparative determinations of the DL. On this basis of induction he erected his law. The law itself may be formulated in the equation -= const., where dR represents that change in a given 1 which is iust able to pro- duce a change in 0% Or, in words: the magnitude of the relative DL is independent of the absolute magnitude of R. Or again, in Fechner's phraseology: the relative differential sensitivity is independe.nt of the absolute magnitude of R. A large generali- sation for so small a body of fact! Of course, Weber may have performed experiments that he does not report; but the internal evidence of his papers is decidedly against this supposition. One can but wonder, in view of the importance which Weber's Law assumed in Fechner's hands, at the little which Weber has to report, and at the carelessness with which he reports it. The  The reference is again to Delezenne: 559- 2 Regarding the pressure experiments, Muller remarks that" [es] lasst sich [daraus] kaum etwas Sicheres betreffs der Gultigkmt des Weberschea Gesetzes im Gebiete des Drucksmnes erschliessen." From the experiments with hfted weights "lasst smh mit ziemhclxer Sicherheit folgern, dass dte Empfindlichkelt fur relative Unterschede gehobener Gewmhte bei Steigerung der absoluten Ge- wichtsgrosse glemhfalls etwas zummmt" (G., 95 f')' õ . ffeber's E.rperiments xix law was, however, to him only one observation among many; interesting and important, but not more important than othe? facts of sensation. Else he would hardly have failed to carry his experiments farther; to extend them to more than just noticeable R-differences: and to mention some of the many everyday experi- ences which illustrate the law. See Fechner, El., i., 34 if, and esp. Abh. d. k. sachs. Ges. d. Wins., math.- phys. CI, iv., 859, 469, It is, perhaps, ndicative of Weber's atutude towards hm laxv that the long paper Ueber den Raumsmn und die Empfindungskreise in der Haut und im Auge (Ber. d. k. sachs Ges. d. Wiss,math-phys CI., 8 Decr x852, 85 frO, which refers to the De tactu and the Tastsmn, says not a word of the constancy or inconstancy of the relanve DL. And it seems clear, from Fechner's remarks in the Abh. ofx859, that he had taken no special paros to press hsobserva- trans on the notice of his scientific colleagues. Cf. G. VIla, La Psic. Cont, x899, 245; Cont. Psych., 9o3, 37. A. Hofier (Psych., 897, 45) writes: "E. H. \Veber hatte selbst (mt Euler, Drobmch) die Beziehungen zxvischen den Intervallen und den Schxxngungszahlen als unter sen Gesetz fallend angesehen; und wenn des auch mcht zutrtfft .... so zegt es doch, dass Weber selbst sein Gesetz nlcht auf die eben merkhchen Unterchmde eingeschrankt winsen wollte' vgl. auch seine Aeusserung uber de Auffassung der Verhilt- msse an Bauwerken u. dgl" The author cannot agree wth thin inter- pretation. There s nothing in the De tactu to bear t out; the ttle of the relevant section of the Tastsinn is against t; Euler and Herbart are noxvhere mentioned. If the concludtng words of the Tastsinn sectran (the words to which Hofler refers) are carefully read, t w11 be seen that, whfie they follow naturally from what precedes, they were not written with an eye to the law. What Weber says, in effect, is smply thin. ,' If you compare weights, lines, tones, you will find a constancy of the relative DZ. What an interesting thng, psychologically, this compari- son of wholes as wholes is I We have it in muste, in architecture, and in the esttmation of weights." Weber is quite right; it is an nteresting thing. But it xvas suggested to Weber by hm work on the DZ; it xs not adduced by him as evtdence of hs lax,, beyond the realm of the Fechner, not Weber, put ' gleich merkhch ' for ' eben merklich ' in the formulation of the law. The extension is warranted by the facts, and is altogether consonant with the sptrit of Weber's enquiry; but t was not made by Weber.--df. Stump[ Tps., i., 337 n.; F. Jodl, Lehrb. d. Psych., 896, 25, 29 fi, :33; O. Funke, in Hermann's Hdbch.,in.,2,88o, 34; and cL, besides Hofler's Psych., Herrag, Sitzungsber. d. kais. Akad. ----------------------------------------------------------- xx Introduction d. Wiss. zu Wien, math.-naturw. CI., lxxii, x875, 313; A. Grotenfelt, Das Webersche Gesetz, 1888, I;8 n.; O. Ktilpe, Arch. f. Gesch. d. Phfi., vi, ;893, 181; Stumpf, Beitrtge, 19Ol, Heft 3, 91 f ; F. A. Muller, Axiomd. Psychophyslk, ;88e, 67; M. Foucault, Psychophysique, ;9o, 3o7; A. Hofler, Vjs, xi., I887,368; Wundt, Das XVebersche Gesetz u. d. Methode d. Mnimalanderungen, I882, 6 (of. 9, 24); or P.S., ii ;885, 3 (of. 5, 19). Weber's predecessors on the experimental sde seem to have been occupmd, one and all, with brightness intensities: Fechner, E1 , i., tSI if.; if. 548. On the mathematical side, they were concerned with ptch and pitch-number, wth the fortune fihysique anti the forlune morale, and wth stellar magnitude and photometry: ibid., i., x., 56, 82,236; ii., 549 if. õ 2. Feehner's Inirpreiaiion. -- If Weber laid the foundation stone of experimental psychology, Gustav Theodor Fechner (8o-887) may be said to have planned, and in large measure to have erected, a whole building. His work covers a period of full fifty years, from the after-image investigations of 838 to the Psychische Massprincipien of 887. We are here concerned only with its quantitative side, i.e., with the writings which led up to and grew out of the Elemente der Psychophysik (x86o: reprinted under Wundt's auspices, with notes and bibliography, 889). It was on the 22d Oct., 85o, Fechner tells us, as he lay awake in bed before getting up, that the thought came to him of "mak- ing the relative increase of bodily energy the measure of the increase of the corresponding mental intensity. "x The general idea of measuring the intensity of mental activity in terms of the underlying physical activity had long occupied him, but had hitherto led to no fruitful result. The new thought was definite; it gave him a starting point; thrown into mathematical form, it even gave him two formulae which later on play a large part in the Elemente. But it did not, of course, give him any measure of sensation. The stimuli could be measured; their precise cor- relation with sensation was a matter of hypothesis. The only thing to do, in default of a sensation measure, was to assume the correctness of the rule, and to put it to empirical test under con- ditions where measurement was not needed: e.g., in the observa-  El., fl., 554; Fechner sketches, pp. 553-56o, the development of hs ideas from I850 to I860. õ 2. Fechner's Interpretat;on xxi tion of simple increase or decrease of sense intensity, of extremes of sensation, of sensations of equal intensity.  Fechner there- fore contented himself, for the time being, with'a brief mention of his new ideas in the Zend-Avesta (i85),--a work which, as he gravely remarks, "does not pretend to the character of exact research." 2 The exact research followed, in the shape of the classical experiments on brightnesses and lifted weights, on visual and tactual distances, in many of which Fechner was loyally assisted by A. W. Volkmann. While these were in progress, he lighted upon Weber's generalisation, and his own principle forthwith became Weber's Law? Confirmation of the law was sought--and found--in various places: notably in the astronomical classifica- tion of the fixed stars by visible magnitude. The fact of the limen, "a datum of everyday experience which has attracted little observation, but on which the whole of the night side of mind depends," * supplied the last link in the chain of mathemati- cal reasoning. Last, not least. the three psychophysical metric methods, of just noticeable differences, of right and wrong cases, and of average error, were worked out with such care and sub- tletv as to raise psychology, once and for all, to the dignity of an experimental science. Of all this work we hear nothing until 858, when Fechner published a paper on mental measurement,  a sort of author's review of the forthcoming Elemente. In I859 appeared a detailed inquiry into the validity of the law in the sphere of visual inten- sity, ø which furnished material for the discussion in ch. ix. of the I Zend-Avesta, if., 373.  El., n., 55'8; Zend-Avesta, oder uber die Dinge des Himmels und des Jenseits, vom Standpunkt der Naturbetrachtung, x85i , if., 3x2 if., esp. 334 ff-, 341,373 if.; of. i., 4o if. a El., ., 64, 134; n., 558; Fmhte's Zests., N. F., xxxi., 1858 , xS; Abh. d. kgl. sachs. Ges. d. Wiss., math.-phys. CI., iv., I859 , 469, 53 x.  El., n., 558; W. Preyer, Wiss. Briefe, 189o , 2o 9. $ Das psychische Mass: in Fmhte's Zeltschrift f. Philos. und philos. Kritik, N. F., xxxn., 1858 , I lc.  Ueber ein psychophysisches Grundgesetz und dessen Beziehung zur Schat- zung der Sterngrossen: Abh. d. kgl. sachs. Ges. d. Wiss, math -phys. CI., iv., 859 , 457 fl. Nachtrag zu der Abhandlung, etc.: her. d kgl. sachs. Ges, d. Wss., math.-phys. CI, xi., 12 Feb. 1859, 58 if. ----------------------------------------------------------- xxii Itrodttction Elemente.  Finally, in 86o, came the Psychophysik itself. We must devote some little space to its analysis. Fechner defires Psychophysics as "an exact science of the functional relations or relations of dependency betveen body and mind." _o Its sphere is thus as wide as the sphere of psychology; there vill be a psychophysics of sensation, of perception, of feel- ing, of action, of attention. etc. a In the present state of our knowledge, however, it will be wise for s to occupy ourselves primarily with sensations, which we may classify as intensive and extensive2 All sensations possess magnitude and form, termed in the intensive domain 'intensity' and 'quality.' We shall be concerned chiefly with their magnitude? The first step in psychophysical metrics  is the establishment of the metric principle of sensitivity.* Sensitivity is a special form of organic irritability or excitability, the organism's capacity of response to stimulation; a it may be defined as the degree of correspondence between sensation and adequate stimulus. "One and the same stimulus  may, even if applied in the same rnanner, be sensed more or less strongly by one observer or one organ than by another, or by the same observer or organ at different times; and, contrariwise, stimuli of different magnitude may, under cer- tain circumstances. be sensed equally strongly. We then attrib- ute to the one observer or organ, or to the single observer or organ at one time, a greater or less sensitivity than to the other, or to the same at another time." o Now we can measure stimuli; and we are perfectly well able to say whether two given sensa- tions are 'equal' or 'alike.' Hence we can measure sensitivity: it is inversely proportional to the magnitude of the stimuli which a El., i., 39- = El., i, wi., 8 if.; Fichte's Z., x858, 2. aEl., i., 3f.,56f.; ii.,86, I. S.,87; R.,  if., 327; Fmhte's Z., 858, 24. Zend-Avesta, ii., 384 if.; W. Preyer, Wiss. Briefe, 89o, '>21.  El, i., I5, 55; Fichte's Z, I858, , 2; I. S., 6 f. * El., i., 5 if'; I. S., 2. Fechner, of course, takes things here too much for granted. Ite should have defined sensation: not a few of his 'sensations ' are, in modern terminology, percepttons. He should also (as we shall see later) have offered evidence of the independent variation of intensity and quality.  Psychophysische Masslehre: El., i., 2t if. * Masspdncip d. Empfindlichkeit: El., i., 45 if.; Fichte's Z., x858. 4 f. 8 El., i., 5.  For a discussion of stimulus, see El., i, 7 if- 0 El., i., 45. õ 2. Fechner's Interpretation XXil arouse sensations of equal magnitude.  Suppose that you can just sense a pressure of 2 gr. at a certain part of the skin. and that I, at the corresponding part, can sense nothi'ng below 4 gr.; then your sensitiqty is twice as great as mine. Suppose that (as Weber found) a pressure of x-5 oz. on the lips is equal to a pres- sure of 4 oz. on the forehead; o the sensitivities of the two parts stand to one another in the ratio 8:3 . It must be understood that, in ' measuring sensitivity,' we are always measuring stimuli, not sensation; we determine what stimuli (or stimulus differ- ences) arouse sensations (or sensation differences) of equal mag- nitude? And it is clear that "the measure of sensitivity, as a measure of mere capacity of sensation, is not to be confused with a measure of sensation itself. Nor does it presuppose any such measure, but only the observation of instances of equal sensations, under like or different conditions of stimulation."  We have to distinguish (x) absolute sensitivity, or S. for abso- lute R-values,  measured by the inverse value of the absolute R-magnitudes which evoke a sensation of the same magnitude, and (2) differential sensitivity, or S. for R-differences. This latter is measured in two ways: (a) as simple or absolute D. $., by the inverse value of the absolute difference of the R-magnitudes, and (b) as comparative or relative D. S., by the inverse value of the ratio of the R-magnitudes.  Suppose that you can distin- guish a pressure of x8 gr. from one of 24 gr., and that I can dis- tinguish only I6 gr. from the same 24 gr. The absolute D. S. are  and -}: yours is to mine as 4:3. The relative D. S. are  ¾ 18 16 . and x¾, yours is to mine as 9: 8.* "Since sensitivity is a variable matter, we have not to measure it as we should measure a constant; but we can seek to determine () its extreme and (2) its mean values: we can investigate (3) the dependency of its changes upon circumstances: and we can x El., i., 46.  De subt. tactus, 98. a El., , 46, 54  12. , 54.  S =sensitiwty, A'--tmulus. See p. xxxvn. of the text 6 E1, i., 5 o. ? The ratios : and , to which the D. S is here made inversely proportional, are known technically as quotient hmens (Qœ). The relative 2œ are more com- monly expressed an the form  and 'r, or  and «. The relatne D. $. would then be 4 and 3, instead of  and , respectively See Fechner, El, i., 244, I. S., 3; R., 397; Stumpf, Tps, a., 298 f; Kulpe, Outhnes, 59. ----------------------------------------------------------- xxiv Introduction (4) make search for laws which hold throughout its variations. These laws are the most important thing."  Our measurement of sensitivity is a necessary first step, but still only a first step, towards the measurement of sensation? "The possibility of establishing the equality of small differences of sensation, or small increments of sensation, under changed con- ditions of stimulation, is the main prerequisite of measurement," 3 but does not guarantee measurement. To measure sensation we must be able to say, not only that our present pain is much more severe than our pain of yesterday, not only that the illumination of two rooms is sensibly the same, but that our pain is 2, 3, 4, ß - ß times as great as the previous pain, that the brightness of the light is IO, TS, 20, . . . times as great as that of the brightness unit. And we must be able to say this in terms of sensation itself, not merely in terms of the stimulus which arouses sensation.* How are we to arrive at exact statements of this kind ? "The difference between two R-magnitudes mav always be considered as a positive or negative increment of the one or the other R-magnitude; and a total R may be regarded, mathemati- cally, as made up by positive increments from zero, increment being constantly added to the sum of former increments, until the full R is present. In the same way, a sensation difference may be conzidered, mathematically, as positive or negative increment c5 the one or the other sensation, and a total sensation may be regarded as made up of positive increments from zero to its full intensity. If we know the functional relation ketween the sum of the R-increments from zero onwards, and the sum of the corresponding S-increments, 5 xve have it eo ipso for the total R and the S which the R releases."  We may, then, get over the difficulty of sense measurement by "having recourse to the rela- tion between the elementary increments out of which we may regard the R and S as built; this requires no measurement of sen-  El., i., 54; Zend-Avesta, i., 373  E1, i., 46, 59 f., u, 9 . a Fichte's Z., 858, 5: this equality is established by aid of the metric methods; cf El. 1., 7 if- Our abhty to equate sensatmns at large s presupposed, e. if., n photomerry and in the tumng of musical instruments ß E1, i., 55, 7 ø El.,i.,'56; ii., 8, I S, , R, 3ooff. P.S., v., 28, Delbreuf, Examen cri- tique, 883, 79, x8, 77; Vmrordt, Zeltslnn, x868, 9- a C=sensatmn; see p. xxxvll of the text. e ILl., , 58 f . 2. Fechnr's l'#terpretation xxv sation, but only... a judgment of the equality of S-dif- ferences or S-increments which correspond to given, measurable, variable R-increments; from it we derive the functional relation of the sums of the increments, and thus obtain the measure of $ in terms of the measured R."  We mark off an S-magnitude in units of its own kind; that is essential to measurement; but the scale which we lay upon the S-magnitude is physical, an R-scale. "In principle, therefore, our measurement of $ comes to this: that we split up every S into equal divisions, i.e., the equal incre- ments out of which it is built up from the zero-point of its exist- ence, and consider the number of these equal divisions to be determined (as if by the inches of a yard-stick) by the corre- sponding variable R-increments which can produce the equal S- increments. We determine the magnitude of the S, which we cannot determine directly, as a multiple of the equal parts which we can determine directly; but we read off the num- ber of parts not from the S, but from the R which brings the S with it, and which can be more easily read." _o So the difficulty is overcome,--in theory. But in practice? Objections are many and insistent. Thus () we are to seize an S in the act of increase; yet actual S are either full-grown, when we meet them, or at least come so quickly to a head that their growth cannot be followed. Now it is true that we cannot measure a full-grown S, since such an S cannot be divided into parts. a On the other hand, no S is born full-grown; it is fact. not fiction, that every S rises gradually to its full height. All that we have to do is to treat this continuous increase of S as the infinitesimal calculus treats a curve: for the same S in various stages of increase we substitute as many different S of the height of these stages.* Again, (2) we are to measure the change of sensation; yet S change continuously, the increments running into one another. The same substitution avails us: for an increasing 1 El., i., 59 f , c. fl. Zend-Avesta, ii., 374.  El., i., 60; ii, t9t f.; Fichte's Z., 858 , 5 f.  These are Fechner's own words. "An die schon erwachsene Empfindung lhsst sich kein Mass anlegen, insofern sich keine Theile darin unterscheiden lassen": Fichte's Z., t858, 8. In the El., i., 6, the last part of the sentence reads' "insofern sich keine quantitative Mehrheit darin unterscheden lasst."  Fichte's Z., 858, 6 f.; El., i., 6 f.; of. Jodl. Psych., 225. ----------------------------------------------------------- xxvi Introduction S in the various stages of its intensity we take a number of S of graded intensity. The method of just noticeable differences, e.g., helps us to determine in this way equal S-increments in the higher and lower regions of the R-scale? (3) In saying this we have answered another objection,--namely, that we are to make our successive S-increments all equal. but have no xvay of ensuring their equality. The metric methods give us a way: the method of j. n. differences gives us equal (i.e., just noticeable) S-increments; the method of right and wrong cases gives us S-differences that correspond to the same r.2 Lastly, (4) we are to sum up the S-increments; but their number is infinite, and therefore cannot be summed. The objection holds: we cannot take, all at once, the relative R-increment that corresponds to a given finite S-increment, since the R, in increasing, itself passes through different magnitudes, every one of which has a right to function, in its turn, as divisor. At the same time, the objection can be met by the help of mathematics. a These are Fechner's objections and Fechner's replies. ' Wth them he concludes his general discussion of mental measurement. The remaining chapters of the Elemente deal wth the subject in detail, under five principal headings: (I) the metric methods; (2) Weber's Law and the sphere of its validity; (3) the limen; (4) formulae of mental measurement, with corollaries and appli- cations; and (5) the transference of the metric principle from outer to inner psychophysics, from stimults to excitation? These topics will occupy us later, in the course of our experiments. A  Fichte's Z., 858, 6, 9 f.  Ibrd, o f. ß  El., ., 63 f , Fxchte's Z., x858 6, 3 f ß The programme of El., . 68 f s not strictly carried out; of. il, v fl.--The 889 edition of the E1 ctes the parallel pa=sages from I S. R, and Massprmc- pmn (P S, / Two dscussons have been omxtted from the above hst ' tlose of El., ., chxn, and n, chs. XXXlii-xxxv. () The former deals wth the Parallel Law, which says that "ff two I½ of dfferent intensity ale apphed to a sensitive organ for a cel-tam ieigth of tme, the absolut & and therefore the exctat o,½, aroced by the /t' dmxmshed by fatigue, the sensed dffelence ]lOiterer, reinruns unchainseal, pe- csely a,t would, according to Webet's law, had the cbjectve']t' been changect m the same ratio "R, 8o, 241. (2) The latter, entitled ' Special lnvestgatmns n certain Departments of Sensation,' deal_ x lth the elav. ons of visual and auditory ellsa_lons and with the ' extensxve ' sensitivity. õ 2. Fcclmcr's D, terpretatio xxvii xvord must, however, be said regarding the principal formulae which Fechner employs, and regarding his attitude to Weber's It is a fact of everyday experience that the increase of a given ]? which shall effect a noticeable change of the corresponding S depends on the magnitude which R has already attained: the stars give no light in the daytime, but give a good deal of light on a moonless nigl.t. \Veber found that this increase of R, expressed as a fraction o$ the total R, remains approximately constant over a wide range of absolute ]?-intensities. This, so far as \Veber ifimself is concerned. is Weber's Law: this and nothing more. Fechner treats the facts on the hypotheses (x) that the S, as a magnitude, may be regarded as a sum of S-units; (2) that, in investigations which mm at the determination of the j. n. d., these units are conveniently given in the j. n. d. themselves, which as 'sensed differences' or 'difference sensations' are equal at all parts of the R-scale; and (3) that Weber's Law may be transferred from the sphere of ' sensed differences ' to that of 'differences of sensation.' x On these assumptions mathematical treatment becomes po.ssible. Let R be the original stimulus, and dR a small incrernent of R,--the d not standing for any particular magnitude, but simply indicating that the increment dR is very small: c[. its use as the - d. sign of differentiation. Then the relative R-increase is -. In the same way, let S be the sensation corresponding to R, and dS x The first two hypotheses we shall dx-cuss later: pp. XlVlii ff.,lxvili. if. The third may be explaxned as follo s. Not all S-differences are sensed The two S may be in dfferent minds, or in the same mnd but m consmousnesses separated by along period of tme. In such cases, comparison is plaxnlyimpossble. But more than this: an S-difference which s sensed by a successive procedure s oftentimes insensible when the l' are smultaneously applied. The dstxnction therefore obtains within a single conscousneas. Now Weber's Law is estabhshed by aid of sensed differences. But "of all the possible ways m whmh a difference may be sensed, we may take as extreme or hmitmg case that n wlnch the very smallest dfference which exists should really be sensed, a case which would designate the maximal degree of dif- ferential sensltvlty. An S-dfference can always be dennfied with such a hmtlng case," and so Weber's Law can be transferred from the domain of sensed dffer- ences to that of S-dfferences. El.,fi.,82ff.; I.S.,9,x, 46; 1.,83,33o, P.S., v, 93 if., zo; Verordt, Zestsinn, 868, x$4 if- ----------------------------------------------------------- xxviii Introduction the S-increment corresponding to dR. We need a formula which shall satisfy (a) the requirement of Weber's Law, that dS dR remains constant so long as 7 is constant, and (b) the mathe- matical requirement that dS and dR vary proportionally so long as they are very small. The formula is: dS c dR where c is a constant, depending on the unit-values chosen for S and R. This is the [undamenal [ornmla of mental measure- roept. 1 From the fundamental formula, together with the fact of the stimulus limen, a second formula may be derived, which "ex- presses a general quantitative relation between the R-magnitude, summed from R-increments, and the S-magnitude, summed from S-Increments.  Consider the fundamental formula as a differ- ential equation, and integrate. Then: S=c log'. nat. R+ C, where C is the constant of integration. Now introduce the limen; i.e., the determination that S vanishes when R has the liminal value r. The formula becomes: o = c lag'. nat. r + C in other words: and therefore: S=c (lag'. nat. A?--1o. nat. r). Translating into the language of common logarithms, we have: in other words: ' I Fundamentalformel: El., ii., 9 f.; I. $, to; R, 84; P.S., iv., t66 if., 2o el. Zend-Avesta, ii., 374 f.  El., i, xo. õ 2. Fechner's Interpretation xxix xvhere k is a constant including the modulus of the common sys- tem. If we make r. the liminal stimulus value,  , we may write: the form in wihch the metric formula, as Fechner term,s it, usually appears in the text-books: Put into words the formula reads: "the magnitude of sensation (S) stands in relation not to the absolute magnitude of stimulus (R) but to the logarithm of the magnitude of stimulus, when the unit of stimulus is defined as its liminal value (r), i.e., as that magnitude at which sensation appears and disappears."  If we call the value R the funda- mental stimulus value, we may say that S-magnitudes are pro- portional to the logarithms of the corresponding fundamental R-values? If we make r:x, we may say simply that sensation is proportional to the logarithm of stimulus: The metric formula accords with empirical results: "(x) in the cases of equality where an S-difference remains the same with change of the absolute intensity of the R (Weber's Law); (2) in the limiting cases where S itself and where change of S cease to be noticeable or considerable [stimulus limen and neigh- bouthood of terminal stimulus].. ; (3) in the cases of opposition between sensations which attain and do not attain to noticeability, in a word, between conscious and unconscious S."  In it, we have "a relation of dependency that obtains universally, not merely for equal cases of S, between the magnitude of the funda- mental R-value and the magnitude of the corresponding S, and vhich allows us to calculate from quantitative ratios of the former the number of units (das Wievielmal) in the latter: wherewith the measure of sensation is given."  The above derivatmn of the metrtc formula is that whmh is gener- ally quoted, and that which stands first in Fechner's exposmon. The formula may also be derived as follows.  Massformel: El., n, 33 f ; I. S., xo: R, x84. Cf. Zend-Avesta, ii., 375. The c of the two formulae are identical  El., fl., 3- a Ib2d.  "Die psychische Intensetat ist der Logarithmus der zugehorigen physschen Intensit.t:" Zend-Avesta, i, 375- a El., ii., r6; c.f Zend-Avesta, ii., 377 fl., 385 f s El., ii., I7. ----------------------------------------------------------- xxx ;ntroduction Weber's Law tells us that the S-dfference remains the same so long as the R-ratio remains the same That xs to say: wheref s the general sign of functional dependency. Let us introduce, as before, the fact of the hmen, setting o for S' and r for the corre- spondmgR'. We have: Similarly, the equation becomes This gives the difference which must be equal to the original difference . That is to say: This, however, is an equation of the formf(xy)=f(x)+f(y), of which we can give a general solution only by takingf(x)=k lo. x,f(y)= k loy, andf(my)k lo xy: where k is a constaut. It follows, then, that ve have to take which is the result reached by our previous argument. We may follow yet a third path. Let there be given three stimuli, R, , R", in descending order of magnitude, together with their cor- responding sensations S, S', S". We know, by %Veber's Law, that These functions must be of such a nature that (s_y)+(s'-s")=s-s", õ 2. Fechner's Interpretation xxxl i.e., that the sum of the two partial S-differences is equal to the total S-difference. This means that R R R' and as,=', we again have an. equation of the formf(xy)=f(x) +/(y), and come to our former result. There is no need here to follow Fechner farther; to work out the Unterschiedsformel and Unterschiedsmassformel, to discuss negative sensations, to trace the changes in the metric formula as it is applied outside of its proper sphere of intensity 0i., =I, 58), etc. Some of these things will occupy us later; some he beyond the scope of the present volume; some, as we shall indicate, may be given to the student as essay subjects. In the meantime, the author cannot too strongly recommend the reading of El., n., ch. xxxii.; of. I. S., ch. xx.; G. E. Mtiller, Z., x., 896 , 6 if. So ar we have been dealing exclusively with outer psychophys- ics, with the relation oœ S to R. Fechner's own thinking began. however, as we saw above/ with a general question of inner psychophysics; it is here, in the relation o S to E, the excitation, the 'psychophysical process' of his definition, = that his chief interest lies; a and it is to inner psyehophysics that he re*urns at the end oœ the Elemente. "Are Weber's Law," he asks, "accord- ing to which S-increments are constant so long as relative R-increments are constant: and the act o the limen, according to which S attains a noticeable value only with a certain finite value of R: to be translated for inner psychophysics into a relation between S and E such that R and R-increment are represented by proportional values oœ E, or not rather into a relation between E and R such that S and S-increment are represented by propor- tional values of E ? In other words: is the dependency expressed by the undamental formula and the metric formula a dependency of S upon E or a dependency of E upon R ?"  Fechner decides, on the œollowing grounds, for the former alternative.  P. xx.; E1, if., 559; Fichte's Z., r858 , 2L e El., ., o- "physical activities which are vehicle or substrate of psychical, and therefore stand m drect functional relation to psychical, we termpsychahysical'" if., 377; I. S., 2.  El., i., IIf.; if., 377; Fichte's Z., 858, ,z; I. S., 56, 2 3; Abh., i859 , 49o; W. Preyer, Wiss. lqnefe, 89o , 216, 225 f. 4, El., if., 428 f. The term here translated by E is ' psychophysische Thatigkeit; ' of. R., aai if. ----------------------------------------------------------- xxxii Introdction () We may say in general that, in view of the.disparity of the physical and the psychical, a logarithmic relation between them is entirely conceivable; whereas, in the light of physical and physiological laws, such a relation between R and E is incon- ceivable. On the other hand, it is, if not a necessary, at least a natural and simple assumption that the relation of R and E, within the limits of the Law's validity, should be that of simple pro- portion. x (2) The magnitude of the sensed difference between two R does not change if our sensitivity to the R be uniformly reduced. It should grow less, if the sensed difference were pro- portional rather to the absolute than to the relative difference of E; for if each of the two R, owing to reduced sensitivity, arouses only half as strong an E, the difference of E is also reduced one half) (3) The same law holds for the pitch of tones that holds for their intensity. If, then, the logarithmic relation is a matter of physiology, it must obtain, in the case of tonal pitch, between vibration rate of E and vibration rate of R: which is inconceiv- able) (4) There can be no doubt that a real difference of E remains unconscious unless it attains a certain magnitude; we do not see the stars in the daytime. And what holds of the DL must hold of the RL: i.e., there must be absolute'magnitudes of E which do not as yet arouse an S. But this does away with the hypothesis of equality of E and S.  (5) Finally, it is only by ascribing liminaI relations to E as well as to R that we can reach a simple and satisfactory explanation of sleep and waking, con- sciousness and unconsciousness, attention and inattention2  El., ii., 429 f. The argument from inconceivability is formally withdrawn in I. S., 92 f. Fechner thinks, however, that the cases of logarithmm relation addu- cible from nerve physmlogy tell rather inhis fayour: 72 ff; of. R., 229 if. On the naturalness of hm own view, see I.S., 65 ff; R, 225 :i., 251 ff On the value of the arguments, see below, pp. xci. if.; J. Ward, Mind, O S., i., I876, 454 if.; Funke, m Hermann's Hdbch., ifi., 2, I88O, 356; W. Dittenberger, Philos. Monats- hefte, ii., r896, 89 if.  El., n., 430; this is the Parallel Law, for which cf p. xxvi. above, footnote. Cf. 1., 24 ø if.; Jodl, Psych., 202, 219. 11 El., ii., 43'  El., ii, 43 if. This argument and its corollary Fechner regards a funda- meral: "so dass mir dm Frage der Uebertragbarkeit des Schwellengesetzes in die innere Psychophysik ene Lebensfrage nicht nur far metne Ausfuhrung der inneren Psychophysik, sondern fur die Moghchkeit einer solchen uberhaupt scheint;" I. S, 7 , of. 82 if.; R., 235ff. (esp. 240) a El., ii., 435, and following chapters; I. S., 28; R., 242 if. õ 2. Fechner's Interpretation XXXIU Weber's Law, therefore, which, empirically regarded, is the foundation stone of psychophysics,  is also in its theoretical sig- nificance a fundamental psychophysical law. Approximately ¾ahd in the sphere of outer 15sychophysics, 2 it holds, we may sup- pose, without exception or deviation when transferred from R to E. a If this be true, Weber's Law will some day prove to be as important and far-reaching in the science of the relations of mind and body as the law of gravitation in general physics. * "Doch sind diess ffir jetzt allerdings nur Ansichten und Aussichten."  It remains to say a word of Fechner's other systematic contributions to psychophyscs: the In Sachen der Psychophysik, 877; the Revi- sion der Hauptpuncte der Psychophysik, 882; and the essay Ueber (he psychischen Massprincipien und das Vebersche Gesetz, 887 (P.S., iv, x888. The In Sachen is a reply to the principal criticisms o[ the Elemente up to 877. Fechner had promised in the Elemente to publish later a special work "Massmethoden und Massbestlmmungen m Geblete der Psychophysik."  Soon after the publication of the Ele- mente, however, he turned his attention to esthetcs, in whmh he had been nterested as a youth; and the new work on psychophysics was postponed for the Vorschule der Aesthetik? The In Sachen, which was necessary in order to clear the ground of objections, s described by Fechner as a sort of first number of the Massmethoden: the second number is, if he hves to issue it, to give "Nachtr/tge .... Berucksicht. gung yon Gegenbemerkungen gegen dm Ausfdhrungen vorliegenden  El, i., 65 if.; Fichte's Z., x858, 8, 24; I. S, 42; R., 292 , n.; P. S , iv, 87.  r. e. within the limits of our ordinary usage of the sense-organ; beyond these limits, above and below, occur ' deviations ' from the law. Fichte's Z., t858 , 8 if.; El., i, 65 , 67; i., 430; I. S, t2, 5 r if., 2I, 2x 3; R., r47 if.; Abh, 859, 464, 53 ø ß a Fmhte's Z, x858, 23, El., i, 68; ii., 435; I. S., i2, 23; R., t92; P. S,xv, 7 o, 87. 4 Fichte's Z., r858, 23; El., i., 68; ii., 435; R., 202, 262; Ber. d. kgl. sachs. Ges d Wiss, math.-phys. CI.. xvi., 864, 4 f. CI. the pessimistic tone of James, Text- book, 892, 468; N. yon Grot, Arch. f. syst. Phd, iv, 898, 263, 266; Ebbinghaus, Psych., i., , 897, Vorbemerkung. a El., i., 68. For further remarks on Fechner's attitude to Weber's Law, and on its relation to the general Masspnncip, see below, pp. cxiv. f. 0 Z:. g'., El., i., 7; R., IO 5. It was never published.  The Zur experimentellen Aesthetik, i. (all published), appeared in 87; the ¾orschule in I876. ----------------------------------------------------------- xxxiv œntroductwn Heftes .... manche, yon fruher her zuruckgestellte, Versuchsredmn uber extensive und Gexwchtsempfindhchket, lnlt Bemerkungen uber dm Massmethoden." We shall have to take account of the I S. m {4 (3)., and we shall note from tme to tmqe tim points at whmh tt marks an advance, in clearness or logical consmtency, upon the Elemente. It contains nothing that m essentmlly new. naturally, since (in Fechner's opinion) "kein ausdrucklicher prmmpieller Erawand" has so far been rained against "das m den Elem. d. Psychophysk aufgestellte Prmmp des Empfindungsmasses."= The Revision is more important. Almost simultaneously with the In Sachen appeared G. E. Muller's Zur Grundlegung der Psychophysdq 878. Muller's intenUon is ,, de Frage nach der Gultigket, Bedeutung und Zweckmassgket des yon E. H. Weber aufgestellten Gesetzes dem gegenwtrtgen Stnde unseres Wmsens gemass zu erortern." The work fails into four parts. the psychophystcalmetric methods; the facts of Weber's Law; the interpretation of Weber's Law; and the sgmficance of the Law tot recognmon. * Ia the third part, Miller offers a physio- logical n place of Fechner's psychophyscal interpretation; not m any merely controvrsml spirit, or wth an eye to personal reputation, for the physologmal nterpretatlon is ,,weder neu noch erwesen;" ,' velmehr kommt es mr lechglich darauf an, de Angelegenhet des Weberschen Gesetzes gewtssermassen n starurn integrum zuruckzufuh- ten und aufeinigedmselbemehr oder weniger beruhrende, binher ver- nachlgssigte oder tiberhaupt unbekannte Probleme . . . die Aufmerksam- kelt der Psychophysker zu lenken." * Here, then, are ' prmcpelle Emwande' m plenty  And the Revision may be considered, in ts conrovermal aspect, as a reply to the Grundle- gung. The book m, however, not stmply polemical. "The principles and methods of psychophymcal measurement, the derivation of the psychophysical formulae, the question of the validity of Weber's Law, the experiments made to confirm it, the controversy between the'psycho- phymcal'and the'physmlogtcal'nterpretations of this law, i.e., be- tween two fundamentally opposed interpretations of psychophymcs at large, vamous principal problems of tuner psychophyscs, and (by way ot introduction) the questton of the range of psychophysms m general, all these things have been dincussed anew and n detafi."s The work may therefore be considered n some sense as a substitute for the Elemente; in some sense as a supplement to t; or yet again as prolegomena to a revtsed Psychophysics.  As to the outcome: "ich bin in kemer rgend- wie wesentlichen Beziehung dahm gefuhrt worden, die in den'Ele- I. S,iv. I S.,2rL aG.,v. ff.  G., vi. f.  :R., lii. f.  R., iv. õ 2. Fcchuer's Iuterpretatzon xxxv menten' aufgestellten Prmcipien und daraus flmssenden Folgerungen und Formeln zu vedassen, sondern im Gegenthefi."  We must sketch a little more particularly the course of the argument in the essay of 8872 This, Fechner's latest work, is also in a very real sense his most modern. Fechner begins wth a reference to the astronomical classification o[ stars by msble magnitude, whmh proves that t s possible "dte Gleich- het empfundener Unterschiede oder auch Unterschmdsempfindungen ß ß ß in verschiedenen Theilen der Helhgketsscala zu constatiren. "a The same thng may be shoxn by help of the method of mean gradations and laboratory brightnesses: if the difference ..4--B s given, we can make a difference B-- C that is equal to it; or f ..4-- C is gtven, we can bisect it at/: in ether case, the sensed difference .4 C s twice the sensed differ- ence .4/5 or 11C? Or again, one may use the method of just noticeable dfferences. It is entirely possible to estimate the equality ofj. n. d. For {x) if we do not assume this possiMhty, we cannot employ the method as a test of Webefts Law; and the fact that the Law has been vetofled (within hmts) by the method s decisive. () In the absence of theoretical or empirmal arguments to the contrary, what holds of large sensed dfferences must hold also of small. (3) Expemence proves that, wthm the limits of an error of observatmn, thej. n. d. may be made equal in introspection. And (4)--though this s truly not an argument for the equahty of the j. n. d. !--i[ we reject the method of just noUceable differences, we can still lkll back upon mean gradatmns and the equahty of supraliminal dfferences to supply us wtth a mental measurement. s We can say, then, hoxv many ttmes a smaller dtfference sensatmn (cor- related wth physmal values that he neartogether) s contained in a larger dfference sensatmn (correlated wth phystcal values that he farther apart). \Ve have, already, a pnncple of mental measurement, and one that is of practical value (astronomy). Of course, since all sensauons are evoked by stimuli, the measurement of sensations revolves a reference to stimuli. If we know that equal dfference sensattons correspond to equal stimulus ratios, and we take any given dfference sensatxon as unit, ve can get n-tmes as large a dfference sensatxon ramply by multiplying the correlated stimulus ratio n-umes into tself. This does not, however, by any means imply that the measurabfilty of dfference sensatmns is 1 1., V.  For a running criticism of Fechner's arguments, see %Vahle, I)as anze d. Phfios., oo if., wth which of. Jodl, Psych., 226 fl. a p.S., iv, xS. On the ' arithmetical principle ' laxd down in the opening par- agraphs, 79, see Elsas, Philos. IV[onatshefte, xxxv., 888, 39 f- ' Ibzd., r83.  Ibrd, r84 f ----------------------------------------------------------- xxxvi I ztr oductiot bound up xvlth the validity of Weber's Laxv. Only, Weber's Law, espe- cially if we regard it as absolutely vahd m the sphere of inner psycho- physics, affords the smplest basis and the most important body of facts for the application of the principles of mental measurement} But xve can pass from the measurement of difference sensations to that of sensation differences. The 29L is an error of estimation, akin to the probable error of physical enquiries. 2 Let us noxv assume (as xve have a right to do) that Webefts Law is valid over a certain portion of the pqy- chophysmal scale. "The ehmnatlon of constant errors of time and space is already assumed in the validity of Webefts Law for difference sensations; and, on this assumption, Weber's Law obtains for the difference sensa- tions independently of the magmtude of the D2; and can accordingly be postulated for the case in xvhich the 29/2 sinks to o, . . . vhen the error of estimation dependent on the 29I_. disappears, the difference sensation coincides with the sensation difference, and the same metric pro- cedure that is applicable to difference sensations becomes applicable to sensationdfferences."a Both alike are measured in terms ofanunit of their own kind; but the units do not correspond,--the difference sensa- tion being always a little larger than the correlated sensation difference, save in the limiting case in which the 29i. is o} Note that, in the change from sensation differences to difference sensatmns, 5t is not the S them- selves that change; the 292; is an error of comparison, of estimation, of memory} We have measured difference sensations and sensation differences: can we measure sensations ? Yes: by help of the RL and arithmetic. Let /, 2, C, . . be stimuli, so chosen that 2 C 29 etc. Then byWeber's A--/-- C' Lav the corresponding difference sensations are equal. So also are (as we have shown) the corresponding successive sensation differences b--a, c--b, d--c, etc. According to our principle of measurement, the sensation difference d--b is twice c--b; if c--b be our unit, =, then d--b=2. Now the differences of given values from o are ldentmal with the values themselves: .r--o=x. Let us suppose, then, that b has the ß S-value o, so that 15'is the RL. After as before, d--b2 (c--b): but, snce b:o, tlns is the same thing as saying that d=2c. Smfiarly, e=3c , [=4c, etc.; and we have the reqmred measurement of sensation} , We have it by grace of theR2;: but what is theRL? May it not be a merely physiological phenomenon ? No: remember that, when an R affects the sensorium, in the waking state, it finds the sensorium ,, not  ]bd., 8 5 if.  Ibid., 88. We return to the point in detail, pp ely. ff below.  .Ibrd, I93.  .Ibrd., 94.  ]bd., 95.  ]xd, 97; c.f. El., i, 6o fl., t9 x. õ 2. Fechtter's Ittterpretatio, xxxvii psychophysically empty, but already occupied by some sort ofpsychophys- lcal excitations." The incoming R and the corresponding œ must, now, transcend this preexistent excitation, pass the ' mixture limen,' "before the S can appear in consciousness with discrimxnable quality and quantity. "2 In this sense there is an innerlimen, over and above the outer, physiological limen. Fechner ends the statement of his own views with a discusston of at- tention? and a reference to his psychophyslcal Weltanschauung} The rest of the article is taken up vith his reply to Elsas s and Kohler} The only further point that calls for mention here is his insistence on the im- possibility of mental measurement xvithout reference to the corresponding œ-values. "Let two stimuli of different magnitude r o, r (e.., two stellar magnitudes) be given; and let us denote the total d;fference sen- sation correlated xvith them by S(n). There is nothing to prevent an experimental determination of the unit, whereby this value s to be measured, either as the just noticeable difference sensation (correlate of the j. n. R-difference) or as an equally noticeable difference sensation (correlate of a given R-ratio) . . . to be found by the method of mean gradations. But if ve are to ascertain hoxv many times the unit is con- tained in S(n), we must (according to Kohler) juxtapose the equal mental steps in consciousness itself,--/. e., without marking off the R between r o and r xvhich correspond to the equal steps,--until we presently attain the total difference sensation designated by S'(n). Let the reader try for himself, whether the measurement can be made without the aid of the intervening R ! Without such aid, the mental steps pass indistinguishably into one another; we do not know where one ends and another begins, and therefore cannot fulfil the requirement of determining their n; it is as if we should attempt to ascertain the height of a toxver by mounting the first staircase and then climbing the rest of the xvay in the air. Besides, there is an initial inconsistency in the argument. While mental measurement is to be attainable, in principle, by itself, without reference to the underlying physical values, yet for the attainment of the mental unit such reference s not only permitted, but expressly demanded."* This survey may fitly conclude with Wundt's words of appreciation. ,' Diese Arbeit des 86-jihngen ist, wie lch glaube, die klarste und vol- lendetste Darstellung des Problems, die er dberhaupt in den beinahe x ]bd., 00 3.  ]'bzd. 20 4. We return to the question of the Z below, pp. xcv. if. a]btd, 20 7 if.; of.. R, 269ff.  ]bt., 211 f * A. Elsas, Ueber die ?sychophysik, I886; Fechner, loc. cal., x62 if.  P.S., iix., 886, 573 if-; Fechner, be. rd, 212 :f-f.  ]bxd., 216 fl. Cf.. A. Lehmann, Die korpefi. Aeusserungen psych. Zustande, ii, I9O2  I I. ----------------------------------------------------------- xxxviii Introduction 4o Jahren gegeben hat, wlthrend deren er sich mir demselben beschtft- igte." 1 õ 3- The Reception of the lillemente.-- The decade I85o-86o, during which Fechner was at work upon the Elemente der Psychophysik, belongs to a confused and depressing period of German political histor? The revolutionary wave of 848 had spent itself without effect; but the movement towards union, inaugurated by the Frankfort parliament, had also received a serious check at the conferences of Olmhtz and Dresden. There followed years of political reaction, such as have occurred again and again in the history of the nations, and such as are almost always characterised by a fruitful growth of science and letters. It is as if the best men of the time, despairing of political progress, had their energies turned perforce into other channels. This may be at any rate a partial explanation of the scientific activity of Germany in the middle of the nineteenth century. We are not here concerned with the advance of the exact sciences; it must suffice to remind the reader that the law of the conservation of energy plays the same part for scientific thinking in the 4o's that the origin of species by means of natural selection plays in the 6o's.  We may, however, mention a few of the most important books in the sciences of life and mind. I-Ielmholtz published his Physiologische Optik, "one of the four or five greatest monu- ments of human genius in the scientific line,"  between 856 and I866, and his Tonempfindungen in 862; du Bois-Reymond's Untersuchungen uber thierische Electrmitat appeared between 848 and 86o; Ludwig's epoch-making Lehrbuch der Physi- ologie came out in 852 and 856; Virchow's Cellularpathologie in 85o, and his Specielie Pathologie und Therapie in 854-862; Lotze's Medicinische Psychologie in 852 and Mikrokosmus in 856-864: and the list might be largely extended. When, there- fore, the Elemente entered on the scene in 86o, it found'itself at once in good company. We might predict that, as a scientific P.S., iv., 477 f. See B. Gebhardt, Handbuch d. deutschen Geschichte, li., 1892, 54o fl. H Hoffding, Geschichte d. neueren Phdosophe, fl., 896 , 552 fl., 567 . James, Psych., ii., 89o, 278. õ 3. The Reception o[ the Elemente xxxix work by a well-known author, it would be assured of a wide and critically trained audience. We must, however, enquire a little more closely into Fechner's standing as a scientific writer. His Massbestimmungen fiber die galvanische Kette (83z) had given him a high rank among physi- cists, and on the death of H. W. Brandes in 834  he was ap~ pointed professor of physics in the University of Leipzig." His work on after-images (838, 84o) was of the same order as the Massbestimmungen, and received its due meed of praise from Helmhottz. "Fechner, der mt einer ausserordentlicheu Selbstauf- opferung auch gleichzeitig eine grosse Reihe genauer, selbst roes- sender Versuche in dmsem Gebiete ausgefuhrt hat, gab zuerst ene gemigende Herletung der negativen Bilder aus dem Princip der Ermudung. Dmse belden Arbeiten [Plateaus tnd Fechners] bezeichnen im \¾esentlichen noch den gegenwartigen Stand der Wissenschaft. " On the other hand, the publication of Nanna oder hber das Seelenleben der Pflanzen (848) and of Zend- Avesta oder fiber die Dinge des Hiramels und des Jenseits (85) must have brought him into disrephte with the main body of con- temporary scientific men. "Die Naturforscher zuckten uber das Buch [the Nanna] die Achsel, und erkliirten Fechner fiir einen unklaren Kopf."  For their philosophy--if they concerned them- selves at all with philosophical questions--was the materialism of Moleschott and Vo and Bhchner, = the materialism that Vogt  Not, as Wundt says, "bei dem Weggang W. Webers nach G6ttingen" (G. T. Fechner, 9o, 9)- Weber went to Gottlngen from Halle in 83, and was forced to vacate his Gottingen chair in 837. Cf. J. E. Kuntze, G. T. Feclaner, t892 , to7, x39-  For Fechner's life and work, see J. E. Kuntze, G. Th. Fechner (Dr. Mises): ein deutsches Gelehrtenleben, 1892; K. Lasswitz, G. Th. Fechner, 896; W. Wundt, Zur Erinnerung an G Th. Fechner, P. S, iv, 47; G. Th. Fechner, Rede zur Fear semes too-jahngen Geburtstages, 9ot, Chronologisches Verzemhniss der Werke u. Abhandlungen G. Th. Fechner's, in El., i., 889, 337 fl.; O, Kulpe, Arch. f. Gesch. d. Phil., vi., 893, 7o, 449; ¾js. f wiss. PtuL, xxv, 19ot, 9 ; A. Elsas, Grenzbote, 888. ap.o,t896, 537,cf.vøl-,I M.,37 f  Lassxxtz, 66. We know that the botanist M. J. Schletden pubhshed awolent attack upon Nanna, to whmh Fechner rephed in 856. The Nanna xxas repnnted, alder I,asswtz' auspmes, in 899, and agam in I9o3  J XIoleschott, Der Kreslauf des Lebens, 852; L. Buchner, Kraft und Stoff, 855: K. Vogt, Kohterglaube und Wissenschaft, 855, and Vortesungen uber den ----------------------------------------------------------- xl Introduction upheld against Rudolph Wagner in the famous Naturforscherver- sammlung at G6ttingen (I854): and with this Fechner had noth- ing in common. It is doubtful, too, if matters were helped by the publication, in I855 , of the work Ueber die physikalische und philosophische Atomenlehre. In this book Fechner settles accounts with the speculative Naturphilosophie of Schelling and his school; 1 but he is at equal pains to show that the atomic theory has no connection with materialism. ø We may say in gen- eral, therefore, that though there xvere many men of scientific eminence who, like }-Ielmholtz, would take Fechner's ,york on its scientific merits, irrespective of his philosophical opinions, he would nevertheless be obliged, in 86o, to reconquer his old ground with the rank and file of the scientifically educated public. What, then, of Fechner's standing as a philosopher, as the au- thor of the Zend-Avesta? We have here no interest in Fechner's philosophical views on their own account; the antimaterialistic Grundansicht which forms the background of the Elemente, and to which "he has given expression in earlier works, TM is some- thing that, as psychologists. we might altogether ignore. Only, in that case we could never hope rightly to understand Fechner. For him, Wundt tells us," die Psychophysik . . ist nichts anderes gewesen als der umfassendste und griindlichste Versuch, den er unternommen, die in dem Zend-Avesta entworfene Weltan- schauung nach der Seite der yon ihr postulirten Beziehungen zwischen k6rperlicher und geistiger Welt exact zu begriinden und so mindestens innerhalb der durch die'Erfahrung gezogenen Grenzen aus der Sphare des blossen Glaubens in die des Wissens zu erheben."  It is possible to over-emphasise this aspect of the situation. No one, surely, who has read Fechner's psychophysi- cal writings, with the Vorschule der Aesthetik (x876) and the Kollektivmasslehre (edited by G. F. Lipps, 897), s can doubt Menschen, I863. To mention also are the earher works of H. Czolbe, Nee Dar- stellung des Sensualismus, I855 , and Die Entstehung des Selbstbewusstseins, I856  Wundt, G. Th Fechner, 9ox, 63 if. 2 Wundt, G. T. Fechner, 9oI, 5 ø: "Aus dem Zend-Avesta st die Atomen- lehre . . . hervorgegangen "; Lasswitz, 7x f- * El., i., xni.; cf n, ix. f.  Wundt, 44.  On the relatmn of these two works to Fechner's philosophy, see Wundt, 5 o, 74 if. õ 3. The Receptton of the Elemente xli that the author has regained much of his prephilosophical interest in scientific work; that he loves analysis and observation for their own sake. On the other hand, no one who knows the Zend- Avesta can read through the chapters on inner psychophysics in vol. if. of the Elemente without realising that the issues there raised had been judged. in principle, ten years before. "In Wahrheit kehren alle wesentlichen Ideen des Zend-Avesta in der Psychophysik xvieder; es sind aber umgekehrt die Grundgedanken der Psychophysik schon im Zend-Avesta zu finden."  "Mir Zend-Avesta hat Fechner die Summe seiner Gedankenwelt gezo- gem Alles, was er spater geleistet hat, steckt in seinen Keimen schon in diesera Buche." _o The glemente is not only a scientific, but also a philosophical work. a It might seem. at first thought. that the year x85x xvould be as favourable for Fechner the philosopher as the year I86o for Fechner the psychophysicist. There xvas no reigning philoso- pher, no dominant philosophical system. Hegel had died in 83L and the break-up of his school followed almost immediately upon his death. Schelling was called to Berlin in x84 and proved a failure. I-Ierbart's influence was rather psychological than philo- sophical. Schopenhauer's work was only just beginning to attract attention. Lotze had not yet made his mark in phil- osophy; Lange and the cry of ' Back to Kant ! ' were still fifteen years away. There were many able men in the field, but no great man; the spheres of existing philosophical influence were limited and local. Suppose that a great man should arise, a man with a message to his fellow-men: would not this division of interest give him his opportunity? Might he not do for philosophy what Helmholtz and the rest were doing for science ? Perhaps: though it is an open question whether, in a post- Kantian age, the reign of science is compatible with any pro- found philosophy, or preoccupation with philosophy compatible with scientific advance. At any rate, Fechner was not the man, and his teaching made but little impression. "Die Zeit," says Wundt, "da Fechners philosophische Schriften zuerst in die  Wundt, 44- 2 Lasswitz, 65. a Foucault, acquainted with Fechner, as it would seem, only in psychophysmal regard (of. hst of works, Psychophysique, 4 f.), makes the *,Veltansicht of the El. derive from the author's psychophysmal theories (i2o) ! ----------------------------------------------------------- xlii Introduction Oeffentlichkeit traten, war fur ihre Wirkung die denkbar ungunstigste."  Strong words, and, in the light of what we have just been saying, startling words! Yet their truth is apparent. Fechner's philosophy could never have become academic, a phil- osophy of the schools. "Wie Fechner seine Philosophie im wesentlichen aus sich selbst geschopft hat, so wird man auch von ihm sagen k6nnen, dass er neueren philosophischen Systemen ein verhiltnissmissig geringes Verstindniss entgegenbrachte. Ftir erkenntnisstheoretische Untersuchungen und fhr geschichtliche Betrachtungen fehlte ihm der Sinn. Natur und Religion--das waren die beiden Pole, um die sich sein philosophisches Denken bewegte." 2 In another era, he might have been the philosopher of the people, with a vogue' like that of Schopenhauer or von Hartmann or Nietzsche; the pietist and mystic, the poet and the analogist, always find followers,--and, if they are born in due season, a very large number of followers. But the popular phil- osophy of the 4o's and the early 5o's was the positivism of Feuerbach and the physiological materialism of which we have spoken above; Fechner's message ran counter to the 'Zeitgeist'; "ftir Fechner war das Universum ein Geist, fur den Material- ismus war es eine Maschine; . . Fechner galt als Phantast, man misstraute seiner Naturforschung; . . Fechner war religi6s, der Grundzug der Zeit aber war. wenn nicht direkt antireligi6s, so doch wenigstens gleichgixltig in religi6sen Fragen; vor allera war er antikirchlich und antitheologisch; Fechner dagegen hatte einen theologischen Beigeschmack. "a The Zend-Avesta ap- pealed only to the little circle of readers who were like-minded with its author; it gained no recognition from academic philoso- phy or from the representatives of natural science, and found no great fayour with the general public? Fechner was fully and painfully conscious of his unpopularity; but he had no intention of giving up the struggle. In the preface to his l. Jeber die Seelenfrage (x86x) 5 he says that he has :alled four times to a sleeping world, 6 and the world has not yet awaked.  G. T Fechner, 9o, 38.  Wundt, 67. a Lasswitz, 66 f.  Wundt, 4.  Ueber dm Seelenfrage, enGangdurch die sicktbare Welt, um dm unschtbare zu finden, 86x. 6 In Das Buchlein vom Leben nach dem Tode, x836; Ueber alas hochste Gut, x846; Nanna, 848; and Zend-Avesta, 85x. õ 3. The Reception o[ the Elemente xliii "Jetzt rule ich ein fnftesmal, und, wenn ich lebe, werde ich noch ein sechstes und siebentesmal 'Steh' auf!' rufen, und immer wird es nur dasselbe ' Steh' auf!' sein." And, in point of fact, the call is repeated in Die drei Motive und Grande des Glaubens (863) and Die Tagesansicht gegemiber die Nachtansicht (x879)2 So far, indeed, is he from giving up, that he tries a new and laborious method of arousing his contemporaries. "In den Hauptwerken, die er in den letzen 3 ¸ Jahren seines Lebens veroffentlichte, anderte er, wenn ich mich des Ausdrucks bedien- en darf, die Taktk seines Verfahrens; ja er knderte diese vor- nehmlich in dem bedeutendsten dieser Werke, in den ' Elementen der Psychophysik,' so sehr, dass fr eine oberflchliche Betrach- tung der Zweck selber als ein anderer erscheinen konnte. " "Die exacten Forschungen sind ihm nicht nur durch philoso- phische Fragen nahe gelegt, sondern die xvichtigsten unter ihnen hat er nur zu dem Zweck unternommen, fiir seine Weltan- schauung eine lestere Basis und zugleich die Hillfsmittel zu gewinnen, um ihr in der Wissenschaft Eingang zu verschaffen." We have already noted that this view, in its extreme form, may require qualification; that it is substantially true cannot be doubted. How far, then, we may ask, was Fechner successful in his ambition ? How well did he succeed, by means of his Psycho- physics, in drawing scientific attention to the doctrines of the Zend-Avesta ? Wundt declares that he was entirely unsuccessful. "Als nach dem Erscheinen der 'Elemente der Psychophysik' Jahre da- hingegangen waren. konnte er sich die Thatsache night verschlies- sen, dass, wenn das letzte Ziel dieses Werkes die Bekehrung der wissenschaftlichen Welt zu seinen philosophischen und religi6sen Ueberzeugungen gewesen war, er dieses ZieI abermals mcht erreicht hatte." * Lasswitz gives a more favourable ver- dict. "Erst als dm Zeitrichtung hberhaupt philosophischem Interesse sich wieder zuwandte, als mit dem Rtickgang auf Kant 5 auch in den Kreisen der Naturforscher der Materialismus  To say nothing of Einige Ideen zur Schopfungs- und Ent'a4ckelungsgeschichte der Organismen, x873.  Wundt, 43. a Wundt, 5o; Hoffding, o]. r2t., ii., 587 f.  To be dated, roughly, from x866, when F. A. Lange published his Geschichte des Matermllsmus Cf. atso O. Lebmann, Kant u. d. Epigonen, 865. ----------------------------------------------------------- xliv Introduction in seiner Einseitigkeit erkannt wurde, als endlich auch Fechner als der SchSpfer der neuen Wissenschaft der Psychophysik dem naturwissenschaftlichen Zeitgeiste einen neuen Tribut dar- gebracht und neues Vertrauen errungen hatte, da kamen auch seine philosophischen Schriften wieder uber die engeren Kreise seiner Verehrer hinaus zu allgemeiner Geltung."  It is not alto 4 gether easy to strike a decision between these two opinions. Wundt, we may remember, was called to Leipzig in I875, and was therefore in close contact with Fechner during the last twelve years of the latter's life. On this ground, as on many others, his words must carry weight. There are, moreover, two import- ant facts which speak for Wundt's view-. The first is that Lotze, a pupil of Fechner's, had worked out a system of philosophy which, having much in common with his master's, was neverthe- less calculated both by form and by contents to appeal far more strongly to his fellow philosophers and to men of science. 2 Com- pare the Mikrokosmus and the Metaphysik with the Zend- Avesta and the Seelenfrage! Lotze, then, would be taken: and Fechner left. The second fact is that Fechner has played a remarkably inconspicuous part in academic literature, in 'pro- grammes ' and ' dissertations.'  On the other hand, we find that the Atomenlehre came to a second edition in 864, and the Btich- . Lasswitz, 67 f. o. Lotze's Logik appeared in 874, and his Metaphysik in 879. On the relation of Fechner and Lotze, see Hoffding, op. r., 567 if., 587 if. a "Das Studium der Fechnerschen Schriften," says Lasswitz (2o3), "ist iiberall in erfreulichem Aufschwunge begriffen." Of the psychophysical, yes; but of the philosophical? Where are the results? [Since this Note was written, Lasswitz has himself reprinted certain of Fechner's works (noticed in their places in other Notes to this õ). There have also appeared four doctorate theses deahng with. F'echner: A. Goldschmidt, Fechners metaphysische Anschauungen, Wurzburg, 19o2; E Stratilescu, Die physiol. Grundlage d. Seelenlebens bei Fechner u. Lotze, Berlin, 9o3; F. M. Ftch, Der Hedonlsmus bei Lotze u. Fechner, Berlin, 19o3; H. Freudenreich, Fechners psychologische Anschauungen, Leipzig, 9o4. That these events, welcome as they are, represent any general  Aufschwung' of the study of Fechner, the author can hardly believe. Stumpf stood, of course, in intimate relation to Fechner and Lotze; and Kilpe, who saw the reprint of the El. through the press, has been outspoken in his appreciation of Fechner's work. It is very natural, therefore, that the occasion of Fechner's centenary should call forth theses from Berlin and Wirzburg. At any rate, there is no other mention of Fechner in the files of the Bibliograph. Monatsbericht since 89 ¸ !] õ 3. The Reception o[ the Elemente xlv lien vom Leben nach dem Tode to a second in i866.  The latter work is, however, hardly more than a pamphlet; and it is only natural that the interest aroused by the scientific portion of the Elemente should bring with it a transient interest in Fechner's other work. The wonder is that it did not bring more; that there was no republication of any part of the Zend-Avesta, or of the Seelenfrage. 'ø We shall probably be safe, therefore, in fol- lowing Wundt: just as we may more safely accept Wundt's char- acterisation of Fechner's system, as "a restoration and comple- tion of the romantic nature philosophy," a than Lasswitz' ideas of its relation to the critical philosophy and of the place it is destined to take in modern thought2 As a philosophical work, the Elemente failed of its purpose; as a scientific work, it had to overcome prejudice: this is the net result of our discussion. If we look at the preface of vol. i., we see that Fechner has been very careful to propitiate his scientific readers. On the experimental side, he appeals to E. H. Weber, "den ich fiberhaupt den Vater der Psychophysik nennen m6chte "; on the mathematical, to Bernoulli, Laplace and Poisson, to Euler, Herbart and Drobisch, to Steinheil and Pogson. "Das Problem ist . . . der That nach schon yon Forschern ge16st, deren Namen eine Gewihrleistung der Triftigkeit der L6sung ist." He acknowledges indebtedness to Volkmann, and, after paying a compliment to Herbart, emphasises the essential dif- ference of the Psychophysik from the Herbartian mathematical psychology. He admits that his Grundansicht is capable of materialistic interpretation, though he himself is diametrically op- posed to materialism2 Is not such an introduction admirably 2 Third, t887 (the year of Fechner's death); fourth, 9oo (the eve of his centen- ary); fifth, I9o3 . Trs. by M. C. Wadsworth, with introdn by W. James, t9o4 .  Fechner looked upon the Seelenfrage as the most fundamental of his works on nature philosophy: P.S., iv, 212. Lasswitz has now (t9oD brought out a second edition of the Zend-Avesta. a Wundt, 59. t Lasswitz, I93 if. Lasswtz' enthusiasm for the subject of his study ts natural. We must, however, discount it, when we are trying objectively to estimate Fechner's position in the philosophical world of his day: something very different, be it remembered, from his position in the history of philosophy.  El., i., ix. if.; of. W. Preyer, Wiss. Briefe, I89o, 223. ----------------------------------------------------------- xlvi Introduction fitted to excite interest and to allay suspicion in the scientific mind ? We have Wundt's word, and we have objective evidence, that the Elemente--as a scientific book--" grosses Aufsehen erregte."  In the very year of its publication, Helmholtz (working, of course, on the basis of the Abhandlung of x859 ) recognised Weber's Law as "eine erste Anmiherung an die Wahrheit" and proposed a modification of the fundamental formula, which Fech- her gladly accepted. -ø Mach, in the same year, began a series of experiments to determine whether Weber's Law held for the perception of time; $ and in I863 published a little volume of Vortrkge fiber Psychophysik.' Wundt pays a high tribute to Fechner in I862, in the introduction to his Beitrge zur Theorie der Sinneswahrnehmung; 5 and again in 863, in the Vorlesung- en fiber die Menschen- und Thierseele. "Fechner verdankt die Psychologie," he writes, "die erste umfassende Untersuchung der Sinnesempfindungen vom physikalischen Standpunkte, durch die zu einer exakten T.heorie der Empfindung der Grund gelegt wurde." 6 Volkmann includes psychophysical papers in his Phys- iol. Untersuchungen of 863 .7 Aubert challenged the validity of XA7eber's Law in 864, on the basis of experiments of his own? Delbceuf made the acquaintance of the Elemente in 864, and car- ried out his classical experiments on brightness in x865-62 Bernstein published his irradiation theory in 868. ø Lotze had said in the Medicinische Psychologie of x852 that he preferred Herbart's mathematical psychology to the formulm proposed in  G T. Fechner, 9o, 5 . P. O., 867, 34, ½. 896, 390; Fechner, El., i., 564 if., esp. 568; I. $., 5, 6 if.; Berichte, etc, $64, 7 f. a Stzungsber. d. kais Akad. d Wins. zu Wren, math.-natum-. CI., li., 2te Abth., Stzung yore 3 Febr 865, 33 f' 4 Pubhshed first m the Oesterr. Zmts. f. praktsche Heilkunde, x863. * See p. xxx  See i. pp. vin., 98.  P. U lm Gebmte d. Optk,j., 5, H 7. 8 H. Aubert, Physiologie der Netzhaut, 865, 49 fl. The first part must have ap- peared in x864: see Fechner, Berichte, etc., I864,  ff.; I. S., x6 if., 5  if., 49 if.; Komg m tlelmholtz, P. O., 896, x2 5.  Examen mmque, 73; l.tments, 56, note. '  Bernstmn, m Reinherr u. du Bols-Reymond's Arch., x868, 388 if. õ 4. Criticism xlvii the Zend-Avesta, --this is, indeed, the one place where the stu- dent of modern psychology is likely to run against the Zend- Avesta,--and, no doubt, discussed the Elemente with his pupils at G6ttingen. Vierordt's Zeitsinn, in which much regard is paid to the Elemente, came out in 868. - Horing's work on the time sense appeared in I866, a and Keppler's taste experiments in x869 .* liere is evidence enough--and there is doubtless much more ---of the interest aroused by the Elemente in the 6o's. We shall presently find evidence that the interest continued through the 7o's and 8o's: witness, now, the publication of Muller's Grundle- gung xn x878, and of the new edition of the Elemente (the first "war schon seit mehreren Jahren im Buchhandel vergriffen ") m 889. Indeed, the interest has never ceased. For the last ten years, it is true, experimental psychology has been growing away fmn2 Fedruer: quahtative analysis has bulked larger in the liter- ature than quantitative determination. 6 But we are now, per- haps, entering upon a period in which we can pay adequate regard to both aspects of psychological work, in which we can set numer- ical values and introspective analyses side by side. And any sort or kind of quantitative psychology must take its stand upon the work of Fechner. õ 4- Criticism.--We may noxv discuss some of the principal objections urged against Fechner's psychophysical system. The doctrine of the Elemente was attacked from many sides and on many issues. It is therefore inevitable that, in setting forth single objections, we do some violence to the literature. Differ- ent men employ the same argument; but they employ it in support  See pp 2o f. 2 K. Vxerordt, Der ZeStsinn nach Versuchen, 868.  A. Honng, Versuche nber das Unterscheidungsvermogen des Horsinns fur Zmtgrossen, 866. I.S., 4 F Keppler, Das Unterschmdungsvermogen des Geschmacksmnnes fur Con- centratmnsdfferenzen der schmeckbaren Korper, 869; Pfluger's Arch, fl., 449. I. S.. x6 if.  See El., i., v. The author has used the edition of 8S 9 exclusively, for quota- txons n thin work. The two e&tions do not tally, page for page; but the differ- ence rarely exceeds two or three hnes; so that the fortunate possessors of the first edition wfil have no &fficulty in finding the passages cited.  Seeol i,I .M,xx.u f ----------------------------------------------------------- xlviii Introduction of different positions, and set it in different contexts. The reader must not be surprised if, on looking up the references which the folloving discussion brackets together, he find a xvide divergence of expression. Nor must he expect that the arguments of which he is in search will be clear-cut and distinct: the very first objec- tion which we take up--the objection that no S is a sum of smaller S-units--plunges us into controversies about negative S-values, about the 'Unterschiedshypothese' and the 'Verhiltnisshy- pothese,' about the qualitative or quantitative nature of intensive differences, about 'pure sensation' and ' apperceived sensation.' It would be well, if confusion is to be avoided, to preface this Section by the reading (over and above the Elemente) of Wundt's P. P., i., I9o2 , ch. ix; Ebbinghaus' Psych., i., õõ 6, 44-46; or Jodl's Psych., ch. iv. Popular accounts of psychophysics will be found in J. Sully, Sensation and Intuition, x88o, 37 if-; T. Ribot, German Psych. of To-day, x886, x34 if. (both of these sketches are, unfortunately, to a large extent out-of-date); Wundt, Human and Animal Psych., x7 if. (  ) Fechner asserts that the S is a measurable m. agmtude, or qtatity, the stun of a certain tmber of S-units.  Now it is clear that, in a certain sense, the S may properly be termed a magnitude (Gr6sse, grandeur): in the sense, namely, that we can speak oœ a 'more' and 'less' of S-intensity. Our second cup of coffee is sweeter than the first; the water to-day is colder than it was yesterday; A's voice carries farther than B's. On the other hand, the S is not, in any sense, a quantity (messbare GrSsse, Quantitht, quantitY). For (a), as Fechner himself recognised, the verdict of introspection in the case of any single S is unhesitating; there is no sign or hint of summation; "an die schon erwachsene Empfindung 1,isst sich kein Mass anlegen, insofern sich keine quantitative Mehrheit darin unterscheiden lisst."  Moreover, (b) we cannot perform additions and sub- tractions, with two or more S, and obtain sums or remainders. If a weak pressure upon our hand is suddenly doubled, we have a more intensive pressure sensation; but the 'more intensive' S is a new S, not the old S with a certain plus added to it: the old  Seeesp. E1.,i.,60; P S.,iv., 85f. El,i.,6L õ 4. Cr,ticism xlix S has entirely disappeared. If a source of sound is suddenly withdrawn to a greater distance from us, we hear a weaker sound; but this ' weaker ' S is not a part of the old S; the old has gone, and an entirely new S has taken its place.  To students of' the present generation, this objection appears, perhaps, the most natural and obvious that could have been urged against Fech- ner's derxvaton of the 'psychisches Mass.' Yet we search m yam for xt m the Table of Contents of the I. S. (of. also3 f, 2I I). It had, neverthe- less, been raised mphctly by Delbeeuf m I873; exphctly by J. Tannery m 875, andbyDelbceufm 877.  Fechner, indeed, though wxthout full reahsation ot the ssue, touches the heart of the matter in hts reply to Delboeuf (I. S , 3  f). "Nun kann Delbceuf entgegenhalten," he says, ,,dass er tiberhaupt blos Contrastempfindungen statuire; rodess ich mene, es sei be ener S hre egene Stgrke, und das Verhaltniss des Plus und Mxnus ihrer Starke zu anderen S zu unterscheiden. Denn wo- zwischen soll das Verhaltniss des Plus und Minus stattfinden, wenn man de S an sich selbst eme Stgtrke versagt; es st denn nichts dazu da In der That aber schemt mir Delbceuf das, was blos Sache der Unter- sctneds-.S' rot, mt dem, was Sache der absoluten S ist, zu verwechseln oder zu vermschen. Ich habe fur jenes dm Unterschedsmass[ormel, fur dxeses de enfache Massformel. Delboeuf hat fur beides blos eine Formel." a Whether Delbceuf was at all clearly conscious of the , quantity obJec- tion  xn hm ltude psychophysque (873)  is, despite hm later statements, 1 It is instructive to compare the following passages. "Sind zwei Tone yon verschiedener physischer Starke gegeben, so kann man sich einen dntten denken, dessen Starke dem U'nterschmde der Starke jener belden gleich rot" (Fechner, E1, i., 48). "Es mr, soviel ich bemerken kann, unmoglich, den Intensitatsbetrag gesondert vorzustellen, welcher zur niederen Starke hnzukommen musste, um de hohere zu ergeben" (Stumpf, Tps., i., x). See also Wahle, Das Ganze d. Philos., 203; Stout, Manual, 3 ø f. e It is tempting to read the ' quantity objection ' between the hnes of certain passages of Henng's criticism: Sitzungsber. d. kais. Akad. d. Wiss. zu Wen, math.-naturwss. CI., lxxii., Abth. 3, Sitzung vom 9 Decr. x875. See esp. the dscusson of Weber's experiments, 36 f. On the whole, however, there can be no doubt that Henng froled to urge ths objection. Cf. A. Meinong, Z, xi., 896, 387. Fechner makes no mentmn of the Tannery letters. It is natural enough that an anonymous correspondence in the Revue scentifique should have escaped his notice a Cf. R., 20o f, 305 .  Published, with ommsions, as first part of the ]lments de psychophysique gnrale et sp&ale, x883 Cf Examen critique, 883,  2 if.; Rev phil., v, x878, 57 if-; Ebbinghaus, Z, i., x89 o, 3, n. ----------------------------------------------------------- xlviii Introductzon of different positions, and set it in different contexts. The reader must not be surprised if, on looking up the references which the following discussion brackets together, he find a wide divergence of expression. Nor must he expect that the arguments of which he is in search will be clear-cut and distinct: the very first objec- tion which we take up--the objection that no S is a sum of smaller S-units--plunges us into controversies about negative S-values, about the 'Unterschiedshypothese' and the 'Verh//ltnisshy- pothese,' about the qualitative or quantitative nature of intensive differences, about 'pure sensation' and ' apperceived sensation.' It would be well, if confusion is to be avoided, to preface this Section by the reading (over and above the Elemente) of Wundt's P. P., i., 19o2 , cb. ix; Ebbinghaus' Psych., i., õõ 6, 44-46; or Jodl's Psych., ch. iv. Popular accounts of psychophysics will be found in J. Sully, Sensation and Intuition, 88o, 37 if-; T. Ribot, German Psych. of To-day, 886, 34 if. (both of these sketches are, unfortunately, to a large extent out-of-date); Wundt, Human and Animal Psych., 7 if- (  ) Fechner asserts that the S is a measurable magnitude, or quatity, the sztm of a certain number of S-units.  Now it is clear that, in a certain sense, the S may properly be termed a magnitude (Grbsse, grandeur): in the sense, namely, that we can speak of a 'more' and 'less' of S-intensity. Our second cup of coffee is sweeter than the first; the water to-day is colder than it was yesterday; A's voice carries œarther than g's. On the other hand, the S is not, in any sense, a quantity (messbare Grbsse, Quantitat, quantity). For (a), as Fechner himself recogmsed, the verdict of introspection in the case of any single S is unhesitating; there is no sign or hint of summation; "an die schon erwachsene Empfindung liisst sich kein Mass anlegen, insofern sich keine quantitative Mehrheit darin unterscheiden 1iisst." - Moreover, (b) we cannot perform additions and sub- tractions, with two or more S, and obtain sums or remainders. If a weak pressure upon our hand is suddenly doubled, we have a more intensive pressure sensation; but the 'more intensive' S is a new S, not the old S with a certain plus added to it: the old See esp. El., i, 6o; P. S, iv., 18 5 f. õ 4. Criticism xlix S has entirely disappeared. If a source of sound is suddenly withdrawn to a greater distance from us, we hear a weaker sound; but this ' weaker ' S is not a part of the old S; the old has gone, and an entirely new S has taken its place. x To students of the present generation, this objection appears, perhaps, the most natural and obvious that could have been urged against Fech- her's derivatmn of the, psychisches Mass ' Yet we search m vain for it m the Table of Contents of the I. S. (of. also3 f, 2 ). It had, neverthe- less, been raised mphcit]y by Delbceuf m 873; exphcltly by J. Tannery m 875, andbyDelboeufm 18772 Fechner, indeed, though without full realisation ot the ssue, touches the heart of the matter in his reply to Delbeuf (I. S., 32 f.). "Nun kann Delbceuf entgegenhalten," he says, ,,dass er tiberhaupt blos Contrastempfindungen statuire; ndess ich meme, es sei bei emer S lhre egene Stgtrke, und das Verhaltniss des Plus und Minus ihrer Starke zu anderen S zu unterscheden. Denn wo- zwischen soil das Verhaltniss des Plus und Minus stattfinden, wenn man die S an sch selbst eine Starke versagt; es ist denn mchts dazu ds. In tier That aber schemt mir Delbceuf das, was bios Sache der Unter- schieds-S ist, mit dem, was Sache der absoluten S st, zu verwechseln oder zu vermschen. Ich habe fur jenes dm Unterschiedsmassformel, ftir dieses de emfache Massformel. Delbteuf hat fur beides blos eme Formel."s \Vlether Delbceuf was at all clearly conscious of the , quantity objec- tion  in his ltude psychophysique (1875) * is, despite hs later statements,  It is instructive to compare the following passages. "Stud zwei Tone yon verschiedener physischer Starke gegeben, so kann man sich einen dritten denken, dessen Starke denl Unterschiede der Starke jener beiden gleich fat" (Fechner, El., i., 48)- "Es ist, somel ich bemerken kann, unmoglich, den Intensitatsbetrag gesondert vorzustellen, welcher zur niederen Starke hinzukommen mnsste, um die hobere zu ergeben" (Stumpf, Tps., i., 21). See als Wahle, Das Ganze d. Philos., go 3 , Stout, Manual, 3 ø f. 2 It is tempting to read the ' quantity objection ' between the lines of certain passages of Hermg's criticism: Sitzungsber. d. kais. Akad. d. Wiss. zu Wen, math-naturwiss. CI., lxxn., Abth. 3, Sitzung yore 9 Decr. 1875. See esp. the discussion of Weber's experiments, 316 f. On the whole, however, there can be no doubt that Henng faxled to urge this objection. Cf. A. Meinong, Z, xi., I896, 387. Fechner makes no mention of the Tannery letters. It is natural enough that an anonymous correspondence in the Revue scientifique should have escaped his notice a Cf.. R., 200 f, 305 . 4 Published, with omissions, as first part of the llments de psychophysique gIIrale et spciale, 1883. Uf Examen critique, 883, 112 fl.; Rev. phil., v, 1878, 57 if-; Ebbinghaus, Z, i., 189 o, 321, n ----------------------------------------------------------- 1 Intoducwn very doubtful. The objection xvas expressly raised by J. Tannery in letters (called tbrth by articles of Rtbot's) published in the Rev. set., I3 Mars and 24 Avril, 875  "Sans doute," remarks Tannery, ,, une sen- sation peut Etre pins ou morns vive, mais cela suffit-il pour que la sensa- tion soit une quantirE ? . Les seules grandeurs que l'on puisse mesurer directement sont celles dont on peut dOffnet l'Ogalit et l'addi- tion... I1 ne me semhle pas qu'une sensation possde ce caractre d'homogEn6itE qui appartient essentmllement aux grandeurs mesurables." Delbuf, who takes up arms on behalf of psychophysics, meets it in terms of his ' Dlfferenzansicht der Empfindung; '2 i.e., in terms of the Reconstruction of 6, not of Fechner's Massformel. ,6 Nos sens," he declares, ', sont des instruments chftrentiels, c'est-.-dire servant & con- stater des chffrences, pa autre chose. Or, quand cette diftgrence est de 2, 3, ß - o degrOs, la sensation est-elle deux fols, trois fols, . . dx fols plus grande que lorsqu'elle est de t degr" (122). "Supposons que l'on constrinse une Echelle de temtes chffOrentes allant du sombre au clair, et chomies de faon que les contrastes sensibles entre deux teintes vomines soient tous Ogaux .... j'aurais certanement une ½chelle qui mesurerait la sensation de lumlre ou de l'obscurit½" (x 24 œ.). "On ne pent pas, en so-mme, prendre lsolCment deux sensations Ogales et les ajouter l'une & l'autre, cornroe on ajoute des poids ½gaux;" but ,' un chantcur . . . procde par ntervalles de ton, par degr6s d'acuit Ogaux, . . . et dles ajoute comme 6gaux" (143)- The difficulty is thus turned; Delboeuf has rescued his differentials: only, once more, they are not Fechner's. "Les differences de sensation correspondant . ces differences [d'excita- tion], sont-elles Egales; sont-elles de mme nature; la sensation est-elle une somme de ces diffOrences" (r43) ?--this is not Fechner's question; and the 'accromsements ½gaux' of Delboeuf are equal increments of ' contraste sensible,' not ' gleiche Zuwtichse der Empfindung.' In the articles written after the Tannery controversy, Delboeuf is quite clear. "La 1oi de Fechner, dsais-je dans l'tude tsycho2bhysique, est insoutenable au point de rue mathEmatique. Elle entraine des cons{- quences absurdes, et la maniOre dont elle est {Stablie ne procure pas a. l'esprit une id{Se bien nette de ce que pent tre la quantit d'une sensa- tion, ni comment, par consequence, elle peut tre represent6e par un hombre. "a And again, on Fechner's principles ,, il est impossible de se i Printed (with the author's name) in Delbteuf's Eldments: see t t ,  13, 36, 38.  Worked out in the Thdorle gndrale de sensibilit (1876; reprinted as second part of the Elements, 883). Cf. I S , I 13 ff.; Stumpf, Tps., i., 7 if. Not to be confused with the Unterschiedshypothese, the ' difference hypothesis' of Weber's Law.  Rev. phil., iii., 877, 241; Examen critique de la loi psychophysique, 1883, 3 ø f. Repeated in Rev. phil., v., t875 , 35; Examen, 72. Yet the reference given is not õ 4. Criticism li faire aucune idle de ce que pent tre la quantit6 de la sensation."l Delbycur himself meets the objection as before2 Tannery had objected that the intensive S-series is not homogeneous. Delbeeuf, in the heat of controversy, fails to grasp the situation. ,, Qu'est- ce que cela prouve," he replies, "sinon que la sensation . . . West pas lsolable ?"a The objection is, however, very serious. It is taken up independently by J. Ward, Mind, i., 876, 464 if. "A host of other sensations--to say nothing of images reproduced--accompames those at the higher end [of the scale], sensations roughly recognised as the stimulating effect of strong light or the strain of heavy weights, and so forth .... Could all these be taken into account, a simple enough rela- tion might be found between their intensity and the intensity of the cen- tral movement [Fechner's psychophysical process]." Fechner's results are then explained in terms of J. Bernsteln's theory of central lrradm. tion;  "the mistake suspected is that the true intensity has been con- fused with a possible mode of estimating t, almost with our memory of the chief objects concerned in it--much as people might confound the intensity of a flood or a fire with the ground covered or the number of farms or houses destroyed." The intensive sensation, as Delbycur ad- mitted, is not isolable, and so the results of measurement are not pure. The objectran is put more strongly hy R. H. Lotze, who declares that a strong sour does not taste the same as a weak, that a shadow does not look the same as its background: there are "qualitative Veranderungen des Empfindungsmhalts, die yon jenen [intenstven] Differenzen der Reize abh.ngen."  Nevertheless, "ich will," remarks Lotze, "kein grosses Gewmht auf diese Bedenken legen ;" only, they must be cleared away before we can admit the j. n. d. as the S-umt.  Cf. C. Sigwart, Logre, ii., I895, 68. to the Etude, but to the Tannery letters. C. fi the summary of I. S, x, in Rev. phfi., 38 f.; Examen, 78 f.  Rev. phil, v., 1878, 6I; Examen, I2O.  For details, see õ 6, below. a Eldments, 4o. Cf. Examen, 33, 4 i; Rev. phil., iii., I877, "43, 247- 4 du Bois-Reymond's Arch., 868, 388 if.; Untersuchungen uber den Erregungs- vorgang im Nerven- und Muskelsysteme, I87t, Absch. iv, 166 if. Cf. I. S., 138 if.; G. E. Muller, G., 374 if.; Funke, in Hermann's Hdbch., in., 2, I88O, 357- a Metaphysik, 1879, õ 258; I884, 511 if.; Outlines of Psych., (I88I) 1886, x 7. Cf. Medicinische Psychologie, I852, 208.  Wundt regards thin "geanderte Fassung des Problems" as "kaum mehr als ein Wortunterschied," "sobaid man nut dm quantitative Messbarkeit jener quah- tativen Unterschiede zugesteht": P.S., fl., 12 f.; P. P.,. i., 19o2, 55 f. But whether we say outright that the ' intensive dfferences ' of common speech are in truth qualitative differences, or simply poser a qualitative change along with the ----------------------------------------------------------- lii Introduction The whole question is discussed by J. yon Kries, in the VierteI- jahrsschrift f. wiss. Philos., vi., x882, 273 if. "Die Gleichartig- kelt der Elemente, welche unsere Raum- und Zeitvorstellung auszeichnet. fehlt eben den intensiven Empfindungsreihen." "In dem starken Tone steckt nicht so und so viel mal der schwache, wie im Fuss x2mal der Zoll enthalten ist und in der Minute 6omal die Secunde. " Cf. Meinong, Z.. xi., 896 , 5 f.; Nagel's Hdbch. d. Physiol., iii., , 9o4, 23 if. Other important refer- ences are the following. 878. G. E. Mtiller, G., 2, seems to imply that the summation of Sis possible: c./'. Stumpf, Tps., i., 42; F. A. Mtiller, Axiom, II6 if, esp. I22. It should, however, be remembered that Muller exphcitlydeclines to enter uponthequestmn,,wormdenn nun egenthch ½he Merkhchkmt oder Deuthchket emes Empfindungsunterschiedes bestehe," wL; c_/. t if, 421 if. In the Psychophysk der Geschtqempfindungen, Muller writes: ,,man deutetden hmrentwickelten Begriff derEmpfindungsm_ tenaltar kurz, wenn auch nicht hinlanglich genau an, wenn man dm Intensitat der Empfindung kurz als den Abstand derselbenvom Null- punkte deftinert; "[man wird] die Intensetat einerEmpfindungnach ihrem Verhaltnisse zu der als Enheit betrachteten lntensitb. t einer be- stimmten Empfindung zu bernessen haben,"--the umt noxv bmng an unit- &stance: Z.,x., 896 , 25 f,35. Muller further notes the complication of ntensive increase by change of quality and of, msmtence' (Eindnng- hchkmt): 27 f. 879. S. Exner, n Hermann's Handbuch d. Physiol., ii., 2,242 f. "Dass dm Druckempfindung welche exn Loth hervorruft, von der Druckemp- findung, welche ein Pfund hervorruft, nut quantitativ verschieden ist, ist nicht Gegenstand der ummttelbaren Empfindung. Gegenstand der unmittelbaren Empfindung st nur, dassdm binden Empfindungenver- schieden sind." 88o. A Stadler, Phfios. Monatshefte, xv., 583 f. "Die Starke einer intensive, we are going a long way towards the doubt or denial of any such quant/- tative measurableness. See Grotenfelt, Das XVebersche Gesetz, 46 f , J L. A. Koch, Z. f. Phil u phil. Kritlk, N. F., lxxx., I88, 8o f.; lxxx., x882, x73; Mun- sterberg, N G, 6, Jodl, Psych., I896 , 2o2. 224, 226, Wahle, Das Ganze d. thilos, 894, xS, x92 f., x95. "Eine Intensitat an den Empfindungen selbst ist absolut nicht messbar," says Wahle (93), "denn sie ist mcht vorhanden" A protest against the use of the term ' quality,' in this connection, is raised by Ebb/nghaus, Z, i., 324 f., n.; Stunipf, Tps., i, 24o; ii, 558  yon Krles is criticised by Wundt, P.S., xr if.; Grotenfelt, Das Weberache Gesetz, 3 x if.; Meinong, Z., xi., x896 , m 4 if, xx4ff. õ 4. Crticsnz liii Empfindung lasst sch nicht auffassen als eme Summe von sound so vel mnfachen Empfindunggraden." Cf. tbzd., xiv., x878, 226, 222; also G. Tarde, Rev. phfi., x., I6, 167 f. 88I. E. Zeller, Abh. d. kgl. prenss. Akad. d. Wiss., phil.-hmt. CI., 3 Mgtrz I88I (publ. I882), 5. ,, Muss man doch einraumen, class sm Bewusstseinserschenungen] sich uns selbst . . . ausschhesshch als quah- tatlye VerXnderungen darstellen." Zeller's paper (R., 332 if.) was answered by Wundt, P.S., i., 1883, 25I; Zeller rephed in the Sitzungs- ber. d. Berhner Akad., I882, i.,295; and Wundt wrote again in P.S.,  , 463. I 882. F. Boas, Pfluger's Arch., xxvifi , 568 if. ,, Man muss demnach wohl annehmen, dass alle Empfindungmntensitaten an hren quahtatven Unterschieden erkannt werden" (572). 882. F. A. Muller, Das Axiom der Psychophysik und die psycholo- gische Bedeutung der Weber'schen Versuche: eine Untersuchung auf Kanuscher Grundlage, passim: e. g., vi., 2, 9, 30 if., 46 if. (',Gr6sse kann nut Objekten bmgelegt werden"), 55 f. (" De Empfindung ist mcht FunkCron des Rmzes, sondern der Reiz Objekt tier F. mpfindung, und dm Empfindungkann somit . . . dutch eine Zahluberhaupt nmht dargestellt werden "), IO6 if. (" Wr ersetzen dm Contrastempfindung yon variabler Intensetat durch das Contrastgefuhl yon varmblem Charakter "), 28, 233 f., 37, I43. 883. Stumpf, Tps.,i., 399. "Jede Empfindung prasentirt sch uns als ein Untefibares." C_f. 42, I2I, 350. 884. P. Tannery, Rev. phfi., xvii , 22 f. ,'Cette hypothese (a saytar x The sentence quoted from Zeller is definite enough. It is, however, doubtful if he appreciated hs own argument, for the reasoning of the paper in general extremely confused. One might take as unit for a gven class of sensatmns, says Zeller, "the average value of the least perceptible stimulus." But 0) j' n. S are "nichts weniger als allgemein bekannte und anerkannte, feste und unverander- liche Grossen;" while (2) "die Aussagen unseres eigenen Bewusstseins . . . sind viel zu unsicher, als class sich . . . auf sie allein dm Annahme grunden hesse, eine gegebene S habe, beispielsweise, &e funfzigfache oder hundertfache Starke der e. m. S dieser Klasse" (6). We may reply to the first objection that it s met by Zeller hm.self, in his reference to 'average value '; to the second, that nmther can we tell, without a yardstick, the fiftyfold or hundredfold of, say, x inch. Zeller then speaks of Weber's Law, and emphasises the relativity of ts measure- ments. "Wir wussten vielleicht, dass ein Ton die doppelte Dauer oder Starke eines anderen gehabt habe, aber ,me lange er dauerte und wie stark er war, konnten 'wr mcht angeben" (io). But to say that the mental must be measured by the mental, and that mental measurement is in so far relative, ls merely a truism If we can say anything at all about "einen Theil oder ein Vmlfaches einer Bewusstseinserscheinung" (9 f-, I5), we can surely measure, and measure in Fechner's way. ----------------------------------------------------------- liv Introductzo que la sensation d'une diff4rence totale est la somme des sensations des dffrences partidles) est absolument fondamentale en psychophysique, et die suppose . . . que les sensations sont susceptbles de roesure, d'ad- dtion et de multiplication . . . Ou bien la roesure . . . ne sera au fond qu'une pure convention, ou blen nous possddons un critdrium qui nous permettra de contr61er les rsultats de cette roesure... Or, en thse gn4rale, le cntrium n'existe pas... I1 y a exception toutefois pour ß . . l'oui'e et la rue." 1886. A. Elsas, Ueber die Psychophysk: physikalische und erkennt- msstheoretische Betrachtungen, vi., 49 if., esp. 56 f. "Und die Emp- findung ? Sm ist gat kein Objekt wissenschaftlicher Erkenntmss; sm gehort nicht zur Natur; sie hat fur den mathematmchen Physiker keme Reahtat; sm lasst sich nicht als ein Quantum mathematisch behandeln" (70). Cf. Phfios. Monatshefte, xxiv., 1888, I43. 888. A. Grotenfelt, Das Webersche Gesetz und die psychsche Relatiwtat, 34 f., 37 if. "Eine Empfindungsintensitat ist, nach dem Zeugnisse der inneren Erfahrung, in dem Stnne eine GrOsse, class sie wachst und abramrot. Jede solche Intensitxt erwachst aus emer Folge successtver Intensitatszuwuchse; insofern ist es einfach eme Thatsache, dass ein gr6sserer Intensitatsunterschied die Summe klemerer, partroller Unterschiede ist, dass sich jede bestimmte Empfin- dung aus den successtven Intensititsstelgerungen vom Nullpunkte an summitt. Eine Addition derselben findet faktisch start... Freilich hat die Addtrung bier nicht vollst.ndg dieselbe Bedeutung wm die Sum- mation extensver Grossen." Cf., however, 179: ,,Die Grundannahme, wovon dte theoretische Darstellung der Psychophys,k uberhaupt ausge- gangen, namhch dass ihre Messungen smh auf die psychschen Intensi- tatsgr6ssen bezOgen, ist durchweg hypothetisch . . . Es bleibt zweifel- hat, ob den psychophysischen Untersuchungen gelungen ist das quanti- tative Moment des Empfindungsvorgangs herauszugreffen." 189o. W. James, Principles of Psych., i., 546 f. "To introspection, our feeling of pink is surely not a portion of our feeling of scarlet; nor does the light of an electric arc seem to contain that of a tallow-candle in itself." 189o. H. Munsterberg, Beltrage zur exper. Psych., iii., 3 if. "De starke Empfindung ist fur unser Bewusstsein nicht das Multiplum einer schwachen Empfindung .... welmehr etwas ganz Neues, in gewmsem Stone unverglemhbar. " Cf. Grundzuge d. Psych., 19oo , 271. 189o. H. Ebbinghaus, Z., i., 324. "Der blosse Emdruck emer Hel- ligkmt besitzt nichts yon der Mehrheit yon Kerzen, aufderen Vorhanden- sein er allerdings vielfach beruht; . . . der Eindruck einer grosseren 1 Munsterberg makes a single exception to this rule, for which see p. cxxxv. below. õ 4. Crincism lv Helhgket mt le&glich etwas Anderes als der ener genngeren." Cf. Psych , L, I902, 506 L g92. J. Sully, I-tuman Mind, L, 89 ,'We shall never be able to regard a gwen sensation as made up of so many units, as we can regard a hnear length or a mechanmal force." I893 O. Kulpe, Outhues [I89 1,4 f. We cannot"conceveofsensa- ttons as dwded into parts;" "thin sensatmn of grey m not two or three of that other sensanon of grey." 894. R. Wahle, Das Ganze d. Phflos., I91. ,, Niemals hat man n einer Empfindung de in ihr stecken sollenden Multipla oder Quanta yon Empfindungen bemerkt." i896. A. Meinong, Z., xi., 97. ,' Es hatte keinen Stun, von einem Iauten Gerausch zu sagen, es enthalte ein leises von ubngens genau der namhchen Qualitfi. t als Teil in sich." Cf. 355, 357 f., 374; and see G. F. Stout, A Manual of Ps5ch., 899, 204, 206. 897. A. Hofler, Psychologm, 4o f., 228. "Es hat keinen Sinn, ene Empfindung als anthmetische Summe zweier Empfindungen oder das Vielfache einer anderen Empfindung auikufassen." 9o2. A. Lehmann, Die korperl. Aeusserungen psych. Zustande, ii.,  I: "eine ._q lasst sich nicht aus einer Anzahl anderer Sauf dieselbe Wese aufbauen, wie man z. B. eine Linie hervorbringen kann, wenn man tone Anzahl Langenetnheiten tn hrer Verlangerung absetzt." Some of these authors (Delbceuf, yon Kries, Zeller, F. A. Mhl- ler) are answered by Fechner in R. (x882). There can, however, be no doubt that Fechner failed to appreciate the force of the general objection. See esp. the reply to yon Kries, R., 322 f. Wundt's position is, at first, that of Fechner. In the Vorles- ungen uber Menschen- und Thierseele, i., I863, ot, he speaks roundly of summing an S from S-units, "indem wir die Empfin- dung in ihrem Wachsen allmb. lig verfolgen." "Es steht uns frei, beliebig grosse Empfindungen durch eine solche Summirung yon Einheiten zu messen." In the P. P., 874, we have the same doctrine. True, there is no definite statement as to the possibility of summation; but the reader feels that the statement is lacking because, to the writer, the fact was obviousß See 287 if., 295, 302 if. (" die intensiven psychischen Grossen k6nnen schlechter- dings nur an ihren Differentialen erster Ordnung gemessen werden "), 306? In the P. P. of x88o, the exposition is changed;  Ufi the letter to the Rev. sci of April 6, x875; printed in Delb,uf's llments, x3o f. zklso P.S., i., (88) 883, 5 if', 8 f. ----------------------------------------------------------- lvi Introductiot we hear no more of S-magnitudes. We are told "dass das Webersche Gesetz auf etwas anderes als auf unsere Schatzung der Empfindungen, d. h. eben auf die Bestimmung des Grades der Merklichkeit derselben, sich unm6glich beziehen kann, well wit darfiber, wie sich die Empfindungen unabhiingig yon unserer Apperception [yon den bei ihrer Schiitzung betheiligten Vorgiing- en der Auffassung und Vergleichung x] verhalten, tiberhaupt nichts auszusagen vermogen." Is summation still possible? Ap- parently,--only that the units of summation are now the Merk- lichkeitsstufen: "so wird eine dem Reiz R entsprechende Emp- findung E als bestehend aus einer gewissen Anzahl n solchef Merklichkeitsgrade yon der Gr6sse k : ff betrachtet werden n k6nnen." The dS of the fundamental formula are "unendlich kleine Merklichkeitsgrade der Empfindung," instead of 'unend- lich kleine Theile' or 'Zuwfichse' of S. 2 Doubt is, however, cast upon this interpretation by remarks in the essay Ueber das Webersche Gesetz, 8857 "Wet einwenden wollte, dass gat nicht die Empfindungen selbst, sondern nut ihre Merklichkeitsgrade gemessen wetden, dem wfirde einfach zu erwidern sein, dass eben die letzteren diejenigen psychischen Elemente sind, die in diesera Falle/berhaupt allein messbar sind" (9). The unit of measurement may be any ' bestimmter Merk~ lichkeitsgrad '; its choice is a matter of convenience (9 f-, 2 f.).  i., 322. Cf. Log/k, ii., x883, 486.  i., 332, 352 f., 356, 358, 360. Ebbinghaus thought at first that the change of view was referable to the Tannery controversy of 875 (misprinted x878: Z., i., 464, note), but afterwards wthdrew this opinion (zbzd., ii., 89, 335 f-). If the change is to come from the outside, why should it not come from G. E. Muller (G., I ff, 226, 4 I2)  But the author would ascribe it rather to the intrinsxc develop- ment of Wundt's doctrine of apperception. This doctrine is itself, in all its far- reaching applications, the psychological successor of Wundt's early doctrine of judgment, which plays so large a part in the Vn. of 863: see, e.g., i., 57, 303 ß We return to the point later: p. lxxL, n. Wundt is criticised by Stumpf (Tps., i, 5 t f.) on the ground that the mm of in- estigation is knowledge, not of Unterscheidungsfahigkeit, but of Unterschmds- empfindlichkeit; and by Grotenfelt on the ground that he offers no proof of the measurabihty of the Merklichkeitsgrade (Das Webersche Gesetz, 47, 64). We shall return to these objections later. Cf. Fechner, R., 268; Meinong, Z., xi., x896 , 124 fl., 256, 263; F. Boas, Pfluger's Arch., xxviii., 882, 574 f.; Hofler, Z., viii. 895, 97 f-; Jodl, Psych., 229, 233 if. a p.S., ii.,  if. õ 4. Criticism lvii So far, there is nothing against summation. "Ein Haupteinwand gegen derartige Feststellungen besteht nun aber darin, dass sich die so gewonnenen Einheiten nicht beliebig addiren lassen wie die Theile eines Massstabes, und dass daher vorerst und vielleicht fur immer die Ausmessung einer beliebigen concreten Empfind- ung mittelst der gewghlten Einheit ein aussichtloses Problem zu sein scheint. Ist auch dieser Einwand zunichst gegen das Fech- nersche Massprincip [of direct S-measurement: 6, 23 if., 3 ] erhoben worden, so kann doch nicht geleugnet werden, dass er die Messung der Merklichkeitsstufen ebenfalls trifft... Dem Einwand . . . kann man ruhig mir der Antwort begegnen, dass. so viel bis jetzt sehen lisst, eine solche Messung nicht einmal yon besonderem Interesse ware" (20 f.). Does Wundt admit the principle of the objection, and make a virtue of necessity? Or does he merely postpone the question until the time shall be ripe for its discussion? "Hier soll nun dem Einwand," he says, "keineswegs, was sehr wohl geschehen konnte, mir dem Hinweis auf die geringe Ausbildung des ganzen Untersuchungsgebietes begegnet werden "; such a mode of rea- soning would be in place only if there were some prospect of our ever wanting to sum the Merklichkeitsgrade. "Jedes Unter- suchungsgebiet bringt wieder seine eigenen Probleme reit sich. Mir der Behauptung, dass die sonst im Vordergrund stehenden Aufgaben in einem neuen Fall gegenstandslos sein wrden. ist darum hier gar nichts getham" This looks like admission: c[. 2 f. In I886, however, appeared a paper by A K6hler--written under Wundt's direction and published in the P.S.  with the title Ueber die hauptsachlichsten Versuche einer mathematischen Formulirung des psychophysischen Gesetzes yon Weber--which takes us back to Wundt's standpoint of 88o. "Auf der Emp- findungsscala geht man immer um einen eben merklichen Emp- findungsunterschied, also die zu Grunde gelegte Masseinheit welter, und markirt auf der Reizscala den zugeh6rigen Reiz- werth. Ist man also auf der Empfindungsscala 6mal einen eben merklichen Empfindungsunterschied fortgeschritten, so hat man eben die Empfindung um 6 Einheiten vergr6ssert" (577): this  iii., 572 if. ----------------------------------------------------------- lviii Z/roaSctœon is Kohler's viexv. "Wundt denkt sich die Empfindung, oder bes- ser den Merklicheitsgrad einer Empfindung s aus einer Reihe yon Merklichkeitszuwfichsen zxa bestehend, und setzt dem ent- sprechend die Beziehung x.  an, wo xx den gleich merkli- chen Empfindungsunterschied und u die Anzahl derselben bedeu- tet, welche man successive an einander zu reihen hiitte, damit die Empfindung von der Merklicheit s entstehe" (595 f.). "Es wird ausdrticklich die Empfindung s aus n gleichen Merklich- keitsstufen As zusammengesetzt gedacht, so dass also ds die Einheit ist, in welcher die Empfindung  gemessen wird" (597). "Man weiss und kann sich eine klare Vorstellung dayon machen, wieviel gleichmerkliche Empfindungszuwhchse ds man aneinan- der zu reihen hat, um den Merklichkeitsgrad der Empfindung zu bekommen, welcher durch k dargestellt wird" (598). Yet Kohler had read Wundt's essay (594, note); and Wundt had read KOhler ! Now Wundt defines the Merklichkeitsgrad of S, in the P. 1TM. of x88o. as "die Entfernung der Empfindung yon jener der Reiz- schwelle entsprechenden Grenze," whether above (degree of Uebermerklichkeit) or below (degree of Untermerklichkeit: i., 356, 358, $6x). If this definition is strictly adhered to, the Merk- lichkeitsgrade can be summed; one can add distances. 1 If, on the other hand, the Merklichkeitsgrade are the imaginary unit- magnitudes out of which a single apperceived S is built, then the objection holds against them that holds against Fechner's sum- mation of Empfindungszuwuchse. \Ve can reconcile the P. P. of x88o with the essay of x885 if we suppose that \Vundt kept, in the former, to the implications of his definition, xvhile he was think- ing, in the latter, of a summation in Fechner's sense. -ø K6hler's exposition (such, at least, is the author's impression) is couched  For a dscussion of ths point, see õ 6, below lXZote that the definltmn meets Grotenfelt's objection, p lvi. above. 2 The suppos:hon s borne out by the fact that Wundt's essay is throughout concerned wth Fechner (3 fl.), and is m some sort a reply to Fechner's cntcmm in the Revision (33 if-), as well as by the somewhat unusual phrase ' concrete Emp- findung ' (zo). It s worth nohng that P. Tannery, who read Wundt's essay with the letter of 875 in mind, whle he finds "de graves concessions aux adversares de la nouvelle science," i e, of Fechner, stfil thinks that "sans doute ces conces- mons ne sont nullement dcsives" (Rev. phil, xvi, 884, t6, 35). õ 4. Criticisdn lix in terms rather of Zuwiichse than of Enfernungen;  but Wundt may very well have put hs own interpretation upon it. This reading of the issue would account, further, for the fact that the P. P. of x887 shows practically no change from the edi- tion of x88o. -ø In the Vorlesungen of 892, on the other hand, we have, without any doubt, a confusion of the two standpoints, of Zuwiichse and Entfernungen. "Suppose that we take an S which has increased bv a j. n. magnitude, and that we allow this second S to increase again by a j. n. d.; the difference between the first and third will be clearer than that between the first and second. And if we proceed in this way, always increasing by a j. n. increment, we shall finalix- arrive at an S-intensity which is very much greater indeed than that of the S from which we set out... If ve wish to learn how much more intensive a second S is than a first, our best method xvill be to analyse the S into those elements xvhic.h are the equivalents of j. n. d." a These intro- ductory words might be explained in terms of either hypothesis. "One S is twice, three times. or four times as intensive as an- other. when it is made up of twice, three times or four times as great a number of equal S-increments. This system of measure- ment presupposes that we follow up S in its gradual increase."  Here we have a return to the position of x863. "To answer all the questions that come up in any sense-department, then, two measurements are in general sufficient; first, the measurement of the constant relation in which S-intensity varies with variations in the intensity of the R;,and secondly. the measurement of the j. n. S. The first measurement enables us to divide up the S-scale; by calling in the aid of R we can mark it off into equal 1 6'f. esp. the critique of Delbeeuf, 6 3 if.  Cf. , 340, 349, 378 f., 382, 383, 386 f wth the passages cited p lv above. There is, t s true, a minor comphcaton. Wundt ratses the question, in 885, how far we may go with Fechner beyond Weber, z e, how far we may argue from ' gletch merkhch ' to ' glech.' He finds the argument vahd wthin certain hmts (P.S., i., 29). He accordingly writes n P. P., ., 887, 34o, that "nur die Bezmhung zwschen dem R und der Empfindungsschatzung bm jetzt unserer Messung zuganglich st," the words ' bs jetzt ' being an addition: c.f i., 88o, 322. He also omxts a sentence m x887 (386) which had in x88o (36o) emphasised the same point. The words ' Ns jetzt ' disappear in 893 (i., 333); the mssing sentence is not re- stored,--probably because the author was correcting the edtmn of 887. a Lectures, 894 or x896, 33 f- 4 Jbta', 34 f. ----------------------------------------------------------- lx Introduction parts. The second measurement gives us its o-point, and thus renders the scale ready for practical use... Suppose that we wish to know the intensity of an S excited by the pressure of  gr. W'e take our scale, and begin with the o-point... We proceed . . until xve come to a pressure of  gr., and then count up how many units of our S-scale have been employed up to that point."  This is the position of the P. P. The same position is taken, per- haps somewhat more definitely, in the P. P. of x893 .-ø It is reas- suring to find that the Vorlesungen of x897 omits the passage objected to above, while the remainder of the exposition remains practically unchanged) According to the Loglk of I895 (n., 2, I78 if.), all ', psychische Erfahr- ungsinhalte" are either intensive or extensive magnitudes. Intensive magnitudes are degree of intensity and grade of quality; extensive are temporal and spatial extents. Every process ewnces, further, a certain degree of clearness and, as dlscriminabte from other processes, a certain degree of dlstlnctuess. Clearness is thus the intensive, and distinctness the extensive aspect of the'Auffassungswerth' of processes, of their relative value in consciousness, or of their ability to get themselves noticed. It might be thought, then, that the Klarheitsgrade or perhaps rather the Deuttichkeitsgrade are the Merklichkeitsgrade of S taken accotint of in x, Veber's Law. This is, apparently, not the case. All six magni- tudes ,,bilden jedes ein fur sich bestehendes Object psychmcher Mes- sung." So far, however, -- Wundt says, -- intensity and quality of sensation have received most attention: feelings, degrees of clearness, etc., have been "noch so gut wie gar nicht behandelt ;" tme and space have been treated "in engem Anschluss an die fur die Intensltitsmes- sungen aufgefundenen Pnncipien" 080). Hence his present exposition will be concerned with the measurement of S-intensity, as a typical case of mental measurement at large. Nevertheless, when we reach the statement of Weber's Law, we fiud that ,, der Thatbestand der Empfind-  2rbd, 38 f.; of. the rest of Lect. fii.  Cf i, 333, 395, 397 f, 4 oo, 4 o2, 4o4 f., 4o6 f. with the passages cited pp. lvi., lix., above. Wundt's acceptance of the quotient hypothesis does not invahdate thin statement: see p. Ixxx. below. a See p. 4 o. The discovery was especmlly reassuring to the author, rance he had written the criticism of the second edition before seeing the third.--Cf. Outlines, 0896 ) 897, 252 (where the translator has misleadingly rendered Grossg by ' quan- tity' m place of ' magnitude '). õ 4. Crzttcism lxi ungsmessungkannuherhaupt mcht als eme Bezlehungzwlschen Emp- finclung uud Relz, sondern er muss als elne solche ZWlSchen den Emp- findungen und der psychologmchen Function der Verglelchung betrachtet xverden" (x93); and the whole treatment (x92 if.) squares with the treat- ment oltheP. P. This is in itself natural. But what becomes of the measurement of S-intensities? And what is the relation of Klarheit to Merkhchkeit ? According to the P. P. (ii., 893, 27I), the Ktarheit of a process depends partly upon its intensity, partly upon a"moglmhst vollstanchg Anpassungder Aufmerksamkeit"(cf. i, 9o2. $52; and this adaptation is in turn very largely dependent upon the adjustment of the sense organ. Deuthchket presupposes acertalndegreeofKlarhmt, and also "andere Bedingungen welche die Unterschedung der emzelnen Vorstellungen beeinflusseu." These other influences are associative: Unterscheldung is a special case of associative asslmlation (n., 442 if.)- Vergleichung, on the other hand, is a matter of appercepttve connectran or dsjunction (476 if-). It would seem, then, that both clearness and distinctness are prelim- maries to comparison, that both alike are necessary to the determination of Merktichkeitsgrade. The Sol the S-centre has merely intensity (see note, p. lxxxfi., below) Passing the hmen of attention, and thus involving the apperceptlon centre, it acqmres clearness and distinctness, and in doing this undergoes a working-over at the hands of association. It it is to be compared with other S, It enters nto the specific process of com- parative judgment; its functloual substrate s a specific distribution of inhibitions within the apperceptive centre. It is, then, only the compara- tively judged X that has Merkhchkeit; the attribute implies that a con- tent of a certain intensity, clearness and distinctness has played its part as one of the terms of comparison in a comparative judgment. How, now, are intensities and clearnesses to be measured for their own sakes? If the only' intensity'that we can measure is a judged- clear-distinct intensity (an intensity of a certain Merkhchkmt), how can the part-measurements ever become real problems? Two answers ap- pear possible. 0) The measurements may present insuperable dffi- culties in practice, and yet be theoretically dtstnguishable; and the distinction may have great methodologmal, if not practical psychological importance. It is m the Logik, we must remember, that thedlfferentla- tlon is made. (2) As in the essay ot 885 Wundt argued back from Merklichkeit to Intensitat, so he may be thtnklng here of a smilar deduc- tive procedure for clearness and dstmctness Wlch of these two answers is correct, the author cannot attempt to decide. Perhaps both ideas were in Wundt's mind when the paragraph of the Loglk was writ- ----------------------------------------------------------- lxii Introduction ten.--For the process of comparison, in logical regard, see Logik, i., t893, 36t if. In the P. P., 1., 19o2 , 553, occurs the following sentence. "Der Zuwachs der Aufmerksamkeit, der erfordert wrd, damit eine gegebene centrale Sinneserregung um den glemhen Klarhetsgrad (z. B. um eln eben Merkhches) zunehme, ist dem Quotienten aus der Erregungs- zunahme m die Grosse der Erregung proportional." That is to say, Ebenmerkhchkelt is brought, as a special case, under the general head- ingofgleicher Klarhetsgrad. Does not thin mean that our question is answered: that ve mayidentfy, outright, Klarheit and Merkhchkelt? In the author's opxmon, the passage is not to be pressed. Merkhchkeit presupposes Klarhelt; and, as we now learn, equal Merklichkelt presupposes equal degree of Klarhelt. Moreover, f we take up a Merkhchkeltsgrad (so to speak) and look at it out of connection, we shall see simply a clear S. It is only functionally, as a term in a judgment of comparison, that the S attmns Merkhchkelt. But ,Vundt s probably more concerned to indicate by the parenthetical instance that he takes , eben merklich ' to mean ,gleich klar'or , gleich merklich ' than he is to explain in terms of his general system what precisely Merk- hchkeit may be.  In the P. P. of 19o2 Wundt is primarily concerned with "die Darstellung eigener Erfahrungen und Ueberzeugungen" (i., ix.), not with compilation. It is, therefore, natural that the question which we are here discussing should have dropped somevhat out of sight. Wundt speaks always and emphatically of Merklich- keitsgrade, -ø and retains the characteristic phrase "Enternung yon der Reizschwelle" as the equivalent of Merklichkeitsgrad.'*  A curious turn is given to the doctrine of Merkllchkeit by G. F. Lipps, Mass- methoden, 9o4, 33 f-; Arch. f. d. yes. Psych., hi, 85 f. The passage might be made the text of an essay. a , I9O2, 466 f., 469, 493 f., 497, 5o5, 54x if., 55x. a i., 498, 5or; of. 548. On the other hand, the term Entfernung does not appea on 497 and 5o2 (c2'. i., x893, 400, 4o6). It is possible, since the doctrine of sense distances has been steadily growing in fayour of late years, that Wundt desired to emphasise, as agmnst it, the adequacy of hs own doctnne of Merkhchket. Such an attitude would be natural, but the fact would remain that the two doc- trines are fundamentally the same --Cf. note, p. lxxxn below. The questran then arises as to which of the two formulations offers the greater advantages for systematto purposes. It would be absurd to deny that Wundt has succeeded both an working Merkhchketsgrade into hs system, and m orkmg out his system in terms of Merkhchket We must, however, remember that Merkhchket and apperceptmn, m Wundt's own development, hae tl.exr roots n õ 4. Crttczsm lxiti We may suppose, then, in spite of the omission of certain relevant passages, that his view has remained unchanged since I893. Two points remain to be noticed. (a) Granted that Fechner's view is wrong, we are still called upon to show how it arose, and whence it derives its seeming naturalness. And again, (b) granted that Fechner's view is wrong, we are called upon to meet the constantly recurring argument that S must be measur- able because it is a magnitude, because we can speak, intelligently and intelligibly, of 'more' and 'less' of it. (a) Fechner's principal error lay in that confusion of S with 2g, of in- trospective datum xwth external condition, to which attention has been called in the text2 The error is so natural that e'en psychologists who have expressly warned their readers against t may themselves fall into the snare2 ,' Eme Tauschung," says yon Kries, "wlrd hier sehr lemht dadurch hervorgebracht, dass man sich m Allgemeinen bemuht. nach der Empfindung objective (und in objectlvem Masse messbare) Wetthe zu taxlren... Wir ubertragen ohne Welteres auf die Empfindung, was zunachst Gultigkeit hat bezdghch der objectlven Verhiltmsse, welche a faulty doctrine of judgment (see n., p. lvi. above; Stumpf, Tps., i., 9 ø n.). Sys- tematically considered, Fechner's sharp severance of ' sensing' from ' &scnm- inating sensations  (El., ii., 85 f.) would seem to promise a better psychology than Wundt's siugle set of Merklichketsgrade: el.. Jodl, Psych, 78 if, 34. We must remember, also, that Wundt's treatment of apperception has unquestmnably been a stumbling-block to very many who have tried to understand his system. It may be retorted that Wundt himself draws the distinction which is here attributed to Fechner: "de Begrifle' Empfindungen haben ' und ' Empfindungen vergleichen,'" he says, cannot possibly "ens und dasselbe bedeuten" (P. P., i., io9 , 542, t.). Granted I But of what avail is t to ,ave sensaUons xf, n compar- xng them, we are brought up short against their Merklichket ? And agmn: t may be retorted that Fechner is unclear, seeing that he makes our apprehensmn of an S-difference an Unterschiedsempfindung, rather than an Unterschedsurtheil or Unterschiedsschatzung {of Wahle, Das Ganze d. Philos., 98). Again granted! But we spoke of the promise of a psychology, not of ts performance. Fechner, as we have seen (p. xxfi., above), was not a systematic psychologist. Cf. Lehmann's critique of Wundt: Die korperl. Aeusserungen psych. Zustande, ii., I9o2 , 17 f.  See Pt. i., xxvi. In the abstract, Fechner was well avare of the danger of confusion; and, indeed, one could hardly set out to write a psychophysics without being aware of it. See, eœ, R., 5.  Cf. Wundt's rejection of Hering's law, P.S., ii., 8, with the P. P, i., 887, 356 or i., x893, 359' Ct.i., x9o, 493 f-, 54 f. ----------------------------------------------------------- lxiv Introduction wir nach den Empfindungen taxiten " The same confusion has been emphasised by many other writers. See, e.ff., Brentano, Psych, .,91 f.; Boas, Pfiuger's Arch., xxvfi., 568; F. A. Muller, Axiom, v. f., 46 if.; J. Tannery, in Delboeu['s ]lments, I38; Ebbing.haus, Z., i., 323 f.; Psych., i., 506 f.; Ward, Mind, O. S., 1., 1876, 460; Mfinsterberg, Neue Grundle- gung, 189o , $, 1I, I16 f.; :Exner, Hermann's Hdbch., ii.,2, I879, 24'-; J. L. A. Koch, Z. f. Phil. u. phil. Kritik, N. F., Ixxx., I882, 174; A. Meinong, Z., xl., 896 , 97, 372 f.; Jodl, Psych., 202; Kulpe, P.S., xx., I9O2, 549 f.; and of. G. E. Muller, Z., x., 4 -; R. Wahle, Das Ganze d. Phfios. u. hr Ende, I894 , 65 f., 76 f., 2o8; Wundt, V61kerpsych., i., 2, 9oo, 52 if. This is the error, and there can be no doubt oftsnaturalness. Every teacher of experimental psychology knovs how difficult it is to dmsocmte sensatmn from meaning (œ e., [rom stimulus) in the beginner's mind.  On the other hand, the ' quantity objection ' is also, as we have said, a natural, even an obvious crticism of Fechner's construction. It is in- teresting to note that thin objectran had been urged against a mathema- tical psycholog.y at large long before Fechner's day. Various passages containing it have been collected by G. Itelson, Arch. f. Gesch. d. Phil., ill , 89o , 282 if. (I) N. Malebranche wrote in 674: "on ne peut deter- mner exactment le rapport qui est entre le vert et le rouge, Ie jaune et le violet, ni meme entre le wolet et le violet. L'on sent bien que l'un est plus couvert ou plus (clatant que l'autre. Mais on ne salt pmnt avec vldence, ni de comben, mce que c'est qu'dtre plus couvert ou plus dclatant . . Sje saisque I'octave est double, . . c'est que je sas que le nombredeswbrations est double en tempsg.al ouquelque chose de semblable; . . . on ne peut cornpater les sons en eux-mmes, ouentant que qualitds sensibles et modifications de l'me." (2) G. Ploucquet, m 765, lsstillclearer: "sit graduslums datus, qui ponatur vei crescere vel decrescere. Quentur, num mcrementaluciset ejusdem decrementa exprimi possmt quanttatibus anthmeticis vel geometncis ? Respondeo negando. Nam lux obscurior addta obscurior mse non facit cla- norera... Id quod percipitur in ipsa vlsione lucis fortioris non est per- ceptio lucis debfiioris et debilioris. Itaque lucis mtensm qua imago non metienda est ex additione minoris et mmoris, sed ex intensione umus ejusdemque imag.inis." (3) So P. Galluppi, in 8i 9: if we say that the light of two candles is twice that of one, t is clear that ,, in questo caso non misuriamo le sensazioni, male cause d esse." "La quantitt ap- pattierie sempre all'oggette della sensazione, e non mai alla sensazione." Cf. F. A. Muller v. Fechner: ,,Grosse ist nicht der F-mpfindung. und 1 Via., vi, 892 , 275 , 286. C.f. the whole discussion, 286 if., 29 if. Cf.i,I.M,4. õ 4. Crztcism lxv hrem Object, dem Reiz, beizulegen, sondern nur dem Reiz. Nur der Rez kann dutch eme Zahl dargestellt werden" (Axiom d. Ps. ph., 1882, 55); and Lotze (speaking of Vorstellungen, not of Empfindungen !) rs. Herbart: "Nun k6nnen wit gewiss Das, was wit erlnnern, m alien Gradabstufungen vorstellen, deren scut Inhalt fahig ist, abet es 1st mcht eben so klar, dass de auf thesen Inhalt gerlchtete Vorstellungsthatigkmt dieselben Grossenveranderungen erfahren k6nnte" (Metaph , 884, 520). (4) Finally, J. A. Eberhard, in 776, raises the 'quantity' objection (though somewhat obscurely) in a form that reminds us of Zeller's later arguments. Eberhard speaks of the possibility of a "Verbindung einer gewissen Menge yon kleinen Vorstellungen zu ener grossern Hauptper- cepUon," and of the "Erhohung Emer emzelnen Perception zu einem gewlssen Grade yon Klarhmt und Deuttichkem" He then continues: ,, de Vergleichung der Grosse dieser Vorstellungen untereinander, nach [dem I Grundstoffe derselben, wurde uns zur Mathelnatk der Seele fuhren .... In der Vergleichung der S unteremander, wtirde [aber] die messende Einheit tone unbemerkbare Vorstellung sein mussen, de eben dadurch zu diesera Gebrauche unttiehtig stun ird, well sic unbe- merkbar ist; und in der Vergleichung der S mir den Gedanken haben wit ganz ungleichartige Gr6ssen, die gat nicht mir einander commen- surabel slnd."--Cf. M. Dessoir, Gesch. d. neueren deutschen Psych., i., I9O2, 365 fl. (b) "Von vorn herein und im Allgemeinen," says Fechner, "kann nicht bestritten werden, dass das Gemtige uberhaupt quanutativen Ver- hdtmssen unterhegt. Denn nicht nur D. sst sich von tuner gr6sseren und geringeren Starke yon Trieben, es giebt gr6ssere und geringere Grade der Aufmerksamkelt, der Lebhafugket yon Ennnerungs- und Phanta- siebfidern, der Helhgkeit des Bewusstseins im Ganzen, wie der Intensitat einzelner Gedanken": El., i., 55; cf. I. S., ; R., 325; W. Preyer, Wiss. Bnefe, 189o, 213. The same idea recurs, e.g'., in 5Vundt, Essays, I885, 155; Lectures, 17; letter m Delbceuf's llCments, 3o; P. P, ., 893, 332 (see also 282, 286); i., 19o2, 466; Loglk, n., 2, I895, 178; K. Vmrordt, Physiot. d. Menschen, I877, 3 I; Grotenfelt, Das X, Vebersche Gesetz, 25 f.,34 f., 54 f.; J. Tannery, in Detbmuf's ]lments, 11, 135; Delbeeuf, ibid., 3 f., I23; L Daurmc, Critique philos., x., I, I882, 324; G. Tarde, Rev. phil., x., 88o, 15o; James, Psych., i., 489 L; A. Elsas, Psychophysik, 59; A. Meinong, Z., 11., 1896, 87, 95, 97, 11o; F. H. Bradley, Mind, N. S., iv., I895,  if.; N. von Grot, Arch. fi syst. Phil., iv., I898, 302 if. How are we to meet it ? So tar as the intensity of sensatmn is concerned, i.e., xvithin the strict limits of Fechnenan psychophyscs, there is really no difficulty. Allthat we have to do is to define, intensity ' from the standpoint of our theory of ----------------------------------------------------------- lxvi Introduction mental measurement. From this point of view, the intensity of $ is an attribute which varies continuously from o in a constant direction. It is, therefore, possible for us, after experience of intensities lying at different points upon the intensive scale, to say--whether from memory or in actual perception--that one pressure IS stronger, one pain more severe than another, or absolutely that a pressure is unusually strong, a pain ex- tremely severe. We mean, tn the first case, that the one pressure or pain lies farther from the o-point of pressure or pain intensity than the other ß 1 in the second, that the pressure or pain lies relatively high up n the scale of intensities that we have experienced. And we imply nothing more than that the dinlances from theo-pmnt are in some way, directly or indirectly, measurable? In reality, the o-point need not correspond with the total d,sappearance of S-intensity. It may be an arbitrary point, set by habit or by the mean capacity of the sense organ. "Outre le jugement relatif que nons potions sur le rapport d'intensit de deux causes ext4rieures agissant sur notre sensibilit4," says Delboeuf, ,, nons potions aussi sur elles un jugement qui a quelque chose d'absolu, en ce' que l'umt4de comparaison est prosee dans la nature mme de notre sen- sbilite;" and this is true ,, abstraction faire de tout terme de compa- raison extrieure." a We have, then, an adequate psychological explanation of the compar- ative judgments and of the absolute statements of intensity that occur in dafiy life. "The light to-night is poorer than it was last night": "What a heavy child !"*--the mental attitude involved in such expres- sions is entirely intelligible. The sensations, points upon the intensive scale, come to us under such circumstances with a rough scale-mark upon them. Otherwise we mght, as certain vrlters do, get over the difficulty by raising the previous question, by challenging the alleged  C/5. A. Lehmann, De korperl. Aeusserungen psych. Zusmnde, n., 9ot, o: "unter der gegebenen Starke E emer Empfindung lasst sich uberhaupt ntchts anderes verstehen, als dm Anzahl ebenmerkhch verschmdener Empfindungen, dm tach zwischen den Grenzen o und E unterscheden inssen." -* Seepp. cxxx if.below.yon I(nes, Vl,278, G.E. Muller. Z,x, I896 ,2, 25; Lpps, Logk, i893 , 22, ct Memorig, Z., x, i$96 ' 357 a ]ldments, 28 f.; cf G E. Muller, G., 394. On the comparison of quahtatve differences, see yon Knes, Vjs, 285 f., G. E. Muller, Z, x., 35. On comparison in terms of ' psychological effect,' see Vjs, 29 ff , Wundt, Logk, ii., 2, 885, 83; Lpps, Stzungsber. d. phllos.-philoI. und d. hmtor. CI. d. kgl. bayer. Akad. d. Wiss, t899 , 384 ff  Judgments of this sort, judgments by 'absolute impression,' play an important part n psychophyscal investigations, where they must be analysed m ddtail. We are here concerned smply vnth their justification and explanation from the stand. point of a gven theory of mental measurement. õ 4. Criticism txvii facts. Mental processes differ, we might say, but do not differ in degree. If we put a merely quantitative interpretation upon their differences, we are failing into the error signahsed above, and confusing S with R. We may know that two Sate setup byRofthesamekind (eg., bywelghts), and may, in thehghtofthsknøwledge, seek to compare them; but we are then really trying to compare incommensurables, as ifwe should assert "die GieichheIt emer Schall- und emer Lmhtbewegung "or estimate ,, die Langengrosse emer Secunde" (yon Krms, Vjs., 274). The position finds support in the very mstances brought against it; for these instances are invariably forinulated in terms of R.  As against Fechnerian measurement, this argument is vahd; as against mental measurement in general, it is too radical. Pushed to its logical extreme, it makes a psychophysics impossible2 Moreover, as we have just seen, a correct definition of ' intensity of sensation ' removes all difficulty. On the wider issue, the author has always beheved that the experi- mental method, qualitative and quantitative, is adequate to the whole structure of mind: this belief' is ntlmated in the text. * It s, of course, by no means universally--perhaps not even generally--held. There are psychologists who maintain that all mental processes are in some sort magnitudes, and that all magnitndes are in some way measur- able. ,, Jeder psychische Thatbestand," writes Wundt, "kann princlpell als Gr6sse betrachtet werden... Intensltat, Qualitat, Klarheitsgrad, raumliche und zeithche Ausdehnung u.s. w. bfiden jedes ein ftir stch bestehendes Object psychischer Messung." * Bradley, too, says that "all psychical phenomena ß ß can, in principle, be measured." s On the other hand, there are psychologists who assert, quite as definitely, that not all mental processes are magnitudes.  Moreover, Wundt after all actually measures only one aspect of one simple process--the intensity of sensa- tion ; and to say that this particular measurement has been carried out because it is the ' typical ' or the ' snnplest ' form of mental measurement at large, so that all the other measurements not yet made must conform to its pattern, is not au argument that will convince the sceptics. Brad- ' See p- xlviii., above Cf.. Wahle, Das Ganze der Phfios, I9-% =o8; Elsas, Philos. Monatshefte, xxv., i888, 38--F. Ptllon regards all our deas of mental magnitude as simply metaphorreal ancient physics was dominated by psycholo- gmal metaphor, modern psychology s m danger of domination by physmal. Crmque phfio, x, t, 882, 389 if. 2 C- G. E. uller's axioms Z, x., I896, I fl. a See Pt. i., p. xxxvm  Logik, Inc. cl, I78 if. See the discussion, pp Ix. if. above.  5Ired, toc  œ g., Brentano, III. internat Congress f. Psych, i22 -. , G. Tarde, Rev. phd., x., i88o, 6. 7 Logik, i8o. ----------------------------------------------------------- lxviii ] tr od tt cl i o n ley, again. declares that his doctrine of the measurableness ot , psychical states ' by ' psychmal units ' has, so far as he is axe are, no practical bear- ing tYr the psychologist And lastly. there s, as we have seen, a great difference between, magnitude ' and measurable magnitude or, quantity.' All mental processes might be magmtudes, and yet no single process might be properly measurable. In fine, the general question is not ripe for profitable dscusson. Oplmons upon t are opinions only. In wew, however, of the steady ad- vance of the experimental method, and of the steady extension of quanti- tative treatment to states and processes but lately beheved to be beyond the reach of measurement, the author has felt .justified in taking the position adopted in the text. () Fechner assumes that all j. n. d. of S are equal, from what- ever part of the inte;sive scale they may be taken. To this it is objected, in principle, (a) that 'just noticeable' does not neces- sarily mean ' equally noticeable,' and (b) that ' equally noticeable' does not necessarily mean 'equal.' The objection, especially in the form (b), is far-reaching, and finds many different ex- pressions. Let us be clear, in the first place, that Fechner does not identify the S-unit outright with the j. n. d. He maintains, on the contrary, that there is room in his measurement system for any sort of S-unit that the investigator chooses to employ. The j. n. d. is taken as unit simply be- cause t reveals itself introspeetively as a constant magnitude in work done by the inethod ofj. n. differences. In this method ,, fasst man den eben merkllchen Unterschied drect als emen fur die Empfindung gleich- en unmttelbar auf... [Es] steht [der Methodel entgegen, class der Grad des Ebenmerklichsems dem subjektiven Erinessen mehr Spielraum lasst, als bei den anderen Methoden stattfindet... Indess lehrt die Erfahrung, dass man sich so zu sagen mt sch selbst uber alas Gefiihl emes klexnen, doch noch sicher genug empfundenen, Unterschiedes verstandlgen, deses, wenn mcht absolut, doch nahe genau, bm verschied- enen Versuchen reproduclren und dutch Vervielfaltgung der Versuche ein gutes Resultat erhalten kann" (El., i., 75; see also R., 2o, I22, 303, 318, 323). x As for the chmce of umt: ,, nach den yon mir aufgestellten und eutvickelten Prmciplen," says Feehner, "kann jede beliebige x Repeated in I. S., 43. Fechner seems to have forgotten the passage in the Elemente: c.f.R., xzo, note. The competence of introspection is denied by Funke, in Hermann's Hdbch., iii., z, '88o, 35 x; c_f. W. Dittenberger, Philos. Monatshefte, N. F., ii. (Arch. f. syst. Philos., 896), 87; Stout, Manual, 3 I. It appears to be knowledged by C. Wiener, Wied. Ann., xlvii,, I89z , 665. õ 4. Critic,sm lxix psychische Gr6sse als eine immer wederzufindende Masseinheit fur psychsche Grossen derselben Art gelten, welche einem Relze angehort, der seinen Schwellenwerth in gegebenem Verhiltmsse ttbersteigt" , R., 333; of. I. S., 44 f,; the course of the argument in P.S., iv., 79 if-, esp. I84 fi; and Wundt, in P.S., i., 19 f. So much in fairness to Fechner. We raise, now, our second question,  and ask: are the j. n. d. equal ? The answer need not necessarily be in the affirmative: we may, e.g'., admit the validity of Weber's Law, and yet maintain that thej. n. d. are relatively, not absolutely equal S-dif- ferences. This belief is, indeed, implicit in a ' metric formula ' proposed, in place of Fechner's, by J. A. F. Plateau. ,, L'ide d'evaluer jusqu'a un certain point les sensatmns physiques," writes Plateau in 872, "s'tait presente  moi une ringtame d'annes auparavant [i.e., in the early fifties], et j'avms commenc sur ce sujet une srie d'expriences .... Comme la metbode que j'a sinvie s'appme sur un princlpe absolument different de celui qui sert de base  la formule de Fechner, et comme, d'ailleurs, le r6sultat qu'elle m'a donnd rdvle en nous une facult parti- culire d'estimation, je ne crois pus sans intrt de la faire connaltre" (Comptes rendus, lxxv., 872,678). Plateau worked by a crude form of the method of mean gradations, and obtained the metric formula S=c.R }, in which c and k are constants. Ths implies, not Fechner's fundamental formula, but the equation: dS .dR which makes the j. n. d. relatively equal S-magnitudes (Pogg. Ann., cl. [ccvi.], 1873, 465 f., 472; Bull. de l'Acad. royale de Belgque, xxxiii., 1872, 376 t, 384; Fechner, I. S., 2). Plateau withdrew hs formula after reading Delbmuf's tude (C. r., 680; Bull., etc., xxxiv , 1872, 261); but the position which he took has been fewred, in various forms, by the representatives of the ' quotient hypothesis ' of Weber's Law. = The critical objection, that ,equally noticeable'does not necessarily mean ' equal,' was first raised by F. Brentano, Psychologie vom em- pirischen Standpunkte, i., 874. "Richtg und a priori einleuchtend ist nut, dass alle eben merkhche Unterschede gleichmerklich, nicht abet dass sie gleich sind. Es mdsste denn jeder gleiche Zuwachs gleichmerk- hch, und darumauchjeder glechmerkhche Zuwachs glelch sero" (9); which remains to be proved Brentano's "Untersuchung tahrt zu dem Ergebnisse, dass jeder Zuwachs der Empfindung gleich merkbch ist,  This question must, for hiqtoncal reasons, be first discussed: see p lxxxh below. e See G E Muller, G,385f , Delbmuf, Examen, 9 x f., J Merkel, P S, iv., 888, 543 f.; x, 1894, 14o, Grotenfelt, Das XVebersche Gesetz, 20, 72, IO4, 49; and later references on the Verhaltmsshypothese. ----------------------------------------------------------- ixx Introduction welcher zu der Intensitat der Empfindung, zu welcher er hinzukommt, in gleichem Verhaltmss steht" (88: Plateau's position). So we arrive at the law that ,, if the intensity of the physical Z{' increases by equal aliquot parts, the intelslty of the Salso iucreases by equal aliquot parts" (89) , although these parts need not, of course, be the same (9o). Brentanois followed, in qtuck succession, by J. Tannery, Hering and Ueberhorst. Tannery remarks briefly (Rev. scl, 24 Avlt 875; Del- boeuf's ]lments, 37)' "quant it cette sensation differentmile qui vient servir d'unitd, il me semble qu'une unit doit toujours rester la mdme, et que cette unit-lit n'est point assez constanteo" Hering enters much more de.eply into the question: Sitzungsber. d. kais Akad d. Wiss. zu Wlen, lxxii., Abth. 3, I876, 3o if. (session of Decr. 9, 875). "Wenn nun eme 5o mm. lange Lmie um x mm,eine500 mm. lange Lmie abet um o mm. wtic.hse, so wiirc}en betde Lmien ½lnen ebenmerkhchen Zuwuchs erfahren, und dmsebelden Zuwuchse mussten, nach Fechner's Satze, for unsere Empfindung ganz glemhwerthig sein. Dleslst offeobar paradox, und zwar wird die Paradoxie ganz handgrelfhch, wenn man solche, den eben merktichen Unterschieden entsprechende, angeblich iraruer gleiche Empfindungszuwuchse sich summiren lxsst" (32). Let a hne of5o mm. increase byj. n. increments until it is oo ram. long; and let a line of 50 cm. increase by as many j. n. ncrements. The second llne xvill be mo cm. long; and ,, dese zugewachsenen 50 cm. nun uod jenezugewachsenen 5omm. mussten uns gleichgross erschenen, denn bmde entsprachen [nach Feehner} gtemh vielen gteich grossen Empfind- ungszuwuchsen der belden ursprunghchen Empfindungsgrossen cf. 323 if.; Funke, in Hermann's Hdbch., ill, 2, x88o, 352). C. Ueber- horst (Die Entstehung der Gesmhtswahrnehmung, 876) beheves that "glechartge Empfindungen, welche noch eben unterschedbar stud, differitch stets urn einen gleichen Bruchthefi lhrer eigenen St.rke yon emander" (20: Brentano's posmon). See also P. Langer, Die Grund- lagen der Psychophysrk: eme kritlsche Untersuchung, 876, x9ff., 59 if.; C. Sigwart, Logic, n., (878) 895, 7o f.; Lotze, Metaphystk, (879) 884, 542; J. L. A. Koch, Z. f Phil. u. phfi. Kritik, N. F., lxxx., 882, 172 ff, [76. Fechner rephesin the I. S., 4-5 if. (:.f. R, x98 if.). "Iassume . . . that the magnitude which the dfference appears to me to have in the experiment depends upon two different things: first, upon the magmtude of the actual S-difference, and, secondly, upon accompanying tarrum- stances [interval between experiments, attentmn, mode of apphcation of 27, mood, etc., etc.]. To this I add the second assumption . . . that, if the attendant circumstances are kept the same in experimentswath variable ]?-magnitudes, the constancy of the apparent S-dfference can õ 4. Criticism lxxi depend only upon a constancy of the true .-,C-difference ß ß ß But it as the aim of every good experimental series in this field to keep the secondary conditions . . ß as nearly constant as possible." In other words: since we are trying to keep all couditlons constant, save the one condition of varying R~mtenslty, it stands to reason that the ' notice- able' or ' apparent' S-differences will at least approximate to the ' real' S-differences. If we are careless, or if the regulation of certain condi- tions is out of our power, there will be errors in our results; but such errors, while they may account for deviations from an uniformity, can hardly themselves serve as the basis of au uniformity (47, 5). On Brentano's law, see 24 ft.; on Langer, 39 f.; and of. further R., 268, 327 ff. Fechner's reply is straightforward, and satisfactory--if one can accept Fechner's psychology. But it is a reply made from within the wnter's system, and as such does not touch the principle of the objection. Delboeuf, in the heat of the Tannery controversy, dinmisses the objec- tion as irrelevant (lments, 43)- ,, I1 me surfira . . . d'allonger mes phrases, et au lieu d'accrossements dgaux, de dre chaque fois des accroissements jugds dgaux par le sens intime . . . Que signifie l'expres- sxon contrasic r6el oppose it contrasic sensible ?" He confesses, later on, that he was more impressed by it than he allowed to appear at the time: Examen, 3 x, note; Rev. phil., x877, 24-2. G. E. Muller (G., 386 if.) disposes of Brentano's arguments by showing that his appeal to fact is mistaken and his syllogism faulty? In any case, the question cannot at present be decided by considerations of theory; we must await the further advance of physiology (389). Herrag is cnticised by Langer, Mtiller, Exner, Delbceuf and Wundt. Muller (G, 39 if) writes: "the metric formula simply declares that vtth equal relative j?-increments the S-increments are of equal magmtude. It does not by any means declare that the Z?-mcrements which arouse these equally large S-increments must also appear equally large. Henng's obJec- tion to the formula is, therefore, no more cogent than an attempt would be, e. if., to refute the statement that the sensation ' red' stands quahta- tvely nearer to the sensation 'violet' than to the sensatmn 'blue,' by the counter-statement that we regard the qualitative change of the external -- as more considerable in the case of transition from red to violet than in the change from red to blue. "a Moreover, on the question of fact, Hertng gnores the results of Plateau's method of supralimmal  On Hering's wexght experiments, 323 f., see at this time Fechner, I. S., 87; Muller, G., 200 fl., 39 i if., 4  if.; Gott. gel Anz., 878, 8o8 if, 8t 5 if.; I)elbceuf, Examen, 87 f-; Rev. phfi., 878, 43; and of. Grotenfelt, Das Webersche Gesetz, 57 f.  ct. Meinong, Z, x., r896, 386.  C'. Memorig, Z., m,, r896, 386 f. ----------------------------------------------------------- lxxii Introduct,o differences (394 f). The experiments "stellen ausser Zweifel, dass die Summatron glech veler eben merklicher Empfindungszuwuchse auf jeder Intensitatsstufe der Gesmhtsempfindungen etnen gleich dutlichen tibermerkhchen Empfindungszuwuchs ergebt." Cf.. Langer, Grund- lagen, 24 if.; though Langer, as we noted above, has his own objectruns (answered by Mtiller, G, 96 ff.; restated n the brochure Psychophy- sische Stretfragen, 893. ) Exner (Hermann's Hdbch., il., 2,240 fir.) urges that Hermg's equatmn of the Ji'-chfferences whmh correspond to j. n. d. of S at dfferent parts of the intensive scale wrenches these differences from their given postmn, and s therefore unjustifiable. Intensive dfferences are quahtative, not merely quantitative. They are equal, if you leave them in their place at a certain height (so to say)upon the vertical line whmh rmes from o to the terminal R; they are unequal, if you cut them out of the line and stand them upon the same axis of abscssas. "De Empfindungen emer besttmmten Gruppe .... z. B. die Empfindungen, welche en allmahlich wachsendes Gewicht hervor- ruft, sind in emer bestmmten Re,he angeordnet. Dte Empfindungs- grosse im FechnerschenGesetze gebt nun den Ortin jener Reihean, welche der durch de gegebenen Reize hervorgerufenen Empfindung zukommt" (243)2 Delboeuf, on the contrary, employs the same al'gU- ment of quahtatve change in support of Herrag. "Supposonsque sur l'une des mains 1 y at 30 d,sques et sur l'autre 3oo," and that we find the j. n. d. in the two cases. "Ces deux minima sont-ils gaux ? . . .  certans 6gards on peut repondre oul, pmsque en degh il n'y a pas de sensation; mats b. d'autres ogar(ls on peut rpondre non, parce qu'en fat la main charg6e de 30 dsques est un autre mdwdu sensible que la main chargee de 300 d,sques. Voulor comparer les sensations de ces deux mains, c'est vouloirtabhrun parallele entre la mameredesentr de deux personnes differentes; bien mieux, de deux personnes dont l'une serat doja puise et l'autre pleine de vte et de force." Fechner's law is, therefore, not m accordance with the facts. ,, mais il pourrail se faire qu'elle fat exacte d'une manire abstrate, c'est-it-dtre, en rant qu'apphque . des organes d'une 6lastreit6 parfaite et toujours apres b. r6agtr d'une fagon adequate" (Examen critique, 2 f.; Rev. phd., 877, 23 ). The objection, then, whtch once was Irrelevant, is now not only relevant, but stronger even than Hering had made it ! Delbceuf's posi- txon is akin to that of yon Kries, Vjs., 882, =74- Wundt (P.S., ii., 885, 8) shows that Hering has subst,tuted for Fechner's law, which asserts that ,' the dfference of two R must increase  C.f. Exner's later exposition: Entwurf zu einer physiologischen Erklarung der psychischen Erscheinungen, i., 894 , 74 if-; Jodl, Psych., 896 , 227; Wahle, Daz Ganze d. Philos., 206. f.; James, Psych., i., 89o, 547' õ 4. Criticism lxxiit proportionally to the R-magnitudes, if equal differences of Sate to be produced," a law to the effect that" the difference of two ) must increase proportionally to the R-magmtudes, f the R-difference is to be estimated as equally large;" and remarks that "dteses [Henngsche] Gesetz st naturhch falsch . . ß Immerhia ist es bemerkenswerth, dass selbst dieses ß . . im allgemeinen jedenfalls falsche Gesetz . . ß in gewtssen Sinnes- gebmten eine ann.hernde Gtltigkett zu bestzen schemt" and "mit dem Weberschen Gesetze zusammenfallt." But valid or not, it s not a law which Weber or Fechner had ever thought of formulating, and the objections based upon it are consequently irrelevant. t Wundt himself had at first no doubt at all but that the j. n. d. were equal S-magnitudes. ,, Die eben merklichen Empfindungsunterschiede snd. ß. ganz gleich gross, denn wgtre etwa der U'ntersched im zweiten Fall grOsser als im ersten, so ware er ja grosser als eben merklich, und das geht gegen die Voraussetzung" (Vn., i., 863, oo f.). ,' Die Grenz- wetthe der Empfindung selbst, namlich die eben rnerkhche Sund die Maximalempfindung, bleben uberall Gr6ssen yon gleichem Werthe . .. Woltte man behaupten, die e. m. S se grosset oder kleiner als eine andere, so wtirde man damit sagen, sie sei gr6sser oder kleiner als eben merklich . . . In jedem Sinnesgebiet ist diejenige S die moglichst grosse, welche das Bewusstsein mehr alsjede andere in Anspruch nimmt. Da nun das Bewusstsein fur alle Stone die namhche ist, so muss auch die Empfindungshohe uberall gletch gross sein . . . Ein . . ebenmerkhcher Intensitatsunterschied ist wieder aus demselben Grunde, wie die e. m. Empfindungsintensitat, ein psychischer Werth yon consranter Grosse. Denn ware ein e. m. Unterschted grOsser oder kleiner als ein anderer, so ware er gr6sser oder kleiner als e. m., was ein Widerspruch ist" (P. P., 874, 294 f-). Unfortunately, this argument is circularß ,, Wenn emer bezweifelt dass alle e. m. Unterschiede einander glemh seien, so gilt thm das eben-merklich-Sem mcht mehr als charaktermtische Egen- thumhchkeit eines constanten Gr6ssenmasses" (Brentano, Psych., i., 9 G. E. Mtiller, G., 389; Wundt, in Delbosuf's tldments, 3o; Funke, in Hermann's Hdbch., m., 2, 88o, 35 ; P. Tannery, Rev. phil., xwi., x884, 2 ; of. Grotenfelt, Das Webersche Gesetz, o5). In 88o we read: "je kleiner diejentge Reizgtnderung st, die errordeft wird, um eme gegebene, in den verghchenen Beobachtungen constant erhaltene Empfindungsan- derung [i.e., eine nach unserer Schlitzung constant erhaltene Empfindungs- anderung] hervorzubrtngen, um so grosset nennen wir die 1Jnterschleds- empfindhchkeit" (P. P., i., 324). ,, [Bei der Metbode der Mimmaliinder- ungen] muss man aber eine Voraussetzung machen, welche m6gl,cher-  Ut. M. Foucault, Psychophysique, I9OI, 185; A. Elsas, Philos. Monatshefte, xxiv., 888, 3  f., n. ----------------------------------------------------------- Ixxiv Introduction weise bestritten werden kann und in der That bestntten wordenist: man muss namlich annehmen, dass die Unterschledsschwelle stets den namhchen Werth habe, we verschmden auch die absolute Intensltat der Empfindungen sero mag" (33T). Since, however, we can never measure S" unabhiingig yon den Vorgangen verglemhender Schatzung," ,, bedarf der Satz, class jede e. m. Aenderung der anderen gleich ist, kemes Beweises." The objection affects the method of mean gradations as much--or as httle--as it affects the methods that measure m terms of the j. n. d. "Erst wenn es sich um die Deutung der . . Resultate handeit, wlrd die Frage untersucht werden konnen, welcher Einfluss den einzelnen bei der Vergleichung verschiedener  Empfindungen wlrk- samen Vorgangen bm den Resultaten zukommt" (332). Webefts law is to be interpreted as a law of apperception (35x); and "der Erawand trifft [dmse] psychologische Deutung gat mcht" (353). "Es kann fur uns em anderes psychsches Mass der Sals das ihrer Merklichkeitsgrade schlechterdlngs nicht geben "(360). Nevertheless, the attempt is made, in 885, to define the limits within which ,gleich merkiich' may be identified with 'gleich.' Wundt argues, precisely as Fechner might have done, ,, dass unsere Beobach- tung oderanders ausgedrtickt das Merkhchwerden tier Erschemungen die einzige Quelle unserer Kenntniss derselben ist, und dass wit daher, so lange die subjektlven Bedingungen unserer Beobachtung constant blelben, ubereinstimmenden Erscheinungen auch elne ubereinstlmmende Bedeutung bmzumessen haben"(P. S, il., =5). Now tile j. n. d. are "ohne Zxvmfel als glemh merkhche Unterschede zu statuiren;" and the 'glech merkhche Unterschlede' of mean gradations are ,selbstver_ stgmdhch' absolute magnitudes: "wlr vtirden alle Principlen der Grossenverglmchungauf den Kopf stellen"if we thought or aimed at anytiling else; hence the j. n. d. are, under constancy of subjective conditions, equal magmtudes. This constancy is attained "wenn [Constanz der Aufmerksamket vorausgesetzt] de mt emander ver- ghchenen Empfindungsunterschlede einer und derselben Refie erosinto- get, unter constanten zeithchen und riiumhchen Bedingungen stattfinden- der Veranderungen angehoren," i.e., when we are dealing with intensities of the same quality, or with continuous qualitative changes at the same intensity(29). Under these conditions we may"unsere Apperception von Empfindungsunterschteden als ein Mass der Empfindungsunterschlede selbst ansehen," for ,,die Voraussetzung emer Propoctmnahtat der l G. E Muller, in his treatment of mean gradatmns, speaks consistently of the Merklichkeit of ubermerkliche Unterschiede (G., 9 ø fid- Thts usage calls dowu Dttenberger's condemnation (Philos. Monatshefte, N Iv., il., r896 , 84}. We can defend it by reference to G, vii. õ 4. Criticism lxxv Apperceptionseffecte mir hren Ursachen . ß ß tuner jeden, auch physlkal- schen Massbestlmmung zu Grunde liegt" (3)- These quotations have been given at length, because the change of position from 88o is marked. Nay more: Wundt's concessions to Fechner seem to contradict his presen. t statements that ' Merklichkelts- grade ' of S are the only measurable psychmal elements (9), and that there can be no "thatschliche Bestatgung" of Fechner's law because we know absolutely nothing of S apart from their apperception (3). We have noted another phase ot tile mcouslstency above (p. lwn.), and have sought to explain it. Grotenfelt (Das Webersthe Gesetz, i58 if.) accounts for Wundt's change of ground in very much the same way. ,' lndem \Vundt die Unabweisbarkelt einer psychologischen Deutung aufzeigte und das Webersche Gesetz auf eln allgemelnes Gesetz der Bezlehung zuruckfuhrte, 1st er doch bestrebt gewesen, die Fechnersche Theorie so welt we moghch unangetastet belzubehalten ; er hat die mathematlschen Formeln Fechners, welche smh alle auf die Unterschieds- hypothese grunden, bmbehalten, und die Hypothese gegen alle En- wurfe zu vertheidigen versucht" (6). There is no reason to suppose that the parallelism of the two lines of thought ever wrought confusion in Wundt's own mind; but the reader must be constantly alert to the context in which a particular statement is made. TheP. P. of gg7 takes us back to the view of 88o 0',349 f, 379) .= The reader should cf. further Lectures, (x892) 894 or t896, 34, 62; A. Kohler, P.S., in., 577 f. The discussion of Wundt's present posmon must be postponed. We returu to G. E. Muller (G., 382 if.). We have seen that Muller, in replying to Hering, appeals confidently to the method of mean grada- tions as applied to brightnesses. His final judgment is less definite; but, on the whole, he inclines to accept Fechner's point of view. ,, The cor- rected metric formula  ß ß ß is, it m true, not yet proved to demon- stratton; at the same time, it is based upon the simplest and most prob- able assumption regarding the magmtude of equally notmeable S-cht- ferences. * The attempts so far made to show that this formula, anti the principle of psychophyslcal measurement which underlies it, are certainly invalid, and must be replaced by other formulas, set out from postulates all of which areunproved, and some of whmh coufilct with one another  Cf. Wundt's own statement, P. P., l, 19o2, 5 Ot. 2 Wth the modficatmus noted aboe, p hx, note. It may be remarked here that Stumpifs note in Z, i., 420 is erroneous; the 'moglicherweise bestreitbar  occurs, as we have seen, m 88o, and not for the first tme in 887. a G , 229 ß Ct. Funke, Hermann's Hdbch., ii, 2, t88o, 35t; P. Langer, Grundlagen d. Psychophysk, x876, zo f, 24, Psychophyssche Stretfragen, 893, 9 if. ----------------------------------------------------------- lxxvi Introduct/on andwthexperience" (402 f.): of. 248 ff.,256ff. , 259ff.,412. On the other hand, Muller is not convinced by Fecbner's argument in the I.S. "If we are trying to find out whether equally noticeable S-increments, added to S of different intensity, are of equal magmtude, then we must first of all raise the question whether the absolute S-intensity itself is not to be considered as an ,attendant crcumstance ' which is of essential impor- tance for the noticeablehess of an S-Increment... The point at issue is, whether we are able certainly to decide the question, in what relation the sensed difference stands to the seusatmn difference; and in particular xvhether this dependency relation is not influenced, among other things, by the absolute S-intensity (or the underlying physical intensity of the R or the E), which would thus appear as an important , attendant circum- stance'" (Gott. gel. Anz., I878,814 f.). The equalmagmtudeofequally noticeable S-dxfferences is thus "zwar mcht unwahrscheinlich, abet doch nicht slcher erwesen" (8t9). Cf. Fechner, R., t99 if. Stumpf admits the logic of the objection, but thinks that it may be dis- counted in practice: Tps., i., 5r f. ,,Wenn ein Unterschied, den wir mcht mehr bemerken, datum doch in der Empfindung vorhanclensem kann, so kann auch em ebenmerklicher Unterschied in zwei Iralien eme verschedene Grosse und zwar in der Empfindung besitzen (nicht etwa bios einer verschmdenen Reizgrosse entsprechen). . . Andererseits durfen glechmerkhcher und gleicher Empfindungsunterschmd, xxenn mcht begrifflich, doch faktlsch unter besonderen Umstanden als zusam- menfallend oder, class wit es sogleich vorsmhtger ausdrucken, als pro- pomonalangesehenwerden. Wennwir namhch m bestimmtenFallen berechtlgt sind anzunehmen, dass sich die subjektlve Zuverlassigkeit = yon einer Tonlage, uberhaupt yon einer Reizreglon zur anderen mcht oder nut in verschwxndendem Masseandert, und wit gleichwol die Unter- scheidungsfahigkeit . . . veriindert finden, so k6nnen xvlr die Ursache dieser Aenderung nur in einer nach den Reizregionen verschiedenen Empfindhchkeit suchen." P. Tannery, on the other hand, thinks that Fechner's assumption is logical, but that the appeal must lie to the facts. "[L'h poth0se] que la sensation de la plus petite dift(rence perceptible reste ldentique it tous les degrs de 16chelle . . . peut tre hSgitime it titre de driftration, s'fi est vrai que les plus petites dffdrences perceptibles sont jugdes gales et que lejugement seul prononce l'galit ou l'in6gaht de deux diff- fences de sensation. Mais on ne peut volt lit qu'une dfinmon, legltime, i, 3  if.; of. ii., 222. In Z., i., 420, Stumpf writes that "dm Frage [nach der Gleichheit der ebenmerklichen Unterschiede] ist experimentell unbeantwort- bar," owing to the impossibility of a comparison of least distances. -q i., 23, 3 . õ 4. Criticism lxxvii je le rpte, arbitraire nanmoins dans une certaine mesure" (Rev. phil., xvii., 884, o). Unfortunately, the facts appealed to against the hypo- thesis are the facts ot the tonal scale (32 f.). Is it not time, now, that the objection be put to the test of direct ex- periment ? Fechner had appealed to introspection in support of his posi- tion; and Mtiller and Wundt, Kohler and P Tannery, have pointed out the agreement m result ot the methods of mnlmal changes and of mean gradations. But uo one has so far set to work upon the two methods, dehberately and of set purpose, with the view of discovering their agree- ment or disagreement. There are, in reality, two possible ways of working. (l) We might take a series of R-values, corresponding to a series, say, of eight successive j. n. d. of S, and thereafter directly com- pare the two half-dlstances, of four j. n. d. each, and decide upon their equality or inequality. This would be a direct method of.experiment: determine the R-differences as a--b, b--c, c--d, d--e, e--f , f --ff, if--h, h_i, and then see if a--e is equal in Stoe--L Or(2) we might deter- mine a fewj. n. d. of S, at different parts of the R-scale, in order to es- tabhsh the constancy of the relative DL, and thereafter work with suprahminal d., and decide whether the same uniformity holds. This would be an indirect method: xt is the method indicated by the authors just cited. Let a--b and h--ibe R-differences corresponding to the j. b-- n. d. of S, and let there be constancy of the relative DE, i.e., let -- a --h If thej. n.d. are equal, then the point e, which lies midway for S between a and i, must be such that e--a_i--e or e=l/' :Either of these tvo methods would, presumably, take us to our goal2 Yes! but the experimental work would be exceedmgly difficult. Liminal determinations are always and intrmsically difficult; and, further, the judgments passed upon j. n. d. and upon suprahmlnal d are, even under the most tavourable conditions, the expressions of radically different mental attitudes. Nevertheless, the attempt must be marie. If the metric methods are to stand at all, they must stand in face of the present appeal. A set of separate methods, yielding incomparable re- suits, would be of small scientific value. Moreover, the attempt has been made. Let us look at the results. J. Merkel writes, in 888, that" es fehlt gegenwartig noch an einer einvurfsfreien expermentellen Prtffung des Webersthen Gesetzes bei denselben Reizst.rken unter Anwendung der Methode der ebenmerkli- x For the methods, see W. Ament, P. S.,xvi., 19oo, 36 f.; of. also the discus- sion in Stumpf, Tps., i., 60 if. ----------------------------------------------------------- lxxviii $n/roduction cheu Unterschiede und der Methode dermttleren Abstufungen" (P. S.,iv.,543). Merkel's own problem is that of the , dependency between R and S' as formulated by Fechner and Plateau. Fechner took dS, dS Plateau 7' as constant. Which of the two is right ? Are we to adopt the , difference hypothesis' of Fechner or the,quotient hypothesis' of Plateau? Does 3' increase in direct proportmn to R or as the logarithm of R ? The questran of the equality of the j. n. d. is ewdently implied in these questions; it is not expressly rained by Merkel. Merkel worked, by comparative methods, wth brightnesses, active pressures and noises. He found in general--our statement is very rough--that the S-mean between two supraliminally different R coin- cides, within the limits of constancy of the relative DL, not with the geometrical but with the arithmetical mean of the/e-values: the e whmh corresponds to the S-mean=__, notl/'.L Merkel expressesthls result 2 in terms of the quotient hypothesis. If it be reliable, it means, from our present point of view, that the j. n. d. are not equal, but increase in sze wth increasing value of '. The result is accepted by L. Lange, a though the conclusion which he draws is not that which we have just drawn. Lange takes the equality of the j.n.d. as a matter of course 032,36), He infers, therefore, that the outcome of a mental measurement depends upon the magnitude of the unit chosen for the .S-scale. If we take a small unit, thej. n. d., we may find, perhaps, that the R-differences ae, e--i are equal for S n the form a--i./7and l/'---i; whereas, ifxve take a large unit, seek to bsect the distance a--i, we may find that the equal R-differences have the form a--a+iand a+i--i. It is clear that a dependency of thls sort, 2 2 duly substantiated, would force us to revise our whole idea of mental measurement, and ultimately ', to work out a new algorithm for the. class of magnitudes of whmh it holds" 039)- Merkel's result is, however, not allowed to pass unchallenged. A. Grotenfelt, also a staunch defender of the quotient hypothesis,--though in a form somewhat different from that given it by Merkel,S--suspects that MerkeI has been judging R m place of S, and demands at least a suspension ofjudgmentuntil the work has been repeated: Das Weber- sche Gesetz und die psychische Relativitiit, 1888, x   f. On theoretical P.S., iv., 888, 54; v., I889, 245 , 499; x., 894, I4o, 203, 369, 507 . Cz' Grotenfelt, Das Webersche Gesetz, o9; Angell, P.S. vii, 421. p.S., x, 894, 25. The paper was practically completed in 886. bee p. 7 ø below. õ 4, Criticism lxxix and critical grounds, Grotenfelt is convinced that "bei steigenden Inten. staten die Grosse des ebenmerkhchen Unterschiedes steigt" 0o3)L Ex- periments upon nome intensities, by the method of mean gradations, were pubhshed in 892 by F. Angell (P.S., vii., 43 if.). They were confined within narrowerintensvellmitsthan those of Merkel; on the other hand, Angell paid more attention to subjective sources of error and to the introspection of his observers. He nowhere expressly lays it down that all j. n. d. are equal; just as Merkel nowhere expressly says that the j. n. d. increase with increasing R. The belief is, however, evident throughout his paper: he assumes that the two methods of minimal changes and of mean gradations are strictly parallel, and their resultsdrectlycomparable; he demands that the latter method, if it is to confirm \Veber's Law, gve the equation a--1/7. i:l/T--z,' he admits Grotenfelt's contention "class das Schitzen der Reizmtenstat o als Mtte zwischen dem Rmzintervalle 4 bis 6 eme grossere Anzahl yon ebenmerkhchenUnterschiedenzwischen4 und o, als zwischen o und 6 m smh schliessen wtirde. "= He finds Weber's Law confirmed by his experiments, i.e., obtains the geometr, cal mean; and declares himself an adherent of the dfference hypothesm. a In the meantime, the question had been discussed afresh by Mtinster- berg2 ,, Wit haben durchaus nicht die Berechtigung, zwei eben merk- liche Unterschiede ohne welteres als gleich zu betrachten... Die still- schwelgende Identlfizierung des gleichmerklichen Unterschiedes mir dem gleichen Unterschied ist eben der prlnzipielle Fehler der urspriinglichen Psychophysik. "s There are, in actual fact, two kinds ofj. n.d. There is, first, the "eben merkbare Verschiedenheit" of S, which does not carry with it a judgment of the drectmn of change.  This form of the YOZ "gehOrt vsllig in sensonelles Gebiet; "* it is valueless for mental measurement.  There is, secondly, the "eben merkbare Unterschmds- empfindung yon bestimmter Rchtung. " This least Unterschieds-S, hke all others of ts Idnd, "bezmht sich auf Spannungsveriinderungen, welche den Uebergang yon einer S zur anderen begleiten, "ø "stammt  Cf. esp. 4 o, 62 if., 95 fl.; also ni, 5 if-, -ø7, 56, 57 if-, 7 I, 76, 9 , o2, o 9, H 3, 79 f-; AngelI, P.S., vii., 4I 5 if.; Merkel, btd., v., 25I.  P.S., yd., 420 f, 431 if., 449 if. Ament remarks off-hand (P.S., xvi., I48) that "dese Forderung (of the geometrical mean in mean gradations) ist in der That nut dann berechtigt, wenn man dm ebenmerkhchen Unterschiede als merklich gleich aufzufassen hat" See, however, Grotenfelt, m4 if.  Op. ct., 468. t In his Neue Grundlegung der Psycb. ophysk, Beltrage, 3, 89ø- SN G,58.  ]btd., 43 f, 49 f, o6 if. * _Ibd., o 7 8 Ibrd, o8. o Ibrd, o7. o Ibld., 25. ----------------------------------------------------------- lxxx Zntroductzn aus den Muskelspannungen,"l and is accordingly measurable? The questran whether the j. n. d. are equal thus becomes a question wh,ch may be answered by experiment? The answer is affirmat,re: experiment shows "dass dieselben Verhaltnisszahlen, welche ftir dxe glelch geschtzten /ibermerkhchen Unterschiede massgebend stud, auch den eben merkhchen zukommen."* "[Wenn] unter Unterschiedsschvelle de eben merkbare Unterschledsempfindung verstanden wird, . . handelt es sich um gleiche Unterschede"a For the rest, we find in practice that the ,,blosse Konstatermg emer Verschedenhet" and the ,,Wahrnehmung ether bestmmten Unterschedsempfindung . . m allgememen sich decken ß "a so that, despite the reference of the former to the sensory anti of 'the latter to the motor apparatus, we are not far from the truth in saying, in ound terms, that all j. n d. of S are equal. We come back to XVundt, and first to the P. P. of 893. So far as Wundt adheres strictly to hs definmon of Merklichkeitsgrad, we' shall expect him to brush aside the controversy between , difference' and ' quotient ' hypothess as irrelevant. Distances are neither quotients nor differences. 8 But we have seen that Wundt, while speaking of Weber's Law as an Apperceptionsgesetz, does not cease to speak of a possible Empfindungsgesetz. His early sympathies are wth Fechner; and in the essay of 885 (P. S i,., 23 ff ) he places himself, Wlth various reser- vations, on the side of Fechner and the difference hypothesis. On the other hand, Weber's Law, as Appercepttonsgesetz, is a law of' relativity. It was therefore natural for Wundt to write in the P. P. of I88o, when he broke away from Fechner, and again in x887, that ,, die Empfindung als solche" might increase, wlthn the limits of Weber's Law, ,, nach dem- selben Gesetze annahernder Proportionalitit wle die centrale Sinneserreg- ung" (t88o, 35t; i., x887, 377, 380); and equally natural that, on the ground of hs appercepton theory. he should decline to discuss the pos- sibfilty further. Now, however, he has Merkel's results, and Grotenfelt's advocacy o the quotient hypothesis. If he seeks to penetrate behind the given Merkhchkeltsgrad to the pure sensation, shall we not expect him to reject Fechner, and (as relatwst) to accept--always under reservation-- the quotient theory ? Tiffs hne of reasoning gives us the key to Wundt's position. "Die -N'. G, o8. a For Munsterberg's theory of mental measurement by concomitant strain sen- sations, see below, pp. cxxxiv. if. a ]bd., 69  Zbd., 9 o f., 93; of. 16. Zba'., o8. The experiments are, unfortunately, so rough and unreliable that Munsterberg's conclusion can carry httle weight. 6 -[bzd IIO, 7 fbzd. IlO f. s Groenœelt, 65, ttt, Ebbmghaus, Psych., i., 3x9 f. õ 4' Crztzczsm lxxxi Einfuhrung dieses Gesichtspunktes (i e, of the doctrine of Merklichkets- grade)," he says, "betet den Vorthefi dar, dass die mathematischen Formulirungen des Weberschen Gesetzes yon dem. . . Gegensatz der Unterschieds- und der Verhaltmsshypothese mcht beruhrt wetden" (i., 404 f). After as before, the apperceived S may be conceived of as a sum of Ivlerkhchkeltsgrade, as a point lying at a certa,n measurable dis- tance from the o-point of the scale of noticeablehess  Formerly, how- ever, he had transferred the noUon of ' gleiche absolute Gr6sse ' from the dfferences of R and apperceived S to the differences of R and Sxn Fechner's sense. :Now that Merkel has brought to hght cases in which "an die Stelle des Weberschen Gesetzes ein proportionales Wachsthum der appercipirten Empfindung mir dem Reize treten kann," he prefers the quotient hypothess. It is still, remember, only by hypothesis that we can say anything at all about ]e and S; what we know are R and the S as "abhangg yon den Vorgangen vergleichen- der Bezehung" It is, however, teatidy intelhgible that a smple pro- porttonality between R and S mght appear, under the influence of these processes of comparison, m more complicated form, as the logarithmic relation of Weber's Law; whereas the latter could hardly give rise to the former (397 f)- As for the formulas, we can (as was hinted above) d]i' keep the dS----c-,  f we understand by S the apperceived S, and by R the central sensory excitement or (what is directly proportional to it) the pure S m Fechner's sense, the S before apperceptlon (4o5),  In the P P. of I902 ths poslt, on is carried to its logical conclusion. Wundt resists that the relation of R to S can never be made the object of direct observation or experiment in psychology, but can be discovered ,, hochstens auf indrecte Weise, etwa dutch de Verglelchung der auf verschledenen Wegen ausgefuhrten Versuche uber die Auffassung der Empfindungen" (1, 467). It Is, however, probable, since Weber's Law is a law of apperceptlon, i.e., of the comparison o! S and not of œ, that ,' the Empfindung selhst wachse, ebenso wle the Smneserregung, . an- nabernal proportonal der Starl, e der ausseren Relze"(54 f) Never- theless, the quotient hypothess receives hstorlcal treatment only; Wundt makes no further attempt to decide, within the sphere of Fechner's psy- chophyslcs, between the &fiefence and the quotient hypotheses (548 if,). x Logk, i, _'z, $$5, x93. "Nun 5x'ird allgemein alas ' Gleichmerkliche ' als eine œdr de Vergleichung gleich bleibende Grosse, und das' Ebenmerkliche ' als das jeder Grbssenverglechung zu Grunde zu legende Mass betrachtet wetden kon- hen"  Cf ., 188o, 355' ', 887, 38o L; i, 893, 398 œ.; i., x9oz, 549'  Cf. Vn., 897, 69 f.; Outlines, (x896) 897, 256- ----------------------------------------------------------- lxxxii 2rnt roduct ion His own exposition s couched throughout in terms of apperception and Merklichket (c.f. the formulae, 543, 547, 549). Merkel's Law of absolute S-estimation (which is m so far an ,, Ausnahmegesetz, els es an eine bestimmte Methode und an gewisse bei derselben festzuhaltenden Be- dingungen gekndpft st": 5o5 f.) is set up alongside of Webefts Law (504 if., 543 if.), and the conditmns of the two forms of sense cornpatroon are worked out m detail (545 fl.). The question of the equahty o[ least degrees o[ Merkhchkett is not dincussed, though incidentally it ts an- swered in the affirm,tuve on p. 553.--The impression left upon the reader is that Wundt has deftrarely turned his back upon the psychophysical problems of oC-intensty, as they appear in the hterature called forth by Fechner's Elemente, and that, agreeably to hs , psychological' interpre- tation of Weber's Law, lie is confining himself strictly to psychological analysis  Simultaneously with the fourth edition of the P.P. appeared Lipps' Grundzdge der Logk. Llpps here takes up a position, as regards the  If we put together the results of the foregoing dmcussions, we may distinguish three principal stages in Wundt's thought. () The Sis summed from j n. d. of .5', which are equal. (2) The appercelved .5 is summed from equal Merklichkeitsgrade. This summa- tion is not a summation of so many little apperceived .5' to make a large apper- ceived .5, but rather a summation of unit-distances from the attention hmen (L 9 o2, 498, 549) along the scale of noticeableness.--The corresponding d. of the underling ' pure ' .5 are, within certain limits, absolutely equal (Unterschiedshy- pothese). (3) The appercelved 5' is summed as before.The corresponding d. of the un- derlying 'pure ' .5 are, probably, relatively equal (Verhaltnisshypothese: 1893), though this fact is irrelevant for mental measurement (i9o2). What, now, of the .,o, bofore ' apperception ? Wundt places the sensory centres and the apperception centre in different parts of the cerebral cortex (i., 893 , 227 f., 23o if.; i., 19o2, 320 fl.). Any 17 which can et up an 7 in a sensory centre arouses S, passes the qimen of consciousness ': the . must, however, evoke the reaction of the apperception centre if it is to give rise to an apperceived .5, to pass the 'limen of attention' (i893 , 398; 19o2, 553). The .5 before apperception is, therefore, a real mental process, not an ' unconscious ' process (Grotenfelt, 59 f.); and we are justified, under certain conditions, in arguing to it from the apper- ceived .5' of our experiments. We experience it in cases of ' Perception 'as op- posed to ' Apperception' (ii., 893 , 267, 275). When, however, we set to work to estimate and compare .5', we must even estimate and compare, i.e., we must apper- eeive.--This is, in effect, Wundt's answer to Stumpf's objection, p. lye. above. The reader must, of course, decade for hxmself how far the above summary does justice to the development of Wundt's psychophysmal ideas. The questran is one of interpretation and evaluation; and the author has, for this reason, given the ummary at the end of the dscussion instead of taking it as a text to expound õ 4. Criticism lxxxiii j. n. d., which far out-Fechners Fechner. ,, Alle Ivlassbestimmungert sind relativ, wenn sic nicht schhesshch auf lrgend welche tn der unmit- telbaren Anschauung gegebene Gr6ssen sich stutzen, oder tin ietztes Element der Messung gefunden wlrd, des selbst keine weltere Messung mehr zultsst, also els absolute Masseinheit gelten kann. Ein solcbes letztes Element bldet des eben Merkliche. Dte Anzahl des eben Merk- lichen ist des absolute Mass einer Grosse . . ß Des eben Merkliche hat ftir die Wahrnehmung namhch--keine Grosse mehr." Since "des Mass de Anzahl glemher Theilgrossen tst, dutch dte eine Grosse ersetzt oder aus der sic zusammengesetzt werden kann," it s clear that the j. n. d. are equal magnitudes. But more than that: they appear to be, for Lipps, the units of all absolute measurement, whether ' physical' or ,mental.' It is not to make our measurement absolute that we have recourse to objective spatial units; it is smply to free the results of measurement from those subjective fluctuations which, ' absoluteness' notwithstanding, attach to our estimation of the just noticeable (I2O .). We pass to the elaborate study of Weber's Law publtshed in 896 by A. Meinong (Ueber dte Bedeutung des Weberschen Gesetzes: Beltrage zur Psychologie des Vergleichens und Messens, Z., xt., 8r, 23 o, 353). Meinong substitutes for the term ' Unterschted' (eben merkhcher, gleich merklicher Unterschied) the word , Verschiedenheit.' , Unterschied' means 'dtfference' in the arithmetical seuse, the amount by whtch one magnitude differs from another: ' Verschledenhett ' means ' dfferent- ness,' so to say,--dtversity, disttnction, unlt keness-2 ,, Daft man," writes Melnong, "im allgemeinen darauf rechnen, dass bet Verschiedenheit der Unterschmdsempfindlmhkeit ß ß ß eben merkliche Verschledenhetten nicht gleich sein werden, so bedcurer im Gegensatze hierzu Glemhheit der Unterschiedsempfindlichket eine wohlbegrtindete Prasumtton fur Gleich- heir der eben merklichen, man kann iabrigens ohne weirefts such sagen: x Later writers seem to have fought a little shy of this Lippsian doctrine. Cf. Meinong, Z., xi., 13o, n.  Cf. B. Russell, Mind, N. S., vi., 1897, 33 z, 334- "A change of length is itself a length, but a change of temperature or illuminatmn is not itself hot or bright. ß . . With intensive quantities, ß ß ß these differences of quantity are not them- selves quantltms. The difference between two intensive quanttles, in fact, dffers from each as much as the difference between two horses dffers from a horse." It is noteworthy that Weber, in his first general formulatxon of Weber's Law, uses the two terms dtscrimen and drentta. of. the translation, p. xvi. above. F. A. Mtiller (Axiom, 1882, 62) insists that the usage is intentrenal; that discrimen= ¾erschiedenheit, and differentia=Unterschxed- F. Boas (Pfi. Arch., xxvlii., 88, 574) and A. Grotenfelt (Des Webersche Gesetz, I888, 41) also employ the term Verschiedenheit. Stumpf prefers Unahnlichkeit (Tps. i., xi1, 122 if.). Ebbing. haus often uses Verschiedenheit {Pfi. Arch., xlv., 1889, 3; Z., i., 189 o, 328) ß ----------------------------------------------------------- lxxxiv ]ntroductœon der gleich merklichen Verschiedenheiten" 033; c.f. 260 f.) As regards the relation of Verschiedenheit to Unterschled: ,, die V. zweier psychm- chen Daten fallt ihrer Grdsse nach weder mir dom absoluten noch mt dom relatwen Unterschied dinset Daten zusammen; abet die Bezie- hung zum relativen Unterschied ist eine ungleich engere" (285). Hence, whfie he cannot in strictness adopt either the Unterschmds_ or the Verhaltnisshypothese,__for if you cannot subtract S, you certainly can- not divide them (385),--Meinong finds that the latter position comes very much nearer the truth than the former (387 f., 402). Vhat Weber's Law tells us is that equally distinct or diverse S correspond to equally distinct or diverse R (363, 37, 397): not S-differences, absolute or relative, but S-distinctions (Empfindungsverschiedenheiten) are logartth- micafly dependent upon R (374 frO' This view is, it is true, contradicted by the results of Merkel's experiments (261 if., 388 if.); but these are readfly brougtt into line ,,durch die Vermuthung, dass hier start der Dlstanzen Strecken verglichen wetden, bei denon an Stelle der einfachen Verg]eichung dm Teilvergleichung eintreten und dadurch der, Unter- schied' im regentlichen Wortsinne zu seroera Rechte gelangen kann" (396). That is to say, instead of judging in terms of interval, aparthess, ' distance ' in the proper sense of the word, Merkel judged in terms of' that which filled the distance, here the tntensive sense-contmuum. We appealed to experiment; and the appeal was answered by Merkel and Angell. Nevertheless, these investigators did not raise the precise question that we desired to have raised: and their results are not in accord. Moreover, in thscussmg Lange and Grotenfelt, Wundt and Meinong, we have come back again to theory and interpretation. In the work next to be mentioned--Ueber das Verhiltnis der ebenmerkli. chen zu den tibermerklichen Unterschieden bei Lcht- und Schallintensi. taten, by W. Ament "we have an experimental study, undertaken with  The reader should, however, compare Meinong, 264 f., note, 396, wth 1Vferkel's statement, P.S., v, t889, 537, and with his results for wide gO-intervals. see, e. 0% Ament's combined Table, P S, xv., ,9oo, 142 ' On Memong's general position, of. /::[offer, Psych., 897' õõ ø-9, 39. "De elnfachste Erklarung der Thatsache, dass die Verschmdenheten der Empfind- ungen yon 3g-und 4g', yon 3 dkœ und 4 dkffglmch merkbch, namlich eben merk- lich sind, liegt darln, dass dese Verscbedeuheiten glech sind:" 232; of. 141 , 249 f. See also Stout, Manual, 899 , 206, 2o 7 f. For the doctrine of ' psychische Arbeit,' c.f. esp, in the present connection, Hofler, Psych., 249 f.; Z., vifi, 895 , 98; Meinong, Z., xi, t896, 126 if., 26o f.; T. Lipps, Grundzuge der Logk, 893 , Io4, 122; and on the doctrine at large F. Boas, Pfluger's Arch., xxvi,i., 882, 574 f-; N. yon Grot, Arch f. syst. Phil., iv., 1898 , 266 if. (with references); Munster. berg, Psych., i., I9OO , 277 if.; V. Henri, L'anne psychologique, 3 bme annie, I897, 232 if. o p.S., xvi., 19oo , i35 if.  4. Cri/iczsm lxxxv the express object of decl(hng "ob mall berechugt 1st, the ebenmerkli- chen Unterschmde als merkhch glemhe aut'zufaen, oder mcht" 037}2 Experiments were made with brightnesses (direct method) and nomes (principally, indirect method). The brightnesses consisted of a series of Marbe greys "zwischen mnem nxcht sehr dunkleu Schwarz und emem dunkloren Grau" (49 papers; photometric limits :3). The noises were given by a Fechner sound pendulum (intensive limits approximately .5o)2 The result s that, in every case, there s "a divergence between dfference determinatmn and dfference comparison," i.e., the two sub- jectlve halves of a given R-distance do not contain an equal number of j. n.d. ,, Thls divergence depends upon the magnitude and the position of the compared differences. Hence we must conceive of the 29i. as a magnitude that increases with increasing R, and must consequently gve up Fechner's assumphon that it is the unit of measurement wthin the sphere of S-measurement at large" 095 t ). The result xs illustrated by the following Figure. Fro. . The values r v r, r a, etc., are R-intensltms, arranged in ascending order: the distance between every pair of successive r represents a ])L. The distances r--r=, ro--ra, etc., increase by equal increments. It is clear () that tile distance rs--r v though it contains tbe same number of  Ament sharply separates the two problems of the ' equal noticeableness' and of the 'equality' of the j. n.d. We return to the former presently. The junction probably accounts for the phrase ' merklich glemh ' in the above quota- tion: ' merklich gleich ' is contrasted with ' glemh merkhch.' In reality, however, there are three questions. (I) Does' eben merkhch' mean 'gleich merkhch'? (2) Does 'eben merklich' mean ' merkllch gleich,' in the sense of introspectively equal, sensibly equal, apparently equal? This question was answered affirma- tively by Fechner; and if we do not take Fechner's word, we shall not take the word of less experienced observers. It is the question which Ament has in mnd at the outset (I35); he wishes to know if the j. nd. are on a par wth other" unmlttel- bar als gieich empfundene Unterschede." (3) If we give this riddle up, we still have the question: Are the j. n. d. equal; does 'eben merklich ' mean 'psycho- logisch glech'? Ths s the questran which Ament actually seeks to answer; 192 fl. In Kulpe's account of the investigation {Compte rendu du IVe Congrs de Psycholoe, 9Ol, I6O if.) the phrase ' merklich gleich ' does not occur; though in criticising Fechner's statements Kulpe uses the words 'subjectlv gleich.' If we assert that introspection is incompetent to decide questlob (3), it is (in the author's opinion) best to eliminate question (2)altogether, and to ask simply: Are the i' n. d. equally noticeable  and: Are they equal ? g El., i., 76 f. See p. 95 below. ----------------------------------------------------------- lxxxvi f ntroduction j. n. d., will appear greater than the distance r--r; (2) that the dtf- ference decreases, the nearer the compared dmtances approach to rs,--so that a comparison of r 4-- r5 with r,--r 6 may even evoke the judgment ' equal; ' and (3) that a comparison of r--rwith r ß evoke a decided judgment of dtfference, although the two distances are alike j. n.d. See Ament, 93 f- Are these results to be accepted ? Tins is not the place for detatled entreism: the author must say, somewhat dogmatically, that the ln- vesttgation has not, in his opinion, proved what Kulpe and Ament thmk it has proved. Concermng the work with brtghtnesses, it may' be pointed out that the )g-seres was discrete, not continuous; that t was very short; and that there are discrepancies m the results from the three O's whmh Ament does not attempt to explatn. If these experi- ments stood alone, the hostile critm would have an easy task. Concern- ing the work with noises, which makes a much better mpression on the reader, one may atleast stress the fact that Kulpe and Ament were them- selves the sole observers. "Schon bei schwerigeren naturwtssenschaft- hchen lJntersuchungen," writes Ebbmghaus, ,, wird bekanntlich (unbe- schadet der gr6ssten Gewtssenhaftlgkelt) verwunderlich haufig eben das besthttgt gefunden, was man erwartet hat. Bei psychologischen Dingen ist de Gefahr so gross, dass man fast als Regel aufstellen kann, alle Experimente, die behufs Bestgtgung emer eigenen Theorte an dem eigenen Selbst angestellt werden, ftir verd.chtg zu halten" (Psych., i., 88). Amentdoes not tell us whether the nome experiments were taken up at the conclusion o[ the experiments xwth brightness; but even if this ts not the case--and it is suggested by the order of presentation-- the objection holds that he has left the enqmry' unfimshed; we must have results from a number of trained O's who are tgnorant of the pur- pose of the work. Moreover, the experimental results offer certain dif- ficultres whtch are not adequately met by appeal to the corresponding brightness expertments. And finally, we must remember that neither of these sets of experiments stands alone. The value which we place upon Ament's research will depend largely upon our appreciation of previous investigations. t x Ament's paper contains an unfavourable criticism of Merkel and a favour- able review of Angell 039 if.). Angell's geometrical mean xs accounted for by the narrow range of his intensive ,' (179). Ament himself is fully alive to the time error and the error of contrast (166, 184 191 ), and has avafied himself of Angell's introspections in the use of the method of mean gradations (17o). But his empirical basis is not solid enough to bear the weight of his conclusmns,-- stfil less, that of Kulpe's far-reaching deductruns: Compte rendu, etc., 64 ff Ament's work is subjected to a severe techmcal criticism by A. Lehmann, õ 4. Criticznz Ixxxvii Ebbinghaus takes stmfiar ground to Stumpf. "Man kann (liesen Enwand (i.e., the general objectton that 'glemh merkhch' does mot necessarfiy mean 'glemh gross')gelten lassen,"he says; and he re- mnds us that the least dtstances perceived as such mdtrect and indirect vtsmn, or at dtfferent parts of the sktn, do not by' any means come to consctousness as equal magmtudes. ,,Trotz aller ungenugenden Be- grundung aber hat Fechner dennoch sachhch das Rchtigegetroffen. Obschon es ntcht selbstversthndltch ist und kaum durch chrekteBeo- bachtung entschteden werden kann, dass ebenmerkhche Verscheden- herten auch gleiche Empfindungsstufen sind,  und obschon se anderswo, z. B. bet Raumgrossen, nicht als solche betrachtet wetden konnen, her bei unseren St.rkeverschtedenheiten der Empfindungen muss es not- wendg geschehen. Dte gegenteilige Annahme wdrde zu wtdersinnigen Konsequenzen fuhren." Ebbinghaus then points out, as Muller and others had done befo?e him, that, tn the case or'brightness intensities, the results gained by the method of mean gradations are in agreement wtth those gained by the method of minimal changes. ,, Dte Gleichhett der ebenmerklichen Helligkeitsverschiedenheten ist also zwar ntcht selbst eine unmtttelbar zu beobachtende Thatsache, aber etne auf Grund der Uebereinsnmmung der betden Gesetzmhsslgkeiten kaum zu entge- hende Annahme. Ist dtese Annahme abet sicher notwendig fur Helhg- ketten und wahrscheinlich notwendig fur Schallstrken, wie soll man sich ihr--wieder  bis zu dem dxrekten Nachwets ihrer Falschheit--fur das Gemeinsame dteser betden Inhalte, namhch eben fdr die Empfind- ungsstrke iiberhaupt, entziehen konnen"? a Ebbtnghaus makes no reference to Ament and Kulpe.  What now, of the first part of the general objection: that ' just notme- Dm korperl. Aeusserungen psych. Zustande, fl. (Die psych. Aequivalente d. Bewusstseinserschemungen), 19Ol, m5 if. Lehmann hmself maintains, upon ex- perimental evidence, the equahty of the j. n. d (12 f, 76 if, at8). He is an- swered by Kulpe, P. S, xvifi, I9O2, 325 ff F S. Wrinch, ibxd, 274 if, asserts that Kulpe's law holds of tone-filled tmes between the limits 25o and 12oo a. On Ament's brightness experiments, of. J. Frobes, Z., xxxw., 9o4, 344 ff-  For this terminology, see õ 6 below.  Tim wteder refers to a simtlar caution, suira, 5o2- a Psych., ., 19o2, 5o f. Cf. Jodl, Psych., 1896, 226. 4 Since the first part of vol. i. appeared m I897, it may well be that certain sheets of the second part were in prmt before I9o2. There is, however, a ef ererice to the Congress of 9oo on p. 444; and on p. 499 (a page of the sheet that contains our quotatton) occurs a reference to a paper of 19oi. Hence we may assume that Ebbnghaus, had he been impressed by Ament's work and Kulpe's discussion of it, would at least have added these items to the hst of titles on p. 495. Ament's article was issued August 7, 19oo. ----------------------------------------------------------- lxxxvii Introduction able' does not necessarily mean 'equally noticeable'? It does not reqmre any long discussion. Logically, t is clear, the question: Does ' eben merkhch ' mean, glemh merkhch' ? comes before the questran: Does , eben merklich ' mean ' gleich ' ? Hmtorically, owing to the form of Fechner's exposition, the latter question was raised first; and those who answer it in the affirmative vill not hesitate to grant the former also. For those, again, xvho make ' Merklichkeit' the only possible terion of intensive $ and S-dfferences, the two questions become, even logically, one and the same question: things that are, gleich merklich are, for psychology,, gleich.' All that we have to do, then, is to collect the references. "Wie gross die Merkhchkeit ist," says Meinong, ,, die sich zuerst geltend macht, indem der Unterschedsschwellenwert eben 0berschntten wird, daruber ist im Begrifle des ' eben Merklichen' eigenthch noch gar nichts vorge- geben: der Moghchkeit nach k0nnte die Merklichkeitslime mit einem hohen wie mit emem niedrigen Merklichkeilsgrade einsetzen, und ob es iramet der ngtmliche Grad ist, dartiber kann am Ende nur die Empiric entscheiden." Whde, that is to say, the 'just' notrecable differences are ' equally ' noticeable differences in the sense that they are, equally just' or ' alike just' noticeable, they need not by any means represent equal degrees of noticeableness: a just noticeable dfference mght be, hardly' noticeable in one context and , easily' noticeable Jn another. The ob- jection is not organic to Meinong's position, and is not further discussed. Hofier makes the question of 'gleiche Merklichket' logically prior to that of 'Gleichhmt. TM The assumption that the j. n. d. are 'glmche Verschmdenheten,' he says, mcludes the assumption ,,dass sch uuser Merken, d. h. Erkennen (ewdentes Beurtellen) der Verschiedenheit, yon vorn herexn nicht anders gegenuber einer ¾erschmdenhet zwischen an sich klemeren, als gegenuber einer Verschiedenhet zvschen an sich grosseren Relatmnsghedern verhalte. Indem dann das subjektxve Moment des Merkens--zwar nicht ganz ausfallt (denn m der That wissen wit ja um Verschledenheten eben nut durch das Merken), wohl abet  Z, xi, x896 , t3 o: el. Ament, P.S., xvi., i35 , note. GroteMelt (Das Weber- sche Gesetz, 888, 9) says: "es schemt einleuchtend zu sein, class verschiedene so festgestellte ebemerkhche Empfindungsunterschiede auch als gleich merklich be- zeichnet wetden mussen." Cf 3&insterberg, N. G., 58; Jodl, Psych., z3; Dit- tenberger, Philos. Monatshefte, if., 896 , 77; Wundt, Das Webersche Gesetz, etc., 88, 30; P.S., if., 885, 5- Kohler (P.S., iii., $86, 577 f.) clearly distinguishes the two questions of 'gleiche Merklichkeit' and ' Gleichheit.' Under the former head he writes: "es ist schwer, diesen Streit theoretisch zu entscheiden;" fortunately, the results of minimal changes are corroborated by those of mean gradation. Kohler, be it remembered, is speaking in Wundtian terms.  Psych., 14;. õ 4. Urtticism lxxxix ein fur beide Verglmchungen constantes Element darstellt, kommt das oblekttve Moment, namhch de Gleichheit der binden Versctnedenhexten remzum Ausdruck"(232). t For the oppositevew, see 249 f Ament, on the other hand, seems to make the two questions logically' co-ordinate. - Ths rs, doubtless, due to the fact that, in his opinion, the j. n.d. are not equal magnitudes For if one has raised the second question first, and has answered it in the negauve, the first question comes up at once as a second problem, demanding separate and co- ordinate treatment. Ament confines himself exclusively to the question of equahty. a (3) Fechner, as we have seen, regarded Weber' Law as a psychophysical law, a lazo of the functional izterdependence of mizd ad body. He adduces, in the Elemente, five distinct, though by no means co6rdinate arguments for his position: ( the disparity of E and S, as contrasted with the homogeneity of E and R; (2) the parallel law; (3) the validity of Webefts Law for tonal pitch; (4) the fact of the limen; and (5) the phenomena of consciousness and unconsciousness, attention and inattention, sleep and waking. The two last are by far the most important and, in Fechner's view. are intimately connected. The arguments of the Elemente and of the article Ueber die Frage des psychophysischen Grundgesetzes reit Riicksicht auf Aubert's Versuche  (864) were criticised m detail by G. E. Muller in the Grundlegung. The In Sachen was reviewed bv the same author in the G6ttingische gelehrte Anzeigen for /878. Al- though other writers, before and after Muller, contributed their share to the discussion, it may be said that Mtiller, a representative of the physiological interpretation of the Law, is mainly responsi- ble for the disappearance of the psychophysical interpretation as a practical issue. Not that this interpretation had---or has--found adherents! The sole acceptance of Fechner's view that is known to the author occurs in Lipps' Grundtatsachen, 883, 76. "Ich weiss," says Lipps,--and the whole passage is hardly more than an ' aside,'- "dass der Streit um die Deutung des . . Gesetzes . . noch entschieden ist. Ich . . glaube, der psychophysischen Deutung. x This passage follows mmedmtely upou the sentence quoted above, p lxxxv.. note. 2 p b.xm, ;35 a/btd, 37. 4 Be. d. kgl. sach=. Ges. d Wtb., math -phyb. CI., xw., 28 Mai 864,  if. ----------------------------------------------------------- xc 2rntroducttbn ich meine derjenigen, die in dem Verhiiltniss des physischen R zum seelischen Vermbgen den Grund ftir den dutch das Gesetz bezeichneten Sachverhalt sucht, einstweilen den Vor- zug geben zu m/issen." Lipps has now withdrawn this opinion. "Das Webersche Gesetz," he writes in i9o2 , "soweit es ein Gesetz ist, ist ein rein psychologisches Gesetz, n&mlich ein Spezialfall des allgemeinen psychologischen Relativitiitsgesetzes der psychischen Quantitit." -- G. E. Mhller, it is true, looked upon Wundt's Beziehungsgesetz, in the formulation of I874, as "nicht eine neue Dentung des Weberschen Gesetzes, sondern nut eine Verallgemeinerung der Fechnerschen Auffassung" (G., 375, note). Wundt had written as follo;vs: "Nach seiner psycho- logischen Bedeutung k6nnen wit [das psychophysische Gesetz] ein allgemeines Gesetz der ]geziehung henhen. Denn es driickt aus, dass unsere Empfindung kein absolutes, sondern nut ein relatives Mass der iiusseren Eindriicke gibt. Reizstfirken, Tonhohen und Lichtqualitiiten empfinden wit im allgemeinen nut nach ihrer wechselseitigen teziehung, nicht nach irgend einer unverknderlich festgestellten Einheit, die mir dem Eindruck oder vor demselben gegeben ware" (P. P.. 42; cf. 35, top). The exposition which concludes with this passage is, without doubt, eqmvocal:a and Vundt's sympathies were at the time very largely with Fechner. But his later statements leave no ques- tion as to its real meaning. At the risk of repetition, it seems worth while to give in this place the chief arguments urged against Fechner's standpoint.  Sxtzungsber. d. philos-philol. u. d. hist. C1. d. k. bayer. Akad. d. Wss., Heft i, 46 f. C.f. t&t., i899 , Heft 3, 4oo. It must be remembered that Lpps' ' psychological interpretation ' s couched m terms of his doctrine of ' psychsche ¾organge', and may easxly be construed back into a psychophysical interpreta- tion. Tb_is Lpp hunself admits. "Dtes hindert mcht, dass es ein psychophysis- ches, oder genauer gesagt, psychophysmlogxsches Gesetz ist fur denjemgen, der weiss, dass dxe psychischen .Erregungen oder Vorgange schlechterdings nichts sind als mechanische, also ganz und gat nach mechanischen Gesetzen begreiflche Gehrnprozesse. Dese Wissenden nun wissen mehr als--man weiss" 0902, 47; of. 899 , 380. 2 Fechner, ,viewing things through psychophyscal spectacles, discusses Wundt's law "wesentlich nur als tone eigenthumliche Modification der physiologischen An- smht" (R., 264). if. Jodl, Psych., 235; ]2httenberger, Phfios. Monatshefte, ii., x896, 97. g 4. Crzt,csm xci There are threetradmonal'interpretauøns'øfWeber'sLaw'  Let us represent the com-se ofexents from stimulation to judgment by the lowing figure: FG. 2. where R denotes stimulus,  exmtaton, the whole chain of physiological (including pychophysca]) processes,  sensatmn, the mentMprocess corresponding to the exctatmu m a sensory centre, and C judgment comparison (Auffassung und Verglmchung). XVe may say, oreming constants, that the ph3smlogmal interpretanon relates the terms as foi- loxus: R I E=S= C. The psychophyscal vew (Fechner's) xvrites: The psychological asserts that: R=E=S II G It s clear at once that the psychophyscal interpretation has agreat ad- vantage over the other two: it s precise, deftrote and unequivocal, whereas the physiological and psychological vews are, as formulated, mere classifi- catory headings, which may cover very dfferent specml theories. ,' The fact of Weber's Law simply asserts a relation between  and reports of the S excited by them, and between these extremes there lies a whole series of mediaung processes, all of which, theoretically considered, may cooperate to give the relatxon its specific character." = Only the psycho- physical viev is, intrinsically, free from ambxguity: for it declares that the logarithmic relation obtains between the physical as such and the mental as such, and demands nothing further than an understanding of these two terms. Here, then, s an addxttonal reason for dsposng of it at thin time. 0) The first of Fechner's arguments was promptly met by the counter argument that "the final stage of the nervous excitation and the sensa- tion, which run strictly parallel to each other, can hardly be anything else than proportional to one another. "a Thin argument is no less x C Dittenberger, opal, 88 f.; Lehmann, Die korperl. Aeusserungen psych. Zustande, ii., 9o2, 6 if.  Kulpe, Outhnes, x63 f. Cf. G. E. Muller, G., 232; Ebbinghaus, Psych., i., 5x4 if., 58. a E. Mach, Stzungsber. d. kais. Akad. d. Wss. zu Wen, math.-natunv C1,2 Abth., lvi, 9 Jan. 8, I2; Ilering, as cited in following note; A. Classen, Zu Physol d. Gesmhtssinnes, 876, 7; C. Ueberhorst, Die Entstehung d. Geschtg wahrnehmung, 876, 2o. ----------------------------------------------------------- x c it rntroductio n apriorstc than Fechner's; but, as Herng points out,t it is one which agrees l)eter than its opposite wth Fechner's phfiosopixcal interpreta- tion otthe relatonofmmdand body? Fechneradmits, in hs rejoinder, that the objection would hold m a case of causal sequence. He denies that:t holdsin the present case of s, multaneous dependency or interde- pendency, anti 11ustrates ties postUon by instances taken from the natural scmnees (length of a pendulum and duraUon of oscfilation, relative length of a curve and its abscissas, etc.)) In the meantzme, Muller had challenged the argument afresh,* reiterat- ing Hering's statement, and adding a further point of his own. It Weber's Law were exact, he says: if it implied, from the physiological standpoint, that E increases exactly as the logarithm of R: then the physmlogical interpretation might appear less, and the psycbophysical more probable. We find, however, as a matter of fact, that the Ltw holds only approximatively and within certain mean hmts.S This fact, that "das Webersche Gesetz nut mt massiger Approximation gilt," is fundamentalfi Fechner is not moved by these arguments.? "What physical prin- ciple is there," he asks, "to explain the translation of the ralio of the intensity of two physmal processses R  into a dzerence of the processes E--E' consequent and dependent upon them, so that an n-fold difference '--E' corresponds to aa n-fold R ½,, And again: "when we are considering Weber's Law, the question s whether more wmght is to be lad upon the exceptmns or upon the rule. so far as the rulers found to hold good. Mtiller emphasses the exceptions; I emphasise the rule."  Sitzungsber. d. kais. Akad d. Wtss. zu Wren, math.-naturw. CI., 3 Abth., lxxfi., 875, 330 f. ' The Identitatsansicht or Zwet-Seiten Ansicht. Zend-Avesta, i., 185 , nl., 4IO ff ;ii.,312ff.; El,i, 5 fl.; ii, 526, 542 f.,etc : R.,i if.; K. Lasswttz, G. T. Fech- ner, 1896 , x5o ff; Wundt, G. T Fechner, Rede zur Feier seines co-j&hngen Geburtstages, 9Ol, esp. 42 if., 83 ff a I. S, 66 if. 67. note, p. xxxii. above; R., 227, 256 if.; G. E. I¾[uller, Gotting. gel. Anz., 26 Juni 878,819 if., 830 if.; 3 Juli 1878 , 833 if. 4 G., 233 if., 366 f.; ct. Jodl, Psych., z32.  G., 236 , 246 f. , Gott. gel. Ariz., 878 , 8 3. a The argument has been urged by Wundt, e.g., since 88o: P. P.,i., 88o, 35 ø f.; x887, 376 f.; x893, 392 f.; 9oz, 494, 540. It is now generally accepted: of. El> binghaus, Psych., i., 499; Jodl, Psych., 221; Lehmann, Die korperl. Aeusserung en psych. Zust.nde, ii, 19o2 , 66. ? R., v. and passim. 8 R., 226. a R., z47 f-, I9 f.  4. Crtttcism xciii Indeed, Fechner's psychophyscal system s, as he htmself suggests, hke atree, whichthewlndsot criticram must rather root more strongly or blow over: m which latter event, we may add, the fallen trunk and scattered branches may be eminently useful for all sorts of purposes, but the tree has ceased to be a tree. Had Fechner given up his argument from a firJori probabihty, he woukl have been forced to revise his whole psychophysical standpoint. To us, who have not to defend ths stand- pmnt, the opposing arguments of Hering and Muller must carry convic- tion. And since, as Ebbinghaus repeats, "die physiologische Auffassung des Weber'schen Gesetzes hlatte such Fechner nach seinem allgemeinen Grundgedanken nahe gelegen, "= we must scrutimse all the more closely hsattttudetothe fact ofthehmen,--a fact which is made to hei l )hm out of hs dfficulties, and whtch may be said to dominate hs psychology? (2), (3) The next two arguments need not detain us. The parallel law s d,scussed by Muller, wth the result that the question of its validity is indifferent, so far as a choice between the physiologmal and the psychophysical interpretat,ohs is concerned. * Fechner himself con- fesses, m the light of Mtiller's critique, that "das Parallelgesetz zwar keinen neuen Gesichtspunct gegen die physmlogische Ansicht ins Feld. ftihrt; wohl aber kommt ein fruher durchschlagend dagegen gefundener [i.e., the aprioristic argument which we have just consxdered] dann mt zur Geltung."s The parallel law may, then, require examination for its own sake, but does not help us towards an understanding of Weber's ' Psych., i., 517 . s The following points may be further noted. Both Fechner and Muller appeal to the results of current physiological enqmry: I. S., 72 if.; G., 294 if.; R, 23I if. Muller lays stress upon certain psychophysical facts (such. as the dependence of the DL upon the quality of R) which tell, in his opinion, against Fechner's vtew: G, 246 fl., 334 if-; of. the reply, R., 248 if, 42 ff The position of the G. is not shaken by the arguments of the [ S.: see G., vtit, and Muller's revtew n Gotttnsche gelehrte Anzeigen, 878, nos. 26, 8ot ff and 27, 833 if- On Fech- ner's postlion in general, see Grotenfelt, Das Webersche Gesetz, 93 f'; Kulpe, Outhnes, 64 f, I67; Wundt, P. P., i., x893, 392 f-, 394 if-; t9ø2, 54 ø f', 548; Hoflar, Psych., 220 f. Wundt points out that it is impossible "de psychophy- msche Deutung mtt anderen Thatsachen unserer tnneren und ausseren Erfahrung n etne innere VerMndung zu bringen." Thts objectton rs, however, vahd only from the standpoint of the Beziehungsgesetz. Fechner regarded Weber's Law as covenng a special class of facts, separate and apart from the facts of physiology tnd of psychologx; but the class was fully wtde enough to demand a law tts owm  G., 266 if.; Gotting. gel. Anz., 1878, 824; Q,r. Wundt, P. P., i., 893, 392; 19o2, 54o; Dtttenberger, Phfios. Monatshefte, ii., 896, 89 f.  R, 24o if. ----------------------------------------------------------- xciv Introduction Law. a The argument from the musical scale is, as ae shall see later, erroneous? (4), (5) Fechner regards it as an especial argument in fayour of the psychophysmal interpretatmn that his metric formula or Iogarithmm formula is adequate both to \Veber's Law and to the fact or law of the hmen "Aus dem reinen ¾Veberschen Gesetz," he says. ,,liesse smh uberhauptgar kmn endhches Mass fiir endliche Empfindungen gewm- nen, ohne dassman dasSchwellenpnnmp zuzmht."s The mathemaucal derivation of the metric formula "wtirde illusorisch wetden, wenn die Thatsache der Schxvelle nicht bestnde, welche daher mt dem Weberschen Gesetze zusammen erst die zulangliche Unterlage .... ties absoluten Empfindungsmasses bfidet. "* The 27L and the Z)L i the dlemene.--lf we are to appreciate the strength or weakness of thin argument, we must know first of all just what Fechner has sad about the two limens in the Elemente We come upon the RZ. and DL as bare facts, which are rather surprising than otherwise. we should'naturally'think that the point at whmh an Sot S-difference begins to be noticeable would coincide with the zero point of the corresponding œ or R:difference. ',In der Thatsache der Schwelle hegt von vorn herein etwas Paradoxes." However, we are led to the coucept of the hmen not only by our dealings with R and S, intensive and extensive, but also by a consideration of the higher and more general conscious states and processes: sleep and waking, atten- tion, thought, etc. This umversahty of the limen suggests its transfer- ence from outer to inner psychophyslcs. Both the Rœ and the have, in spite of their seeming strangeness, a high teleological import- ance, as secunng freedom from interruption and an uniform state of perception. 8 So much on general grounds. Fechner then proceeds to give the numer,cal determination of the hmens, and the laws of their interdependence, in the various sense departments." He brings the 'homogeneous' RL and DL of customary psychophysmal discussion under the more general heading of the ,mxture hmen ' (MZ.), a notion that is destined to play a large part in his system. "Suppose that a stxmulus B is added to a stimulus or stimulus mixture _d, and that one seeks to determine the value of B at which the increment begins to be I 1 , I43, 8o f.; Stumpf, Tps., i., 85; J. Ward, Mind, O. S., i., I876 , 455 if.; J. yon Knes, Die Gesichtsempfindungen u. ihre Analyse, x882 o9.--On the value of the parallel law as a bridge between outer and inner psychophysics, see Wundt, G. T. Fechner, i9ox, 47-  See below, pp. 232 if. $ I. S., 88. Ei., fi, 34, 431; of. i., 238 f.; Benchte, etc., I864, x; I. S.C7 f., 2.3, 70 f.,87 f. 88, 2.  El., i., 2.38.  ]'bid., 246. ?]btd., 239 , 248 f., 251. 8 œbtc/., 249 if. 9 ]bzd, 254 if. õ 4. Crztwism xcv noticeable as such, or to allow a dtffevenee to he felt from the mere effect of ,/. Of all the possible magnitudes that .4 may possess. one may magine the case lnxvhmhtis=o: then we have the instance of the ordinary homogeneous RL. Slmfiarly. of all the possible quahUes that 1 may evince, one may imagine the case in vhmh t is oi the same quality with B: then we have the instance of the ordinary homogeneous .DL."  No investigation of the laws of the $rZ proper has as yet been made? The RL now takes its place in the metric formula; a the DZ. is in- cluded in the Unterschiedsmassformel.  In the mportant chapter m xvMch he distinguishes sensation differences from sensed differences or contrast sensatlons, Fechner remarks that the determination of theDL imphes"einen h6heren Bewusstsemsact"than that of the Rœ,though both the higher and the loxver are accessible to measurement and com- prehensible under a single principle. s Finally, he transfers the hmen, along with \Veber's Laxv, from outer to inner psychophysics, where he makes very extended use of it;  and he insmrs that the physiological inter- pretauon of theRL -- to the possibility of which hels by no means blind ? --is ruled out of court by the parallel fact of the 22Z,. ,' Diese [physiolo- gische] Deutungwird schondadurch unhaltbar, dass sic nicht auf die Unterschmdsschwelle tibertragbar ist, und unstretg muss classelbe Erklarungsprinmp fur bede Schwellen ausreichen."  Such, m briefouthne, is the teaching of the Elemente as regards the limens. Mt2ller's Allark ujbon l]ze RL.--Mtiller begins his criticism, very per- tinently, by raising the previous question. "Dass das Gesetz der em- fachen Rmz-oder Empfindungsschwelle . . . fiir die gussere Psycho- physk besteht," writes Fechner, ,' daftir liegert offenkundige Thatsachen vor. "a ,, Untersuchen wir zunachst," retorts Milllet, "ob denn wlrkimh die sogenannte Thatsache der Reizschwelle als eine in Wahrhmt con- statirte Thatsache zu betrachten sei." 0 The upshot of his investigation s ', dass (lie Frage nach der Existenz der Reizschwelle eine ziemlich heikele ist."n This conclusion stands to-day as it stood in I878. Thus Ebbmg- haus, writing in 9o2, may be said simply to summarise Mtiller. ,, In almost all sense departments," he tells us, ,, xve are constantly receiving, at least during the waking state, weak sensations from what are called  El., i., 33  f. Zbid., 334 f. a El., ii., 3, etc.  Zbzd., 96ff.  .rbzd., 85 f.; of.. I. S., 84, 99.  El., ii., 428 if, 43/ if. ? Zbid., 43; I. S, 82 if.; c.f. Berichte, etc., 864, 2, 5 8 El., ii., 43 ; I. S., 83 f. s I. S., 82. 0 G., 237. The reader does not need to be reminded that Muller is, in strict- ness, replying to the .El. and not to the I. S.: see G., vii. f. n G., 239. ----------------------------------------------------------- internalstnmuh (noises of heartbeat and respiration, touch stnmuln troro clothing, weight of our hmbs, ldmretlnal Inght). Hence we are dealing m every case snnply wth small increments of stimuli already present and already in some way operative, only that these stimuli come in the one instance merely from the orgamsm itself, while in the other they come both from the organism and from its external surroundings."  If, then, ve push the matter to Its logical conclusion, we are bound to look upon all limens as 29œ; the separation of the Hœ from the Z)œ may be con- vement in practice, but will be wrong in theory. Elsewhere, Ebbnng- haus draws this conclusma: "es exlstiert im Grunde our ein elnziges Phanomen, namllch das der Unterschiedsschwelle, welches sich bei allen moglichen Werten der objektiven Relze m gleicher Weise geltend machr." 2 The question has been much discussed, and s not easy to settle. We shall rewew the evndence later.  In any event, enough has been said to show that the ZeZ. is precarious ground from which to argue for the psychophysical and against the physmloglcal interpretation of Weber's Law.  2Vliller o the Helation of he RL to the ZL.--We might expect, there- fore, that Muller would urge the ' shakiness' of the RL as an argument against the metric formula, which presupposes the fact of the limen as well as Weber's Law. This, indeed, he does, when he is working out hs own psychophysical formula. * At present, he prefers to argue that, ,, auch wenn die Reizschwelle zu den bestconstatirten Thatsachen der Sinneswahrnehmung gehorte," it would still yield no evidence in favour of the psychophysical nterpretatlon. And, in fact, he has not the least dnfficulty in showing that the physiological view 15 adequate, and adequate in more ways than one, to the fact of the hmen.  He argues, further, against the brackeUng together of the Dœ with the HZ.. "Man sollte meinen, die totale Verschledenheit der beiden in Rede stehenden Schwellen w.re emleuchtend."= For (a) the perception of S-differences is, on Fechner's own admission, a conscious act of a higher order than the simple sensing of different H; (b) the .DL has to do with the dif- ference of two S-intensities, the RL not with differences of Sor of H, but with totalvalues of H; and (c)the DI. is dependent upon such condi- tions as lapse of time, of which the HL is wholly independent.* We must  Psych., i, 49 o.  Z., i."a,72. a pp. cxvi. if., etc.; cf in the meantme E1, , 24 o, 255; I. S., lO.3 œ; I{. Aubert, Physiol. d. Netzhaut, 865, 42 f.; W. Preyer, Grenzen d. Tonwahrnehmung, 876, 65 if.; Delbeeuf, ]ldments, 34 if, 66 fl.; Stumpf, Tps, i, 379 if., e?. 382; Jodl, Psych., 171 fl., 205 ff-, 227; O. Funke, in Hermann's Eldbch. d. Plxysol., iii., 2, I88o, 327 . ß G., 239. 5 G., 227 if.  G, 239 if.; Funke, doc. dr. ? G., 244. "G, 243 if. õ 4. Crtticzsm. xcvii bear in mind that, while Mtiller is arguing seriously, he is also arguing hypotheucally. If there is an RL m Fechner's sense, a snmple sensing of a least sensation, then this RL ns something radically dnfferent from the J9.L. More than thns the argument does not say. 7he Lzmeus zn lhe I. S.--We return to Fechner's exposorion in the I. S. Here Fechner emphasmes the vital importance of an inner bmen for inner psychophysics, and dscusses certain physmlogmal mvestigatmns that seein to bear upon the point3 He then declares the physiological explanatnon of the RZ. to be nnadequate, if only for the reason that nt is madequate to the relatedL. 2 Txvoph}siologicalnnterpretatiønsøfthe f)5 are proposed, and found wanting  Qmte apart froIn the DL, how- ever, there are facts of attenuon that lead dnrectlyto the assumption of an inner œZ..  Fechner next passes on 1o deal xxnth the RZ. m the light of hm negative sensation values, s and finally comes to the J/fL. The R and ]'2 that he below the I/L modify consciousness, at the expense (so to say) oftbelt ownlndvnduahty: ,'sie gehen unbewusst m einem allge- memern Bexvusstsemsphanomen a uf" ,, I)urch the Thaisache der Mnschungsschwelle word der Schwellenbegriffuberhaupt . ß ß mcht auf- gehoben, sondern our verallgemeine rt-"* Here is, perhaps, an improve- ment in detail, but so systematic advauce upon the Elemente * Th sOL in J&dler's Revw.--Muller's rex, new of the I. S. is concerned with three principal points: lhe metric methods and the range of ¾abdlty of Weber's Law; the denvatmn of the metric formula from Weber's Law; and the Interpretation of the metric formula. To Fech- her's argument that what holds of the Dœ must also hold of the Rœ, Muller replies as follows. O) A physiological explanation of the Rœ, implying a proportlonality of S and E, implies absolutely nothing as regards the noticeablehess of S-dnfferences. In the f6rmer case we are talking of the dependence of S upon psychophyslcal activity; m the latter, of the relation of the difference sensatnon to the S-difference. Wilere is the connection ?  (2) If, hoxx e,er Fechner's argument contains a challenge to the physiological interpretation ,you must offer some sort of psychophyslcal representation of tle difference sensatmn,--and then you must make the S proportioual to the E,--and then you run  I. S., 7 ø if. Cf. G. E. Muller, Gott gel. Ariz., 878, 89 if.  Zbzd., 83 if. a fbtd, $4-. An explanatmn in terms of the J-/'Z s dinmissed, o6  /bid, $5 ff' .5 Ibrd, 88 if.  fbd, m 5 f., R., 258.  Zb2d., m6. Fechner has orgotten the corresponding passage in El., i., 33 ; rf. R, x79. 8 pp. xo2 f, m4 f. mark, in Fechner's opinion, an advance in clearness of ex- position. 0 Gotllngmche gel. Anzeigen, 26 Juni I878, 826. ----------------------------------------------------------- XCVIII , Introduction against the DZ :' we may rejoin that there is, of course, a material sub- strate of the difference sensation, and that it may best be regarded as akin to that of the difference tone (of. the thermo-electric current m the thermopfie). This, differential process' will be stronger, the nearer to- gether the primary R stand in time; it will ,ncrease with increase of the difference of the two underlying nervous excitations; but it need not be set up by any and every d,fference between them. The physiological in- terpretation is thus fully adequate to the fact of the D/.. t It is true that the adequacy is hypothetical; but we really know nothing of the psychophys- ical representation of the DL, and must therefore fall back on hypoth- esis. For this very reason, however, Fechner should not appeal to the DZ in support of a particular interpretation of XVeber's Law. He him- self ,, denkt sich dieselbe als unmlttelbar abhangig yon dem Logarithmus des (dutch die Verhaltnissschwelle dvidierten) Verhaltmsses der belden Nervenerregungen: was allerdtngs eine etwas eigenthumliche Art von psychophys,scher Reprasentation emes psychlschen Actes ist." 2 The Zimens in lhe R., and Fechner's Re;My to Miiller.--Fechner, as the reader will have foreseen, holds fast by hm own opinions. "Gegen die Thatsache der Unterschiedsschxvelle," he says, "lasst sich nicht streiten; abet man kann versuchen, die ReizschwelIe dutch Rtickfuhrung auf die Unterschiedsschwelle zu eliminiren. Inzwmchen sind die dafur geltend gemachten Erfahrungen durchaus unbeweisend."a He reviews the sense departments, and argues that, at least in many cases (sound, taste, smell), the organic excitations may be presen.t without arousing sensation. It would be wrong to maintain, in the spirit of the D,fferenz- ansicht, that ', einfache Empfindungen uberhaupt nicht flit sich, sondern nut in sofern sic von anderen unterschieden werden, also als Compo- nenten yon Unterschiedsempfindungen, bestandf;ihig sind." After as before, then, the fact of the limen may play its part in the metric formula. 5 As regards the physiological interpretation of the Rœ, he writes: ,, em schwacher Reiz kann fur die Empfindung erstens dadurch vetloren gehen, doss er, wegen Erschopfung dutch dm iusseren Medien, schon gat n,cht bs zum Empfindungsnerven gelangt, zweitens dadurch, doss er wegen Erschopfung im Netyen selbst mcht bis zum Sensorium gelangt, drittens abet endhch dadurch, doss er, zum Sensorium gelangt, unter der innetch psychoplqysischen Schwelle bleibt."  That is to say: the existence of an Rœ may be clue, in certain cases, to the intervention of  GSttingische gel. Anzelgen, 26 Juni 878 , 827. C¾. Stumpf, Funke, Hermann's Hdbch., ifi, 2, 188o, 346 fl., 349, 359.  ]-d., 828 f. a R, 78 f.  bd., 97. s 2-bd., 83 f., 89, t94, x96 (of. G, 228, note), 204 f, 223. o œ4id., 235 if., esp 24o Tps., i., zo4; õ 4' Criticism xcix physical or physiological obstruction, but there is no evidence that it is always due to such causes. On the contrary, the proof offered is quite inadequate; so that the inner hmen, xvhose existence is vouched for on other grounds (results of physiological enquiry, facts of attention), is at least not imperilled by the physiological arguments. As regards the bracketing of the two limens, Fechner says: "wenn dos Princip der inneren Schwelle ftir Unterschiedsempfindungen besteht, so ist kern Grund, es fur einfache Empfindungen abzulehnen .... Eine Ansicht, welche dos Verschw,nden der hoheren Unterschmdsempfindung mir dem Verschwinden der niederen emfachen Empfindung unter einen gemein- samen psychophysischen Gesichtspunct zu fassen vermag, ist in erheb- lichem Vortheil vor emer gegentheiligen, welche es n,cht vetmug." l Here is a direct rebuttal of Mtiller's objections. Has Fechner, in the R., worked out his position n greater detail, or with more special refer- ence to the nature of the limen ? Let us see. The R. avowedly confines itself to a "Zuruckrufung der verschmdenen Modificationen, unter welchen dos Schwellengesetz auftritt," and to ,, Zusatzbemerkungen zu den frihern Betrachtungen." 2 F,rst comes the revmw of the senses, in the nterest of the RL, to which we have already referred. This is followed by an mportant paragraph on the ML. Given a complication of psychophysical conditions, a, b, c, d, . . , and the liminal value of c (the value correlated with a qualitative and quan- titative dtscriminabfiity o{ the mental process 7) will be not absolute but variable, changing wth change of the concomitant conditions a, b, d, . . Later, we are told that the fundamental psychophystcal formula take account of the Rœ and the Dœ, but not exp[icitly of the ML In strict- hess, the DL of the waking state should be translated into a corresponding gff. L, though the more the invading R exceed in intensity the preextstent E-mixture the more nearly does the pure Unterschiedsmassformel ap- proach to validity. And there has been no need, in practice, to recognise the DZ as an JffL. In the same way, the principle of the RL is com- plicated by the principle of the Mœ, though we can by no means do away with the Rœ. Theoretically or formally, it is a special case of the more general Mœ.  It is clear that Fechner is coming to think more and more of the The Rœ and the DL appear to be, both alike, limtting cases of the ML. x R., Sx if., esp. 54. Of Miiller's ' differential process ' Fechner remarks (t) that the analogies of the difference tone and the thermo-electnc current are not illumi- nating; and (2) that any process to which the difference sensation is proportional must=O when the sensation=O: there is no room for a Dœ: 253. a R., x77. a ]bd., I79 f.; P.S., iv., 2o7.  Id., 9z f.  œbd., 93- ----------------------------------------------------------- c Introduction The case of the OL is s,lnple enough: but wouM Fechner admit an A']' in the event ofa ps.chophysmallyempty sensorum ? Assuredly. Here s an argument winch he alleges as a "defimtlve Erledgung der Frage" of the tuner )?œ. "Mathemafisch tlefer gehend, hat slch (he ranere Empfindungsschwelle zur Sicherstellung ihres Daseins gat mcht erst auf dm Untei-schedsschwelle zu berufen; sondern folgt mathematlsch claraus, dasszuvorderst eme Relzschwelle, ohne emprsch constatirt zu sen, mathematsch nothwendg ausdem Weberschen Gesetz folgt, und zwar nicht bloss aus dem renen, sondern selbst aus dem mtsemen Abweichungen nach *ltillers Wese zusammengefassten."  The argument is none the less characteristm that Mtiller hmselfhad indicated the reply to be made to t.  But how s the œL an .l'ff ? The formalreductons worth very little. Hering and Mtiller, be t remembered, had challenged Fechner to show the compatlbfiity of theœ ith hmown system. Fechner now declares that "das Hervortreten des menschhchen Bewusstseins aus dem Allgemembewusstsem als emer davon unterschedbaren Besonderheit eben so an emer hnrechenden Erhebung des ihm unterhegenden psychophyslschen Processes uber den allgemenen Process hangt, als das unterscheidbare Hervortreten emer Sonderbestimmung unseres Bexx usst- seins an emer entsprechenden Bedingung nach dem Princp der Xhsch- ungsschwelle hangt. " Here we have the ansverto our question. The . corresponds to the first humanly conscious process differentiated fi'om the processes (of the same or of dfferent kinds) current n the general consciousness. As these processes never sink to the value o, the A'L must always be an ,rZ,--but an z}:rœ of what we may call the first order. Snce the , mxture ' of the .,I/'Z refers only to the processes of the general consciousness, and the . of the Elemente s st11=o, the 2?f_ may also be considered, as before, a hmiting case of the œ of the second order, of the human zlfff_. The reduction is real as regards the Jk'Zœ of the first, formal as regards that of the second order. The argument, then, is stratghtforward enough: but, of course, the previous questran remains, --the question why the differentiation from the general consciousness should involve a limen at all. The I44der View.--Our last quotation suggests, however, that we may bare been unfair to Fechner. May not the final explanatmn, ol which we are m search, be tound m hs connected treatment ot attentmn, of sleep and waking, of consciousness and unconsciousness ? For he declares in the El. that "de Verhaltnisse zwischen bexxusstem und un- bewusstem Vorstellungsleben, Schlaf und Wachen, allgememen und 1 I., 254; cf 204, 224, and 262, note. e G, 373 f-; rf. R.. 2o5f a R., e56 if. õ 4. Criticism ci besonderen Bewusstseinsphanomenen, kurz die allgemeinsten Verhalt- msse des Seelenlebens eine sehr enfache und befnedgende psychophy- ssche Reprasentation aufGruod derVoraussetzung, dass der Schwet- lenbegriff au f de psychophylsche Bewegung ubertragbar se, zulassen... Nach all' dem halte mh es mcht lur elne unsmhere Hypothese, sondern fur elne Foderung der ganzen thatsachllchen Sachlage, auf welcher wr zu fussen hahen, dass viehnehr de Empfindung yon der psychophysischen Thatigkeit, als dese vom Reze mq Stone der Fundamentalformel und Massformel abh.ng." These are words ot assurance, and t behoves us to consider the ewdence upon whmh the assurance rests. Fechner appeals, m the first place, to certain facts of attention anti inattenuou. We may become aware, n an after-im.xge, of an object which, as presented, dtd not come to conscmusness; we may not hear a question addressed to us, at the tme t s asked, but may recall t to mnd when we come out of our brovn study; the surgeon may see the blood flow before he has pierced the skin? All this means that "the psychophysical actwty, released anti represented by the sumulus, must exceed a certain degree of intensity, if it is to become conscious"; a ,, es geht etwas in uns fort, de psychophysische Thatigket, deren Functmn sie [Empfindungen, Vorstellungen] sind, und woran die Moghchkeit des Wederhervortrittes der Empfindung hangt, nach Massgabe als (he Osctllatmn des Lebens oder besondere innere oder ussere Anlgtsse die Bewegung winder uber rite Schwelle hebert." * Any nervous organ or structure may be the seat of psychophysmal actiwty; and this acm-ty, prowded the exctauon attain a certain intensny, must gve rse to sensa- tmn. Fechner wfil hear nothing ofa specml part of the nervous system, a cortex, or sensorlure m Muller's sense, to whmh the excitatton must first be transmitted, ,' Wit konnen . . ß den engeren Seelensitz als den Leibesthefi bezemhnen, worin dm psycbophysmchen Thatigkeiten de Schwelle zu uberstegen vermogen." s ,' Zu jeder Zest wrd es elne Stelle im Nervensysteme, ß ß ß respecnv Gehm, geben, wo de psychophyssche Thangket am starksten st, und bier kann man den jeweiligen . . . Seelenstz m engsten Sinne suchen. Von diesem Puncte aus wetden die Bewegungen mt abnehmender Starke dutch den ganzen Tract nervoser Fasern im Gehirne, Ruckenmarke, Nerven gehen, der damt in Verbmdung steht, und m sowet se uber enen gewtssen Grad der Starke, dm Schwelle reinhen, auch beitragen, alas Bewusstseln uber the Schwelle zu hebert . . . Ob nun Ruckenmark und Nerv auch nach Abtrennung yore Gehirne noch psychische Functmnen vermittela konnen, wrd darauf ankommen, ob se nachher noch psychophyssche Bewegungen  El.n,435. a bd., 438.  ./d., 432 f Ct. Wundt, P P., m, t9o 3, 64  Zbd-, 439.  Zbtd, 39 . ----------------------------------------------------------- cii 2rntraduction yon hmreichender Starke, um die Schwelle zu ubersteigen, erzeugen Is not the circle amazing ? Let us quote Mtiller. "Fechner's theory of the seat of mind is tenable only if Fechner's psychophysical law is tenable; for only on the basis of th,s law can the theory accotint for the cases in vhich excitation is present somewhere in our nervous system, without craning to consciousness in a mental state. On the other hand, hm assertion that various facts of the sensory attention, etc., furnish the psychophyscal foundation of the A'Z, and so of Webr's Law, rests upon the assumptmn that his theory of the seat of mind is correct, i.e, that tte nature and locality of the nervous organs in which an excitation is set up are entirely irrelevant for the question, whether the nervous excita- tion shall or shall not give rise to conscious sensation; for Olaly on this assumptmn can one argue unconditionally, from the cases where nervous excitation is present vithout a corresponding conscious sensation, that the bodily activities which immediately nnderlie sensalton must exceed a certain liminal value, if they are to arouse conscious sensalton at all . . . And yet Fechner thinks himself justified, on the ground that certain facts of the sensory attention appear--if we assume the correct- ness of a theory of the seat of mind which itself depends upon the cor- rectness of Fechner's psychophysical law--to furrash the psychophysical foundation of the _RZ and of Weber's Law, in making the statement that his psychophysical interpretation of the metric formula is , not an inse- cure hypothesis, but a reqmrement of the whole body of empirical facts upon which psychophysms must be based '! " Crculanty could hardly go farther. In face of it, we need not follow Fechner through the chapters on sleep and waking, on partial sleep and attention, and on the relation between the general conscmusness and its particular phenomena;  it is enough to refer again to Mtiller's criticism.  This is not to say that the chapters tn question are not worth reading: on the contrary, they, together with the chapter on the measure of bodily activity which they presuppose? form one of the most interesting and instructive parts of the Elemente. The circle n Fechner's thinking is far removed from any logical inaccuracy of the vulgar sort. It is rather due--if we may use a favourite word of Fechner's own--to the ' solid- arity' of his system, to the organic interdependency of all its parts, to El., ii., 4e7. a G., 35 ø f. El., ix., 439 if-, 449 if-, 452 if-; rf.. 5x9 if., 526 if. G., 352 if.  El., i., 2i fl. Lasswitz refers to the chapters on Energy and on the Seat of Mind as "Bei- spiele fur de meisterhafte Klarheit und Durchsmhtigkeit, mir welcher Fochner schwierige Fragen zu behandeln verstand:" G T. Fechner, 82. õ 4. Critœcism cii[ the fact that it is a ' tree' and not a bundle of sticks. ,, Reasoning at every step he treads, Man yet mistakes the way :" the hnes might have been written of Fechner. But did Fechner acknowledge the circle, when it was pointed out ? Naturally not. The R. is concerned only to meet Malllet's objections, to offer in its turn objections to Muller's positive views, and to repeat, in fuller and more precise form, the exposition of the Elemente. t The soli- darity of his system blinds Fechner here, as it blinded him before. Let us take a single instance. Muller had remarked that, on Fechner's theory of the seat of mind, a ganglion which regulates, say, the peristaltic move- ments of the intestine would, if the excitation transcended a certain liminal value, form part of the "engeren Seelensitz"just as truly as a region of the ports or of the cortex. Fechner replies, a httle indignantly, that he has already stated "dass Reize, die durch den weiteren Seelen- sitz (d. h. den K6rper ausser den engeren) verlaufen, mcht eher Empfind- ung, Bewusstsem erwecken, als bis sic zum engeren Seelensitz gelangt sind. " This is quite true; but tt does not meet Mfaller's objection. For what is the ',engere Seelensitz?" Fechner, however, continues. "Mag in einem Darmganghon die psychophysische Erregung uber der Schwelle sein, so bleibt sic uns unbewusst, so lange nicht der ganze Tract yon Erregungen, der sm mir dem Gehirn verbindet, reit uber der Schwelle ist: "'and Muller ought to have known this, since it is to be found in the chapter on Psychophysische Continuitt und Discontlnuit.t. a But we find in that chapter that a principal wave (individual conscious- ness), which runs its course continuously above the principal hmen, may carry surface waves, which are discontinuous above and continuous only below their own hmen. The discontinuity means simply that the cor- responding mental processes are &scnminable within one and the same individual consciousness? How, then, is Miller answered ? Indeed, the reader who, checked by Fechner's reproachful words, returns to the inner psychophysics of the Elemente with the idea that Mailer has done the psychophysical theory njustice, wfil lay the book down with the renewed conviction that Muller is right. The fact seems to be that Fechner, in 882, s inclining to draw the limits of the "engeren Seelen- sttz" more narrowly the. he had done in 86o,--while he steadily refuses to admit any change in His general attitude to the question. The Limens in lhe Massprincœpien.--It remains now to consider the treatment of the two limens m the essay of 887, Ueber die psychischen  See 242 fl., 269 if., 284 if.;  :I8, 266 fl. The I. S. has little to say on these matters: see 6 f., 7o f., 85 if., 97 f., 2x8 f.  R., 243, note; El, ii., 39 I. a El., ii., 526 if.  Ibd., 54o. ----------------------------------------------------------- Massprincpien und das WeberscheGesetz We have already sketched the course of the argument, and shown how Fechner advances from tile measurement of dfference sensations to that of sensation differences, and from lhe measurement of sensation differences to that of sensations? We begin at once, t}lerefore, wth the DZ. The/9/5, says Fechner, "bedeutet unstreitig" a Schatzungsfeh]er, an error of estimation. When the ]? upon whmh . of different magnitude depend, and consequently these .5  themselves, do not coincide n time and (or) space, the estmmtmn of their differeuce is attended by acon- stant error. The non-coincidence in tme and space affects both the directTon and the magmtude of the error of estimation. 'I'he error of direction can be eliminated, if we take the me.qn result of series in xvhich temporal and spatial positions have been reversed. The error of magni- tude (so to say) cannot be eliminated. If intensive Sate to be comparect at all, they must be compared under condTtmns of temporal or spatial difference: otherwise, they run together. Tile exmtence of the /9/5. is accordTngly due to the "mcht beseitigbare zetlich-raumhche Nichtcoin- cideuz der ReTze, mlthin psychophysTschen Erregungeu." The theory is supported by the following arguments. (a) The tact of constant errors of time and space is universally ad- mitted; the present theory sets these errors m their true light. For, after elimination of errors of direction, it still remains ,, beiderlei Lagen gemein, dass eine Nichtcoincidenz iiberhatfil besteht; und hieran hangt auch etwas gemeinsames, dass n.mlich eine Abweichung yon der wahren Grosse des Unterschiedes startfinder, worunter die Thaisache der Unter- schmdsschwelle nur als Grenzfall begriften ist." (b) As a matter of experience, the magnitnde of the /9L depends essentially upon the tem- poral and spatial relations of R, increasing (other things equal) with the temporal and spatial difference of J?. (c) The theory is directly con- firmed by the results of experiments upon extensive S. Take two rods, the one of oo, the other of o space units. Lay them In the same straight hne, so that the one forms the extension of the other. You will not be able--such, at least, is the general rule--to tell them apart. Now lay the one over the other: the difference becomes notmeable. The result may be transferred at once to the sphere of intensive S', wilere ex- periments of the kind are not possible. It may, perhaps, be objected  P. S, iv, i6i if. The first part of Fechner's essay s, as we have noted, taken up wth a criticism of Elsas' Ueber die Psychophyslk, x886 Elsas rephes to Fechner in the Philos. Monatshefte, xmv, I$88, 129 if. In both works, Elsas strenuously mmntmns the physiological, or rather the physical character of the JPZandthegOZ. SeeUe. d. Ps.,4ff.; Ph. Mh., x45f-, x5 x ff-  See pp xxxv. if. above.  4. Crzticzsz that, when we compare the two rods, we are merely uncertain as to whmh of them Ts tile longer, whereas, when we compare intensive S', we pas a posittve judgment of equality. But thTslsnot true. There is the same uncertainty of Glelchschatzung in tile mental sphere as there is of Glemhl,eltsbestlmmung in the physTcal.  What now of the relatton of the two llmens ? TheDœislndisputably an, mnerhmen; the two S lie before us, for dmcrlminatlon, andif the S are present, theTr psychophysmal conditious must be reahsed. The same explanation cannot hold for the RL, where only one S is involved. ,, Allera es wlrd sich zelgen Inssen, dass, wenn es auch Falle geben kann, wo der Relz sich wlrkhch nicht bis zum Sensorium fortpflanzt (physio- logical explanation), doch auch in dem Falle, wo er sich bis dahin fort- pflanzt, aus einem anrleren Grunde als dem der zeltlich-raumlichen Nichtcolncidenz eme gewisse Grosse der, durch den Relz erweckten, ps. ph. Erregung, kurz inhere oder ps. ph. Schwelle ,hberstiegen werden muss, un die zugehorige Empfindung bemerkhch werden zu Inssen."  The explanation is, in principle, famlhar to us from the R. When an R reaches the sensorturn, it finds some sort of psychophyslcal excitation already in progress. We have therefore to distinguish the pre-exastent , the invading E, and the concomitant E,--the persistence of the first under the action of the second. The pre-existent E is a highly complex affair, a resultant of the current train of ideas, of some form of common feeling, of the action ol foreign stimuli. If, now, the invading 7 falls below a certain degree of intensity, it "geht unbewusst in dem vorging- igen resp. mtgehenden Bewusstseinszustande auf." The pre-existent consciousness is intensified, or qualitatively modified, but the new E is not separately remarked. A band may not be heard amid the clamor of an excited crowd, although the instruments add considerably to the total noise. We may not notice the lighting of a concert hall; nevertheless, our hearing of the music is "etwas modxficirt" by the degree of illumina- tion. In this sense, then, there is no izner lznen: every psychophysIcal xcitation, great or small, serx's to enhance the activity of consciousness. ontrariwise, if the S that corresponds to the invading .' is to be ,, besonders auffassbar," the Emust transcend a certain limmal intensity. If the band is to be heard, Tt must play with a certain loudness; the air is then "elne ihrer Qnalitit nach unterscheidbar gewordene psychische Erregung," although the concomitant E (the noise of the mob) may still give the tones a rough and harsh character. In this sense there 2s az inner limen, an Mœ, the passage of which determines the separate effectiveness of the invading œ for consciousness. As the S of Weber's Law and the psychophysical formulae are always and everywhere "die 1 p.S., v., 188 if.  [bd., 202 f. ----------------------------------------------------------- cvi rntroduct ion besonders ouffassbaren Empfindungen," the recognition of this inner lmen is inevitable? But, if the ,, Mischungsschwelle an die Stelle der Rezschwelle trltt," the )?œ Is a Dœ ! Yes: not a Dœ proper, but a Da/'L, an Unterschleds- mmchungsschwelle. 2 Different principles are involved in the two cases. The principle of the limen m the 2)œ is the temporal or spatial thsparty of the two R compared. The principle of the bmen in the R/. or DI/_rL is the necessary competition of the invading Z' with pre-existent œ. This latter principle holds even in cases where there is no foregoing consciousness: when a chfid is born, e.g-., or when one wakes out of a dreamless sleep. For ,,soll smh alas Bewusstsein des Menschen als Sonderbewusstsein aus dem me schlafenden Bewusstsein des allgemeinen Gemtes, der an alas allgememe [psychophysische] System geknupft st, herausheben, so muss (lle ps. ph. Erregung des M'enschen em gewmses Verhaltmss zur ps. ph. Erregung des allgemeinen Systems, worein er eingetaucht ist, ubersteigen, welches unter alas Prmcp der Mischungs- schwelle trm."  And yet the fact of the Rœ is ,,der Thaisache der Unterscheds- schwelle analog ! " It is surely true, on the contrary, that the two limens are divorced as widely as Muller hmselfconld desire. The determina- tion of a DE, may be complicated by all manner of pre-existent trains of deas and common feeling and foreign stimuli: yet, m prin- ciple, the error ot estimation of the 29 depends simply and solely upon the temporal and spatial dinpanty of rheA'. That is one thing. Every invading œ has to fight for its separate existence with the rest of con- sclousnessorwtth the general conscousness, and loses strength in the st'uggle. That is another thing. The 9œ is pure Fechuer. The or DVœ m--is t not ?--pure Herbart. Remember that it was Herbart who introduced the notion of the hmen into psychology. utzta..y. () 7'he ]-zm'ns.--Here, as so often, .F_hner seems to have caught a ghmpse of the right path, while he fol]owed the wrong. tie felt, from the first, that the two limens should go together; and the fee]ingpersmted to the end. Yet he brackets them m the El.m order to prove xvhat cannot be proved, the existence of an inner.h'œ, while he treats them separately, the one m the Massformel, the other in the Unterschiedsmassformel. When he finds another way of derivin an inner A'œ, he lets the DL take its own course, making no more effort to keep it in touch with the ]?L than is expressed in the single word  P. S, iv, 2o 3 if.; }R., 79 f- 2 p. S, iv., 207. One might also say, of course, a QAffZ, a quotmnt nixture limen. a p.S., iv., 2xx f.  Ibrd, 96.  I,d., 9o.  Sturnpf. Tps, i, 387 f. õ 5. Our Debt to Fechncr cvli ,analogous.' On the basis of the Elemente, Muller was justified in saying that Fechner had confused things that were totally different. On the basis of the same Elemente--and still more on the basis of the sub- sequent treatises--Ebbinghaus is equally justified in asking: "wie kann man nut, wenn man die Dlnge ohne Hintergedanken betrachtet, ganz und gat Zusammengehoriges so auseinanderreissen ?" \Ve can say hut little for a theory that exposes itself to such contradictory objections. (2) lite ]>sychoiShysical Xyslen.--" When Fechner maintains," says Muller in his recapitulatmn, "that certain phenomena of the sensory at- tention and other hke facts are compatible only with the psychophysical interpretation of the Rœ and of Weber's Law, we can confidently reply that this assertion rests upon a number of assumptions that are in part untenable, in part at any rate unproved: on the assumption, e..ff., that Fechner's theory of the seat of mind and of the significance of the inter- connection of all the nutritive processes in the human body = is correct, that during sleep consciousness but not psychophysical actiwty s wholly in abeyance, etc. With the same right with which Fechner takes his stand upon these assumptxons, we might ourselves, on'the basis of other assumptions, assert that only the physiological vew of Weber's Law affords a satisfactory explanation of the phenomena of the sensory at- tention, of sleep and waking, etc"a The reader will not hesitate to subscribe to this criticism. ,, Kern emziger seiner [Fechner's] Gedanken," says Ebbmghaus, "hat sich als stmhhaltig erwiesen. " "Wohlan," Fechner would have answered, "so wet es--the system--eben feht schlagt, hat man es zu verlassen."  õ 5. Our Debt to lYeeither.--We have declined to admit Fech- ner's contention that the S is a measurable magnitude, the sum of a number of S-units; we have, vith some little hesitation, admit- ted that all j. n. d. of S are equal, coupling our admission with the proviso that we shall. be allowed presently to define the j. n. d. in our own way; we have rejected, once and for all, the psychophysi- cal interpretation of Webefts Law. It would seem, then, that the building  which Fechner planned and erected is for us a mere heap of ruins; that the tree to which he likened his svstem has been rooted up and laid prostrate. Shall we let this inference pass, dismissing the "dear old man . . with his patient * whim- sies" for other and "more nutritious objects of attention "?s Z., L, 472. Psych., i., 57 . Patent ? El., i., 2 if. a G., 365 . Cf. P.S. iv., x87. 0 I. S., 2t 5, Nachwort. 8 James, Psych., i., I89o, 549. ----------------------------------------------------------- cvid fntroductwn In the author's belief, such a course would not only be unjust to Fechner, but would also argue an extreme dmness of scientific vision on the part of the man who followed it. Here are the reasons. () Fechner was the Schdpfer, the originator, the creator of psychophysics. \Veber's experiments were there, and would doubtless have borne fruit; Hering, we may suppose, vould have written his Bekrage and his Lichtsinn, Helmholtz xvould certainly have written his Optik and his Tonempfindungen, Wundt would in all likelihood have written the Physiologische Psychologie and founded his laboratory, if there had been no Fechner. But there can be no donbt whatsoever that, without Fechner's creative xvork, without his demarcation of the province of psychophysics as a separate science, the progress of experimental psychology, and therefore of psychology at large, xvould have been sorely delayed. Rightly to appreciate Fechner's originality, one must know the scantiness of the materials that lay to his hand in 85o, and one must realise the inadequacy, practical and theoretical, of HerbarCs formula. Rightly to appreciate his historical import- ance, one must remember for how many years he stood at the centre and focus of psychophysical activity. There is another point. Fechner's work xvas systematic; psychophysics xvas born full-armed and mature. The system covered a varange, swept together a vast body of hitherto dis- connected facts. It took account of everything, from the classi- fication of the stars to the phenomena of dreams, from the come- and-go of memory images to the emergence of mind out of the all- pervading world consciousness. But a system invites criticism, not from a few specialists, but from all the workers in every field of the science. We know that the criticism was forthcoming. And no one, surely, will be found to say that the critical work of Wundt and Hering and Muller and Delbeeuf has been merely negative in result, that the doctrine of the Elemente has not provoked its critics to reconstruction. Their own utterances should be decisive. In fine, then, we are indebted to Fechner, first, because in founding psychophysics he paved the way for experimental psychology, and, secondly, because he threw his conclusions into õ 5. Our Debt to 'cchncr cix a form that attracted widespread attention and challenged the criticism of men of very varied scientific interests. It is important that the student, xvbo is naturally influenced by' James' estimate of Fechner and of psychophyscs, should understand the hgh esteem in which Fechner is held--even in hm own country. We have already quoted Wundt's apprecmtion in the Vorlesungen of 863.  In 887 \¾undt writes: "Fechner . . . st der Begrender der experimen- tellen Psychologie geworden. Die Psychophysk, dmer anbaute, war nur die erste Eroberung auf emem Felde, dessen weirere Bestznahme erhebliche Schvierigketen nicht mehr bteten konnte, nachdem enmal dieset Anfang gemacht war :" P.S., iv.. 477; of. G. T. Fechner, I9O, 49, 54, etc. So Kulpe: "wit sehen m der Fechnerschen Behauptung und Durchfuhrung funcuoneller Verhfitntsse zwmchen psychischen und physschen Processen die endguluge Begrtindung ether exacten Psychol- ogle .... All' dieser Unvollkommenhet und Unwissenschafthchkeit [der alteren Psychologie] hat Fechner im Pnncp ein Ende gemacht. Er hat uns den Weg gezeigt, auf dem aileen . . . psychologmche Gesetze in der strengen Bedeutung dmses Wortes erreicht wetden konnen:" Arch, f. d. Gesch. d. Phil., vt., 895, 78 f.; of. I8 f. and Lasswitz, G. T. Fechner, 84, 89 if., 9 I, etc. It is needless to multiply references: Fechner's critics are practically unammous n their recognition of Fech- ner's general services to experimental psychology;  and t is to the memory of Fechner, "der yon allen verehrte abet yon allen auch angegrtffene Grets" (Stumpf, Tps., i., 66), that Ebbinghaus dedicates hs recent Grundzuge. Even Delbceuf, who writes in a moment of pess,msm that "les hypotheses scentlfiques reconnues fausses . . dmparmssent presque toujours dans un profond oubl sans lmsser plus de traces que les neges d'antan," eveo Delbceuf declares that "le mrte de Fechner est au- dessus de route dmcussion" (Examen, wL, 2). James alone refuses to swell the chorus of praise. "The only amus- ing part oft is that Fechner's crmcs should always feel bound, after smiting hm theories hp and thigh and leawng not a stink of them stand- mg [szc], to wind up by saying that nevertheless to him belongs the inzfierishable fflory of first formulating them and thereby turning psychology into an exacZ scienc (!) ": Psych., i., 549. Thin is not pre- cmely what the critics say. That apart, however, we may reply, on the personal side, that German criticism is not remarkable for ts amemtms, and that, although Fechner's own pupfis--like Herng and Lotze--mght let their gratitude colour their polemm, other cntms would hardly show 1 See p. xlvi. above. - = See e.g., Foucault, Psychophysique, 9o, 484. ----------------------------------------------------------- Introduction the respect they shov to Fechner unless they meant it; and, on the material sde, that the rightness or wrongness of a man's theories does not of ltsetf decide his value for science. We return later on to James' own estimate of Fechner's work. Let us now consider the value of that work in its systematic aspect. Scientificliterature is enrmhed in two ways: h tile wrtmgofmono- graphs and by the wrmng of systematic treatuses. The two activities are, on the average, characteristc of two dfferent types of mind. We expect that so-and-so will turn out, every fexv years, a new bit of work which wfil carry our knowledge a step farther into some hitherto unex- plored region of fact; we appeal to so-and-so for a correct mapping of the fields already explored; and, as a rule, we do not look to the first for system or to the second for original ideas. Now the monographer has one very obvious advantage over the systematst. Systems, in an age of scientific activity, are out of date almost as soon as they are pub- lished; the next month's magazines may necessitate a recasting or rewriting. The investigator, on the other hand, provided that he has followed a critical method, may hope that his contribution to science x 11 be permanent. Thin advantage is objective, and cannot be done away with. But themonographerhasa further, subjective advantage. Ever since the revival of science, the birth of a ' new ' physics and biology and psychology, the tendency has been grooving to look upon the systemattar as a worker at second hand, and to regard the investigator as the true and typical man of science. We may acknowledge, fully and cheerfully, the measure of truth whmh this dea contains; but xve should not let the idea run away with us. A system which is competentlywrltten repre- sents as much ,psychsche Arbeit'as mauy monographs, and may be every whit as valuable on the critical and comparative as the mono- graphs are on the constructive sde. The distinction which we have drawn between the two kinds of scientific achievement holds for the main body of scmntfic workers. Tile rule admits of many exceptions, and of exceptions of all degrees. The best men, of course, are both investigators and system makers. Fechnerhimself, and Fechner's successor, Wundt, wouldhave attained scientfic eminence by original research, if their systematic work had never been doue, or again by the writing of the Psychophysik and the Physlologische Psychologie, if they had never published their special investigations. What the author wishes to emphaslse now, however, is the value of the Elemente as a system. ¾Ve have found that the leading ideas of the system are wrong. Well ! a pioneer does not always strike the most practicable path. But suppose that its leading ideas had been rght. It must still have been recast within ten years. Does it so much õ 5. Our Debt to Fechncv cxi matter that the ideas have not stood the test of criticism? The important thing s that the system xas there to criticise; that Fechner laid hs new science before his contemporaries in complete and systematic form, thereby challenging the critical fire of philosophers, psychologists and physiologists. even ofphysmistsandmathematmlans. A negative merit ? On the .contrary. ltlsldle to speculate on what might have hppenedif Fechner had been rght: weare, perhaps, not so very sure ourselves of what the final 'right' of quantitative psychology may be. But that Fechner's thought was so wide-reaching, ts expressran so 'solldary,' ths was a positive virtue in the representative of nox el standpoints and untried methods.  So far we have spokenngeueratterms. To make tile matter concrete, let us compare Fechner xwth Wundt. Fechner's prxncpal object and interestm the Elemente is the estabhshment of an inner psychophysms: "die aussere Psychophysik ist . . . nur die Unterlage und Vorbereitung ftir die tiefer fuhrende innere Psychophysik "(El., ii., 377). And inner psy- chophysics is the exact science of the relations of dependency between psy- chophysicaI and mental processes,--typmalty, between E and S. Wundt, in x893 , describes his physiological psychology as "eine Wissenschaft, welche die Bertihrungspunkte des lnneren und ausseren Lebens zu ihrem Objekte hat," and declares that ', alle ihre Untersuchungen werden endhch in der Frage gipfeln, wie ausseres und inneres Dasein in lhrem letzten Grunde mir einander zusammenhangen" (P. P., i., x; of. 6, and ii., 644 if). Is not Wundt's avowed purpose a direct continuation of Fechner's work ? Truly, there is a great difference in the manner of execution. Fechner, although he "was gifted with unusual talent for subjective observation, "= was not a psychologist; he has no system of psychology. "Seine ganze Psychologie, so welt sic sich auf eine Inter- pretation empinscher Thatsachen einlasst, besteht in der Anwendung des Schwellenbegnffs auf die verschiedensten psychischen Vorgange . . . Das, was de eigentliche Aufgabe der psychologischen Analyse 1st, die Aufzeigung der Mannigfaltigkelt und Verschiedenheit der psychischen Vorgange, bleibt . . . vollig im Hntergrund .... Das ganze Interesse Fechners gehort eben mcht der Psychologle als solcher an" (Wundt, G. T Fechner, 83 f.). Wundt, on the other hand, is nothing if not psycho- logical; it is he who introduces the phrase 'experimental psychology' into the hterature (Beltrage, 86,m.); and he re, beyond all questran, the first psychologist of the 'new psychology.' a There m, then, a great 1 Cf. Fechner's own summary of his work (1882) in W. Preyer, Wins. Bnefe, 189o, 225.  See vol i, I. M, 389 . s He, and not Lotze  The student who turns from Ladd's preface in Lotze's Outhnes of Psychology (IS$6, w f.)to Lotze himself, th the hope of finding ----------------------------------------------------------- cxii Introduction difference between the El. of x86o, and theP. P. of 1893; Fechner is driving at nature philosophy and philosophy of religion, Wundt at psychology. None the less, Wundt is indued with Fechner's mantle. The founder of modern psychology is the direct heir and successor of the creator of psychophysms. t VCe must, theretYre, take issue xv]th James when he declares that "Fechner's book was the starting point of a new department of literature, which ]t would be perhaps impossd)le to match for the qualities of thoroughness and subtlety, but ofxvhich, in the humble opinion of the present writer, the proper psychological outcome is just riorhinos" (Psych, i., 534). In the first place, on James' oxvn showing,--for he says that Fechner set out to establish a numerical relation between the mental and the physmal worlds,--there is no reason why we should look for any psychological outcome. Fechner was a psychophysm]st, not a psycholo- gist. When he Iounded psychophysms, he &d all that he set out to do. Secondly, however, if ]t be urged that the two sciences are so mt,mately related that some psychological outcome ought to have resulted, we reply that Fechner rendered essenual service to psychology, though a service vhlch it is not easy to estimate m any sort of quantitative way, by the impetus winch he gave to psychologmal expenmentatlon at large." And thirdly we may point out that James himself recognlses one aspect of this service to psychology. "The psychophysic law controversy has prompted a good many series of observations on sense-discrimination, and has made &scusslon o[ them very rigorous" (534). "Incidentally to the dlscussmn of it . . . a great many particular facts have been discovered about dscrimmation xvhich merit a place in this chapter" (539). But the chapter is a chapter of a Psychology, and is headed ' Discrimination and Comparxson ' ! (2) How much of Fechner's completed work is valuable to us, as experimental psychologists, at the present day? What the firstfruits of modern psychology, will assuredly be &sappointed. Lotze is a factor in the rise of experimental psychology, his influence was favourable, and he made a notable contribution to the science m his theory of local signs. But, on the whole, he is rather surprisingly unmodern. Really, Lotze is a metaphysician with physmlogical training,--as Herbart s a metaphysmmn versed in mathematics.  The matter s, m the author's opinion, somewhat overstated by Lasswitz, 90, and not quite correctly stated by Kulpe, Arch, etc., I8 3 f.--The introductory pages of the P. P., i., 9o, are much more distinctly psychological (and therefore less psychophymcal) m tone than those of the earlier editxon: see esp. 3 f. The change is natural: Wundt is, and has always been, a psychologist; and the riper hs genius, the farther does he travel from Fechner. After as before, however, the statement holds that Wundt s Fechner's direct successor. ' Wundt, P. P., i., 19o2, 7. õ 5. Otzr DebX to Fechcr cxiii parts of the building still stand ? What shoots from the tree are still living ? First and foremost, we owe to Fechner the comprehensive development and theoretical interpretation of the metric methods. The method of just noticeable differences seems to have been employed first by Delezenne (826); then. much more extensively and successfully, by E. H. \¾eber (83 and later). The method of right and wrong cases is due to Vierordt (Hegelmayer, 85= ). The method of average error was worked out by Fechner and Volkmann (856-7). All three methods are discussed in the Elemente,  with general and special cautions. rules for the ellm- ination of constant errors, formulae for the mathematical evalu- ation of results, etc.. etc. Much has been done since Fechner's day: we have new methods, new refinements of method, above all, a better understanding of the interrelations of the methods. In principle, however, our current laboratory vork is based upon the xvork of the Elemente, and the student who enters upon quantitative psychology is entering the school of Fechner. = Secondly. we owe to Fechner the concept of the DL, and the thorough exploitation of the differential sensitivity. It is, per- haps, hardly too much to say, with Ktilpe, that "er hat . . . in der Unterschiedsempfindlichkeit die Fkhigkeit entdeckt, &e uns zu einer allgemein giltigen Analyse unserer inneren Vorgange anleitet." a At any rate. the advance which psychological analysis has made in the last forty years--an advance which is unparal- leled in the history of psychology--is referable in large measure to the introduction of the DL as a working concept. Thirdly, we owe to Fechner a number oœ psychophysical inves- tigations, which are important both extrinsically, for their results, but also and more especially intrinsically, as undertaken with an overt psychophysical purpose and carried out by means of the psychophysical metric methods. Fechner employed the method  Plateau's method of mean gradations (xvorked out, in the rough, about ]852 ) was unknown to Fechner at this time, though t is in some sort anlacipated by Fechner's reference to the classification of the fixed stars. In the I. S., he wel- comes the new method, and subjects Delbeuf's experiments to a critical examina. tmn: 22, 178 fl.; of. W. Preyer, Wiss Briefe, 89o , lo 9. a Cf. Foucault, Psychophysique, 9o, 4, 483 f. 8 Arch., etc., ----------------------------------------------------------- cxiv Introduction of just noticeable 4ifferences in the spheres of "intensive light sensation, visual measurement and temperature measurement," that of right and wrong cases in his elaborate work with lifted weights, and that of average error in the spheres of visual measurement and tactual measurement. Fourthly, we owe to Fechner the sole conception of mental measurement that has stood the test of 'inside' criticism: the idea of measuring S by laying-off units of its own kind, and of standardising the units by aid of their correlated R. The thesis that equally noticeable (including 'just' noticeable) differences of S are equal, i.e., may be employed as S-units, is, as we shall presently see, accepted by the majority of experimental psycholo- gists at the present time. We do not, of course,--the point has been made several times in vhat precedes,--regard the single S as a sum of S-pieces, or the S-unit as a little bit of a larger S-mag- nitude. Fechner did: though Fechner, too, had floating ideas of 'distance' measurements in psychophysics. But our modern view is simply a reinterpretation of Fechner's Massprincip, not an entirely new view, put in place of Fechner's. The value of Fechner's work on the metric methods cannot be ques- tioned: see G. E. Muller, G., 45; Wundt, P. P., i., I893, 34I; 19o2, 475. We may regret the non-appearance of the Massmethoden, but we probably have its essentials in the R. and the Massprinctpten. It could hardly have ncreased our obligaUons to Fechner in this regard. The one positive mistake that Fechner made was his overestimation of Weber's Law. There can be no doubt that he exaggerated its psy- chophysical importance, its range of validity, and the degree of accuracy with which it can be formulated. Let us be clear, however, that in all this Fechner made no error of principle. He was simply wrong in fact. When he said that Weber's Law is a findamental law of psychophysies, he was guilty of overhasty generalisation, of inadequate induction,--but of nothing worse (Kulpe, Arch., etc.,  82; Lasswitz, G. T. Fechner, 86). And he himself insists, over and over again, that his principle of mental measurement is independent of Weber's Law. See Fichte's Z., I858, 8 f.; El.,' i., 65; ii., 33: "[es] lasst sich das ganze Massprmmp vom Weberschen Gesetz unabhngg darstellen," and the Verallgemeinerung, 19 if.; R., 333: "dieses Mass setzt keineswegs prinmpell und wesent- lich die Gdltigkext des Weberschen Gezetzes voraus"; I. S., 7; P- S., iv., I8X,87, 93. At the beginning and end of his work, in I858 and m õ 5. Our Debt to Fechner cxv 887, he sounds the same note of warning. ,' Auch hat die Unteruch- ung im Interesse der moglichsten Verallgemeinerung des Masses hiernach kemeswegs wesenthch darauf auszugehen, das Webersche Gesetz moghchst zu verallgemeinern, was lecht eme bedenkhche Neigung mit- fuhren mochte, es uber die yon Natur gesteckten Granzen hinaus zu verallgemeinern, oder Bedenken hervorrufen mochte, dass es zu hebe des Masses daruber hinaus verallgemeinert worden sey, sondern man wird ganz unbetangen fragen konnen und zu fragen haben, wie welt recht es, wie weir reicht as mcht; denn auch dahin, wohm es nicht recht, reichen doch die drei Methoden, die dem Masse diehen und somtt das Mass" (Fichte's Z., xxxfi., I9); of. P.S., iv., 87. He lad extreme emphasis upon Weber's Law . so that Muller remarks that "[Fechner] vxellemht allzu sehr Ctbersieht, wie wemg sen Name als Begfunder der Psychophysk yon der Rtchngkeit seiner Deutung des Weberschen Gesetzes abhgngt" (Gott. gel. Anz., 1878, 836). Buthe never pruned his Massprincp to the vahdity of Weber's Laxv. When, therefore, James asserts (Psych., i., 545) that "it is in the theo- retic interpretanon of Weber's Law that Fechner's ortgmahty excluswely consists," he is confusing fact with principle, and thus doing Fechner a palpable injustice. Fechner's orginahty consmrs in his endearour after a psychlsches Masspnncp, and he had formulated all lns leading xdeas before he ht upon Weber's generalisation (El., ii., 558).  As for the work that grew out ot and clustered round the Elemente, ,, those xvho desire this dreadful hterature," says James, "can find it; it has a ' disciplinary value'; but I will not even enumerate it in a foot- note "(549)- Whether or not a hterature is 'dreadful' to one depends, of course, on the measure of interest one takes m the subject matter: James does not find the literature of space perception dreadful, and the 5o pp. of his ch. xx. gve footnotes galore. Psychophysical hterature is far from easy. But it is largely controversial xn form, and the aver- age reader enjoys controversy. What is stfil better: the chief expositors of the science have been endowed with a saving sense oi humour. Wundt says of Fechner that "vxellemht hat Niemand m seroera Leben mehr gestritten als er, und gewms hat Nxemand weniger Fetnde gehabt als er" (P.S., iv., 476). If we had this single fact to go upon, and knew nothing at all of Dr. Mses, we mght be sure that Fechner had humour. One need not read far to find it. Delbeeuf had it, too; and Wundt has it, although he was once" le professeur sdrieux, qui ne ba- x So far as the author is aware, Fechner never, of his own initiative, refers to Weber's Law as" the psychophysic law:" ct. James, 533; Wundt, P. P., i, 9o2, 496: though in the heat of controversy he accepts the phrase from Aubert; Ber etc., 864, I if. ----------------------------------------------------------- cxvi Introduction dine pas" The only man of eminence who, if we may venture to judge in so dehcate a matter, is perhaps lacking in humour m Muller: and Malllet makes up by thoroughness. Remembrance of this lack, be it noted, will take the sung from a good deal of Mtiller's crlnclsm. Small matters t And yet James' Principles is so great a work that its lightest words carry weight ;1 and the author is convinced that the particular words which he has been discussing have done real harm to the catme of experimental psychology in America. Young students be urged to ' plough through the difficulties ' of Fechner's books, if they are presently to become psychologsts: and James' critmmm, which mainly a criticism of temperament and not of reason, gives them an ex- cuse to shirk these difficulties. Maxima debetur puerto reverenna. õ6. l,e½ontntction--The theory of mental measurement which this book accepts has been set forth in Pt. i., pp. xxi. if. Its cardinal points are () the bracketing of the two lindens as facts of friction in the neural machine, and 2) the substitution of sense distance for absolute sensation magnitude. The limens thus become irrelevant to Weber's Law,--except in so far as the DL is an instrument of analysis at large; and Weber's Law itself becomes a law, not of sensation intensity, but of our estimation of sense separateness within the intensive continuum. It remains now to trace the development of these new ideas, and to see whether any sort of agreement obtains among modern psycholo- gists as regards the general problem of quantitative psychology. One may say, a little paradoxically, that the work of recon- struction began with Fechner himself. Thus Fechner considers the j. n. d. of S as differentials in the mathematical sense, as least S magnitudes. "Nun halter abet doch die Differential- natur weder der einen noch der anderen S an, zwischen denen der Unterschied bemerkt wird; auch ist alas S-Differential sehr wobl zu unterscheiden yon dem Unterschied der objektiven durch den es verursacht wird... Als sehr kleine S-Grosse wird mirbin die S einer sehr klemen Distanz . . betrachtet... Abet ß . die einfache Folgerung z. B., dass, wenn das Differential eines S-Wertes die S einer sehr kleinen Distanz sei, class dann notwen- digerweise ein endlicher S-Wert die S einer gr6sseren Distanz sein  To quarrel with Southey and Old Caspar is, perhaps, merely to break a but- terfly on a wheel. The poem is, however, singularly fatuous, and its quotation singularly inapt. See J R. Seeley, The Expansion of England. $$4, 3 o. õ 6. Ncconsructwn cxvii msse und gar nichts anderes sen konne, findet sich nirgendwo klar und bundig ausgesprochen in den Elenenten der Psychophy- sik. TM The idea finds expression of a sort in the third deri- vation of the metric formula? It occurs again in a letter to Preyer (22 and 23 Jan., 874): "in der That fasse ich . . . die positiven S-Werthe nicht als daseiende S schlechthin, sondern als Entfernungen von dem.. NulIpunkte des Daseins. TM It occurs still more clearly in the Massprincipien of 887, where Fechner begins his exposition with stellar magnitudes and the method of mean gradations:  so clearly, indeed, that even the reader who knows his Fechner experiences something of a shock when the discussion slips back again into the beaten track of the Elemente. "Die bei Fechner unzweifelhaft vorhandene Vor- stellung dayon, dass S-Grossen eben Distanz-S sind, ist also gekreuzt und in den Hintergrund gedrangt durch andere Vor- stellungen." s Nevertheless, let us nt forget that the idea is ' unzweifelhaft vorhanden.' The first positive step on the path to reconstruction was, how- ever, taken by Delbceuf. The limen has, for Delbceuf, no psychological importance whatsoever: the trait of mental measure- ment is a sense distance, a contraste sensible. (a)The 2;imez.--Delbreuf prefaces his explanaUon of the œZ and the aDZ by the following argument. Let us grant, as the hmen theory re- quires, tl.xt for the lndefimte number of R comprised between two points on the R-scale the number of S is hmited. A gas jet, e.z., gives an infi- nite number of degrees ot illumination, according to the position of the plug; but these luminosities, from the bare shimmer of lght to the blaz- ing flame, are correlated with a restricted number of thstnct S. Noxv suppose thatwehave passed over a certain number of these S, that we have (in other words) determined a certain number ot DL; and that the plug stands in such a position that we are on the verge of getUng a new c, of completing another DL. At ths point we have a determinate S-ln- tensity correlated xwth a flame of a determinate luminosity. Let us abstract from all the work that has preceded, and start out again from this point. What will happen, when we turn the plug ? \Vill aturn of ahair's breadth give us a new S? Surely not: such a  Ebbinghaus, Z., i., x89o, 463 f.  El, fi, 36 if. a Z., i., 35 f.; W. Preyer, Wiss. Briefe yon G. T. Fechner u. W. Preyer, 89o, 47- t P. S, iv., W9 if. 6 Ebbinghaus, Z., i, 465 f.; Psych, i, 5 TM. ----------------------------------------------------------- cxviii rnt r oduct ion result would run counter to our previous experiments, as well as to the theory of the hmen. Must we, then, turn the plug afresh through a hmi- hal angle ? Surely. But then we can, by repeating the procedure, n- terpolate as many different S as we like between potnts whmh, on the theory, gave room only for a single S! There ts no escape from the dlemma. Delboeuf argues from this llustrauon i that S is a contmuous function of R. "Je pense . . qu'it chaque excitatton determinCe corresp. ond une sensation aussi determme... Mas, d'un autre c6t, je concede que, pour que la consmence fasse une titsunction entre deux sensations, d faut qu'fi y air entre elles une difference finie. Or, je n'accorde it ce tait aucune importance." The explanatmn of it is, stmply, that "I hnfini- ment pettt se congott, mais ne peut se percevoir... Tout corps en mouve- ment avarice a la fagon des aigudles d'une montre, par peUts sauts terrmttents... Ce que nous disohs du mouvement, phnomne trteur, s'apphque exactement au changement, phnomne tntneur... Leseuil n'adoncaucunemportancepsychologique. "a The discontinuity of changes m the physical universe ts due, in the last resort, to the atomm constitution of matter (of. the phenomena of molecular cohesion in the thermometer, or the reststance of the air to a moving body)? The ds- continuity of changes, under certain conditions of observatton, m the mental sphere is explained as follows. Sensation arises always from a disturbance of organic equilibrium. ,,L'exmtaUon est une rupture d'quihbre, elle prodrot une tmpresston sur l'ammal. Le phnomene interne correspondant it l'impression est la sensation; c'est donc l'effet senstble provenant d'une rupture d'equthbre." s "Nos sens sont des instruments dffrentiels; la sensa- tion . . est due it un phenomene analogue Let R, be of the force of the sensitive organism (the movement-process ofnternal stimulation), and R that of the surrounding medium (the movement-process of external stimulation). Then Webefts Law, with constant omitted, becomes X--log : not, as Fechner wrote it, S----log R. According to Fechner, S increases in arithmetical progression when R  Examen, z7 if.; Rev. phil., v, 878, 29. The same reasoning appears in G. E Muller's Zur Psychophysk d. Gesichtsempfindungen, Z., x, 79 f. = Exanien, 9; Rev. phi1., a Examen, I= 9 ff; Rev. pMl., 3o if.  Examen, 3 o f.; Rev. phfi, 3 o f.  Elements, 82. e tlments, 72; of. 36, n. The doctrine of the relatewry of S is discussed at length by Stumpf (Tps., i., 7 if.), who makes great fun of it; Delbmuf's Dfferenzan- sicht falls under case (at), 5 if' Stumpf gives the most important references up to 883. See p clx. below. õ 6. Reconstruction cxix increases n geometrical progressran. It is rather the case that S-incre- ments increase m artthmetical progressran, xvhen the correspondmgR-m- crements mcrease n geometrical progresston; or, in better phrastng, that successive S-contrasts are sensed as equal when the corresponding R-differences increase geometrically. I At the same time, not every /e ts capable of arousmg a sensatton; "le miheu arabrant peut prouver desvartationsdont l'0tre senstbleest absolument recapable de s'aper- cevoir."2 There are four caseslnxvhtchahmenistntroduced- 0) The vatrations n the intensity of R may be toosbght to arouse 3'.- when the temperature ot our room ts practtcally constant, we have no sensattons of warmth or cold. (2.1 The vatrattans may take place too sloxvly: we douot notme, as we stt through alecture, how bad the atr of the hall has become. (3) The organism is flexible, accommodates tself readily to its surroundings: we do not notice the change of atmospheric pressure as we ascend a mountain. (4) In another sense, the orgamsm s not flextble enough. "Pour qu'i1 y at sensation dtstmcte, il faut que le mouvementext0rteur rencoutre des lmentsqui aient, par leurnature mme, un mouvement harmonique, ou qui somnt susceptibles de le prendre. Les organes de sens nesont rien d'autre que des sdrtes ou des famceaux de parefts Olments. C'est pourquoi le son n'agtt pas sur la mmn, m la lumre sur l'orefile. ,, Pour que donc la sensation nit heu, il faut que l'tmpression alt une certatneimportance; maisilfautencoreunorganedesens. Au change- ment physique, en effet, correspond bien un nouveau tat sensible; mais la sensalton n'est pas identique avec cet ½tat; elle rpond it la variation re{me, c'est-it-dtre au changement entant que sefaisantet non en tant quefait. Or, le changement comprend deux termes, le present et le passE, et l'tre sensible doit les saisir en mgme temps pour sentir. On va voit que l'organe tle sens est la condmon de la posstbiht d'une pareille comparason." a The concept of the limen, then, is of no value for psychology. It is possible to reahse a continuum of sensatmn: and this fact alone would prove that the theory of the limen is not rigorously exact? Yet there are four conditions under whmh a limen appears. Does Delbeeuf mean that the limens, RL and DL alike, are explicable in terms of physiology, and- therefore have no psychological significance ? Or does he mean that, though they are mental phenomena, they are irrelevant to the problems of mental measurement ?  Elments, 76; c/q. 45; Examen, 143; Rev. pb. il., v., t38. = llments, 95 a l16ments, I95 if'; Examen, 35; Rev. phil., v., 33'  Examen, 38 , Rev. phfi., 34 f- ----------------------------------------------------------- cxx Introduction We must remember that Delboeuf gave Ins views to the world in a series of essays, not in systematic torm, and that the v,ews changed somewhat from essay to essay. Hence it is very difficult to answer the questions just propounded. hi his note on Miiller's G., Delboeufremarks, propos of the hmen: ', qumque les ralsonnements de l'auteur sment, en ganeral, nutres que les miens, je tiens it noter cette singuliare coincidence dans nos sentiments. "1 This looks like the physiological interpretation. only that Mtiller confines himself, in the G., to the RZ, and takes the DL for granted. Again: Delboeufinclines to a physiological interpretation of Weber's Law? He woulclnaturally, then, takethe]gZphyslologically. On the other hand, we have passages like this. "Je consols bien la sen- sation cornroe ayant la faculte de s'accroi'tre d'une maniare continue; mas les diffCrences finies frappent seules l'esprit, et les differences inter- mediaires aussi finies et en nombre indefini restent non perues... Je veux faire ressortir que les phenomOnes sensibles ne different pas en cela des phnomanes materiels. Ils sont continus, en ce sens que tousles changements s'y tiennent; mats ils sont dlscontinus, en ce sens que ces changements ne s'y sinvent pas d'une manire umorme et presenteric des phases de ralentissement et des phases d'accleration, des phases en pu,ssance et des phases en acre, des phases de pr0paration et des phases d'action."3 Once more, then: not every Re  arouses S. Why ? Phys- Re is so near to unity that no differential excitation ,ologically, because  reaches the cortex ? Or psychologically, because the S corresponding to a particular 2? is not ' distinct' enough to ' strike the mind ' ? ß In the author's opinion, the latter alternative is that which Delbeeuf accepts. Only, he conceives of the discontinuity of S always and everywhere in terms of physical or physiological. analogy (helped thereto by Ins physiological interpretation of Weber's Law), and can therefore declare the two limens to be psychologically valueless, without com- mitting himself to a purely physiological view of them. (b) The Sensv Unil.--Delbcnuf substitutes for Weber's Law the three laws of degradation, of progression, and of tension. The first declares that "la sensation, it peme produite, s'affalblit, parce que la difference des forces , et _R tend it devemr nulle"; "la sensation est plus vive it  Examen, 7; Rev. phxl, 56.  Examen, 65, 85; Rev. phil., xi, 877, g62; v., 1878 , 42. a Examen, 35 f-; Rev. phil., v., x33. The reader should c.f. ]lments, 75, n. and the Tannery letters, esp. le. 14ments, 143. See also Stumpf, Tps, i., 34, n.; Grotenfelt, Das Webersche Gesetz, 5 f., 3, 20 f. n.; Fechner, I. S., 27 if., 94 if..: R., 78, 303 f. õ 6. Reconstruction cxxi .; son dbut, et va err s'affaibbssant jusqu'a ce qu'elle s'etmgne."l The second is the uniformity S=k 1og, with whmh weare already familiar: "la sensation provtent d'une dfference ou d'un contraste, et les contrastes successds dinvent, pour tre sentis 6gaux, correspondre it des differences relles de plus en plus tortes. c'est l& le fond de la Im de Weber. "= The third law says that ', fi exlste pour la quantt6 R un maxtmum et un minimum oCt la tension est extrame et touche it la rupture; et la facult6 d'accommodatton . . . est determinee en dtendue parces valeurs extremes de , . . . Cette tension, cette marche vers la rupture est accompagnee d'un sentment d'pmsement. TM Delboeuf's general theory of sensitivity has not found Cavour with later psychologists. Muller sharply crltlcses the law of progressran (G., 400 if); Stumpf will hear nothngof the lawof degradation (Tps., l., 7 f., n.); andFechner andStumpf, as we know, reject the Dtfferenzansicht of S (I. S., 32,I 13 if.; R., 300 if.). Nevertheless, as regards the subject matter of sense measurement, Delboeuf hits the nail squarely on the head. 4 S-increments are increments of contraste successif, sense distances. Partly, no doubt, this view of mental measurement is suggested by the theory of the relativity of S at large (,' tl n'y apas de sensation sans con- traste") ;s partly, lJy the character of Delboeuf's experiments. The method which he employed was Plateauks method of mean gradations; and ff one sets out from this method, one naturally tends to think of S-distances, or S-differences, as the objects of measurement, and to ignore what Fechner calls the absolute values of S. We come to the choice of the umt. "Qu'est-ce &propcement parlet que la mesure? C'est . . . unedoubleseriedes nomhres partantdeo clans les deux sens: . . . 3, 2, ,o, x, 2, 3 ß ß ß , l'mtervalle entre les nombres 6cant remph par une portion tteta chosen. mesurer. portion que l'on appelle unili .... Quand donc on evalue lhntenslta dune sen- satran, on dott pour cela se servir d'une unitd de sensatmn."  Delboeufthen gives the filustraton of the scale of greys? and concludes: "II suffit . . . de faire commencer les ternres sombres it nne lurelace  l?.lments, 7 o, x73 ff-, 192; Examen, 37 f, I43; Rev. phil., in., 245 f.; V., 39. 2 Ilments, 42 if., i7 f., 75 if., x93; Examen, 38 f., 5  f, 4 if-; Rev. phfi., m., 246 , 254 f.; v, 138. a Elements, 44, 46 if., I79 if., 94; Examen, 40 f., 43 f.; Rev. phfi., iii., 247; v., 39- ß Cf. Ebbinghaus, Z, i, I89O , 32. * Examen, 6; Rev phfi., v., 5 .  C'f Fechner's own procedure in the Massprincpmn, Phil. Stud., v., I79 if. ? Examen, 99 f-, I3; Rev. phfi, v., 5 ø , 57- a Quoted trom the Tannery controversy, p. 1. above; repeated n Examen, 17; Rev. phfi., v., 60. ----------------------------------------------------------- cxxii 2rntroduction egale & o, c'est-h-dire  l'obscunte complete, el de rendre bour unil de roesure le contrasle entre deuzr leinles quelconques volsines ou loig- nges."' ,' La sensation est, dans ce procede, mesuree par une unite de sensation."  Thin definition of the unit of sense measurement, and the banishment ol the limen from the metric formula,* consntute Delboeuffs two chief services to quantitative psychology. Next in order  comes Wundt, vho in 88o defines Merklich- keltsgrad as "Entfernung der o c yon einer der R-Schwelle entsprechenden Grenze" (P. P., i., 358). We have already dis- cussed Wundt's position in detail, and need here say no more of In 882, the problem of distance measurement was clearly stated by F. Boas (Pfl. Arch., xxviii., 575 f.)? "Die Formu- 1 Examen and Rev. phil., loot. ctt.  Examen, 18; Rev. phil, 6o. a Examen, 125; Rev. phil., 127. * Next, if we omit occasxonal utterances of Preyer's. see Elemente der reinen Empfindungslehre, 1877, 2o, 43; c./;. Ebbinghaus, Z., i., 484 f. a in the P. P., i., 19o-% 549, Wundt says that the Rezschwelle der Empfindung is probably "eine rein physiologische, in den A uslosungsbedngungen der centralen Sinneserregung begrundete;" hs own formula  ./l.rm C , where ./1I=Merkhch- kelt, contains an attention lmen, as Fechner's dS:C - contaxns a stimulus hmen. Cf. 543' the bmen, emplncally regarded, m made up of two factors, a physxologacal and a psycholocal Smdarly, the psychologmal DZ is a matter of attentmn: "the increase of attentmn which is necessary if a gven central sensory œ s to increase by the same degree of clearness . . . is proportional to the quo- tient of the œ-increase into the magmtude of the œ" (553): there are, however, physlologcal condmons which affect t in various ways (494, 539 f-). Both the attention-/; and the attentmn-DZ have, of course, physiologmal substrates ß 54 , 55  f. Ct. Stumpf, Tps., i., IOO ff For Wundt's views of the hmens, see P P., 1874, $3, 91 (the nature of the />L is here not discussed, and nothing s stud on p. 722 of the attention-Z); 85o, , 349, 35 ø , 353' 355, 356; x8S7, i., 375, 376, 38of, 381  , I893, i, 39 ø f, 392, 398 f, 399 f.. 405; n., 272 C'f Lectures, 63; Vn., 1S97, 67, Outhnes, 897, 26'9, 0.54 , P. S , u., 1885, 34 if- It is perhaps worth noting that the reader will find nothing about the hmmal functmns of attention or apperception in O. Staude, Der Begriff der Apperception m der neueren Psychologe, P.S., i., 192 if.; Wundt, Zur Lehre vom Willen, b*d., 337 ff , Kulpe, De Lehre vom Wllen m der neueren Psychologie, *bd., v, t889, 427 if.  Foucault (Psychophysque, 36) gves hm first place, chronologically, under the heading ' La roesure de la dssemblance.' Ths, however, is entirely to miss the significance of De]bmuf's writings. 6. Reconstruction cxxiii lirung, welche Fechner der Grundaufgabe der Psychophysk gegeben hat, lisst sich nicht aufrecht erhalten, da seine Vorausset- tung des Bestehens yon S-Intensit:iten nicht zutrifft. An Stelle der Beurtheilung von S-Intensitaten muss man die yon S-Quali- tiaten setzen.... Das Problem in seiner correcten Fassung lautet: wie ist die Verwandschaft zweier 3' abh:ingig Yon den R-Gr6ssen, xvelche die S verursachen?" 'Relationship' is only ' another expression ' for "Grad der Verschiedenheit" (572). The j. n. d. is "die Einheit des Verwandschaftsgrades" (573)- Measurement of Verschiedenheit is rendered possible () by the fact that Merklichkeit, the principal characteristic of Verschie- denheir, is constituted of Leichtigkeit and Sicherheit des Urtheil- es, and both 'ease' and 'certainty' are measurable magnitudes (574); (2) by the qualitative differences of the single or limiting S (575); and (3) by the inaccuracy of recognition,--the more nearly related the S, the greater is the probability of their identi- fication, and conversely ( ibid. ).--Beyond this statement of the problem, and sketch of a programme of vork, Boas does not go.  Stumpf in 1883 interprets the metric formula in Del- bceuf's way, though without Delbceuf's complications of tension and degradation. "Man kann der Fechnerschen Formel eine Bedeutung vahren, wenn man den Starkegrad einer S durch ihre Distanz v9m St&rkeminimum charakterisirt. Das logarith- mische Gesetz wird dann zwar nicht ein Gesetz der S sondern der S-Distanzen sein" (Tps., i., 399)- The early sections of the Tps., i introduce us to the mportant con- cepts of Empfindungsstegerung and Empfindungsdistanz. "Das Zeichen, wall man es auch auf die S anwenden, kann als Ausdruck elnes Steigerungsverh.ltnisses bentitzt werden, aber der Betrag der Steigerung ist mcht abgesondert vorstellbar" (43 , of. 2, and Fechner, El., ., 48). "Unter Dstanzen verstehen wr . . . mcht blos raumliche und zethche sondern auch qualitative und solche der Intenstt. und definiren das Wortdurch: Grade derUnahnhchkeit"(57). The section on Analysm and Comparison (96 if) treats n detafi of the four immanent relatmns of S("sie stud den Snnesempfindungen mmanent, mcht erst durch das Urte11 hmengelegt ." 97): number (Mehrheit), progressran (Stegerung),  See p hfi. above  In a prewous paper (lot. ct., 562 ff ), Boas makes large theoretmal claims on behalf of the method of mean gradatmns. ----------------------------------------------------------- c x x{  ftroduvtwn stmdarity and fusmn. ,,Fassen wtr zunachst das Bemerken emer Stmg- erung oder enes Gradverhaltmsses in's Auge. Was darunter zu yet. stehen, lehren zunachst und am deutlichsteu die Intensitaten aller S Zwschen je zwet als unglemh erkannten Intensitaten finder eine Steiger- ungstatt; wit nennen die eine grosset und dte bezughche S stirker. Mir dem Begrifle der Steigerung 1st zuglemh der emer bestimmten Richtung gegeben, m welcher sie stattfindet" (IO 9 f.). We have al- ready, m vol. i., I. M., 54 fi, touched on Stumpf's doctnne of Aehnhch- kelt. Ou the relation of simtlanty to progression, he has now three things to say. (I) It is tempting to subsume progression to similarity. ,' Stegerung, konnte man sagen, sei nur da vorhanden, wo em Inhalt B einen anderen .4 vollst.ndig in sich enthalte und noch etwas zu demselben hinzuftige, wm die h6here gegenuber der niederen Intensitat." But it is not correct to say that the higher intensity ' contains' the lower. More- over, vhen xve add tone to tone, we get no quahtative progression, although the second impression 'contains' the first, but only a tonal complex (Zusammensetzung) wth or without increase of intensity. (2) It would, perhaps, be more nearly true to say that progression s a kind of simiMe similarity. Wherever we have the possibility of progres- sion, we have similarity; and the imperceptlbihty of progression, m a progressional magnitude, means always the hghest degree of stmfiarity. On the other hand, however, not all szmilars are progressrenal. Hence it is best, for purposes of exposition, (3) to let the two relations, progres- sion and smilarity, stand side by side as separate things (I2 f.). Progressran and smilarity are, then, to be kept apart; though some slmtlars admit of progression, as does similarity in general ( o). Dis- tance is the inverse value of degree of stmilarity ("der Begriff der Dlstanz gr[indet sich darauf, dass Aehnlichkeiten allenthalben graduell abstmbar sind:" 2). In sensauon intensity, we have a characteristm which brings all three concepts together. Defining dstance in tins widest sense, as degree of dissimilarity, Stumpf goes on to discuss the possibihty of distance judgments (2 frO, the mental mechanism of the estimation of distances (26 if.: we return to thin potnt later), and the general contritions of the rehability of dis- tance comparisons (28 frO' The special question of the comparison of quahtattve tonal distances (4 if., 247 if., etc.) will occupy us in a later Section. Judgments of intensive distances in the sphere of tone and noise are dtscussed n 392 if., in the section whmh gives the reconstruc- tion of Fechner's metric formula. In the course of hm discussion, Stumpf calls attention (i., 24 if., 25, 395 L; i., 560)to Fechner's cutaneous experiments by the method of equtvalents (El., i., 3 ); to Plateau's and Delbeeuf's work with degrees õ 6. Reconstruction cxxv of brightness; to the suggestions ofHering (Zur Lehre vom LIchtsmne, [t873-4] I878, 57 if.) and ofF. Boas (Pfluger's Arch., xxvil , I882, 56x if) regarding the method of mean gradattons; to the actual distance comparisons of Helmholtz (Sensauons of Tone, i895 , i24 f.) and of R. H. M. Bosanquet (Philos. Mag, 5 Ser.,viii., 879,299ff.); and to Ebblnghaus' reinterpretation of the mettin formula. It m curious that he says nothing of Delboeuf's reconstructive work. Delbeeuf was on the right road in 875, and had become absolutely clear in xg78.-- 'vVhat, now, of the limens ? \Ve must remember that psychophysics, for Stumpf, is simply a chapter in a ', messende Urteilslehre" (Tps., i., 54); "de Messung der Beziehung zwischen R und S bildet ein Restprob- lem," whose solution depends upon the adequacy of our psychology of judgment (53). The primary things for hm are, then, the Urtefis- schwellen of.5' and of S-distance; the RL and the ./9/. are secondary matters. (I) There can be no doubt that we have unnoticed and unnoticeable S. "Es kann in einem Klange oder in emem Gergnsche em Ton enthal- ten sein, den wit wegen semer relativ geringen Starke bei aller An- strengung der Aufmerksamket nicht heraushoren konnen" (t., 34 f.; Kulpe, Outlines, 29i ). Hence there is a \Vahrnehmungs- or Merklich- keitsschxvelle, ,' eine J?-Starke, unterhalb deren en Schall selbst bm hochster Aufmerksamkeit und sonst gtinstigsten Bedingungen nicht mehr wahrgenommen wrd" (379). Is there an 27/. ? Yes: very weak R cannot make their way through the obstacles of the pertpheral organ, and there is "Resorption schwchster Erregungen in der comphcrteren rune ten Leitung" (ibid.). Can we ever determine the R/., i.e., ',din Wahrnehmungsschwelle dutch extrem gnstige Bedmgungen mzt jener ganz oder beinahe zur Coincidenz bringen ?" That depends, mainly, on whether we can ever get absolute attention anti absolute freedom from dmturblng 27 (in the present case, absolute silence). "Ersteres ist ge- wins nicht, letzteres wahrscheinlich nicht der Fall; doth wird in be\den Beziehungeu unter gunstigen Umstanden wenig fehlen" (380). (2) Similarly, there s a judgment-hmen for S-dfferences. "Wre, wo wit bei hochster Aufmerksamkmt keinen Unterschied mehr finden, auch allemal keiner in den S vorhanden, so ergabe sich, dass jeder Sinn uber- haupt nur eine S hatte Es seien a, b, c .... z die sammthcheu Ton- c, xvelche bei einer allmaligen Erhohung der Schwingungszahl des Ton- ](' yon der unteren bm zur oberen Horgrenze auch yon den getibtesten nnd auœmerksamsten Beobachtern ehen mcht mehr als verschzeden (a mcht yon b, b nicht von c, c nicht von d, u.s. w.) erkannt wetden: so 5vare unter obger Voraussetzung zwschen allen diesen Ton-S wirklich kern Untersched, es waren sammtliche Tone vom tiersten his zum h6ch- ----------------------------------------------------------- cxxvi rntr oduct ian sten in der S elnarider gleich, es gabe nut eznen. Und welter, da jene Beobachter factisch a yon c unterscheiden, so wire a:b, b=c, und doch a mcht=c" 0., 33, 37; of. if., 222 f., esp. n.). There is also a .DL in the strict sense, "ein Unterschied zwischen ß wel œ, denen kern Unterschied in der S entspricht" 0., 32 f'). We cannot, however, directly measure Unterschiedsempfindlichkeit, but only Crnterscheidungsfthigkeit (3 ø n, 49 n ). Hence the determination of the Dœ sensu smcto is always a matter of inference. Given equality of attention and of reproductory conditions, we can argue from variation of the judgment-hmen to a parallel or proportional varmtlon in the 2)L: we cannot do more, since there may be a ' constant' in the judgment-hmen, i.e., the S-difference may have to transcend a certain limina} amount be- fore it can he remarked or judged (37, 52), .What the .D.L is, whether a physiological or a mental phenomenon, Stumpf does not say. The reader should cf. i., loo if., x83 if., 35 if,, 357 f.; and the references and cross references under Schwelle, fl., 576. It is clear, from the above discussion, that there is a good deal of similarity (more, perhaps, than these psychologists themselves would like to admit) betveen the views of Stumpf and of Wundt. There is an ob- vious difference n starting-point: Wundt sets out from Fechner's posi- tion, trom )g and S; Stumpf, twenty years later,  sets out froin the opposite extreme, from the judgment: and there are very many differ- ences of detail. In general, however, anti especially if our interpretation of Wundt's Merkhchkeitsgrade is correct. the attitude of the two men to psychophysmal problems is much the same. C/ Stumpf, i., 66.-- It wfil be remembered that F. A. Mtiller (Das Axiom der Psychopiy- slk, 882, o6) substitutes for Fechner's 'Contrastempfindung (:emp- fundener Unterschmd) yon variabler Intensltat' a 'Contrastgefuhl yon variablem Charakter.' This use of a secondary criterion is critlcised by Stumpf, i., 87 if. Ebbmghaus also points out that S of different modalities vary greatly in degree of affectire colouring. "Man hat be- hauptet, verletet durch dm Analogle der Tone, der Bewusstseinszustand beim Anschauen aequidistanter oder mcht aequidistanter Helligkeiten sel en Geffihl, er gehore also in alas Gebiet, dem Harmoniegef0hle, Dsharmoniegef[ihle, Zahnschmerzen, u.s. w. geh6ren. Offe,abar ist nichts wereget der Fall als dies. Gerade das unterscheidet Tone und Helhgkelten .... dass jene mxt ausserordentlich pragnanten, dlese mir ausserordentlich schwachen emotionellen Beimischungen empfunden wer'den" (Sltzungsber. d. Berlin. Akad., 887, St. xlix.,  Decr., xoo8).  Wundt was born in 832; Stumpf in I848. The Vn. appeared in x863, the Tps., i. in 883.  Cf.. F. E. Beneke, Psychol. Skizzen, i., x825, 47; Stumpf, Tps, i.. 177 f.; ii, 84. õ 6. ]econstruction cxxvii So far, then, ve have the new idea of mental rneasurernent set forth in Delbceuf's essays, where it is obscured by the writer's theory of sensitivity; in Wundt's P. p., where it s obscured by the author's apperceptive terminology: and in Stumpf's Tps., which is a technical psychological monograph. It has not yet been expounded in such general and generally intelligible terms as to take its place, in the text-books, alongside of Fechner's formulae. x The work of popularisation is noxv undertaken by Ebbinghaus, in articles of I887 and i89o ' and in the Grundzuge of I897-x9o. "Warm und wodurch," asks Ebbinghaus, "wird... das Rgurnliche nurnerisch bestirnrnbar?.. Zwei Orte sind bloss hbereinstirnrnend oder nicht hbereinstirnrnend in ihrer Lage, sonst nichts. Werden abet drei in getracht bezogen, so k6nnen die zwischen ihnen bestehenden Ortsverschiedeheiten, die Distanzeb verglichen verden und diese sind nicht rnehr nut gleich und gleich, sondern sic sind auch gr6sser und kleiner in Bezug zu tin- under und narnentlich kbnnen sie als Vielfache voneinander beur- teilt wetden... Ganz dieselbe Art yon Messbarkeit, die fur das raurnliche Ernpfindungsgebiet besteht, besteht (ira Princip) auch fur alle ubrigen Ernpfindungsgebiete; diejenige Messbarkeit Ernpfindungen abet, deren Fehlen man so oft als etwas Besonderes der Farben, Tbne, Gerhche u.s. w. hervorhebt, besteht aucl ftir das Raumliche nicht" (Z., i., x89o , 36 if.). "An und fur sich betrachtet hat nicht eine bestirnrnte, sondern jede beliebige iso- lierte Ernpfindung in quantitativer Hinsicht den Weft o, 5ede ist als Grbsse eine Nullernpfindung? Ganz ebenso wie jeder Ort oder Punkt des Raurnes quantitativ gIeich Null ist, so auch jede E1ernentarernpfindung; beide hubert eben keine Dimension, und Grosse oder Zahl sind dimensionale Gebilde" (468 œ.)o As to the limen: "wenn die Schwellenernpfindung nicht rnehr noch weniger den Weft o hat wit jede beliebige andere isolierte Ernp-  It m noteworthy, e.g., that Grotenfelt--although writing a monograph, although writing in I888, and although writing from a wide and thorough knowl- edge of the general literature--says not a word of the Tps. Where so much has to be read, one is apt to choose one's books by their tities. 2 Cz . Wundt, p. p, i., x893 , 407 n; and of. B. Russell, Mind, N. S, vi., 897 , 337: "in a quantity, taken n isolation, we cannot discover any of the properties of quantity." ----------------------------------------------------------- cxxvifi Dtgrod. ction findung, so kann auch die Eigenschaft der loganthmischen Formel, fur R--- oc-o zu liefern, in keiner besonderen Bezie- hung zu der Schwellenempfindung stehen sondern muss etwas sein, was zu jeder beliebigen anderen Empfindung in derselben Beziehung steht... Es existiert also im Grunde nur ein einziges Phiinomen, nkmlich das der Unterschiedsschwelle, welches sich bei allen mSglichen Werten der objektiven Reize in gleicher Weise geltend machr. Ausserdem abet besitzt fhr die Empfind- ung.. der (angenaherte) Nullwert des Reizes gar nichts besonders Ausgezeichnetes vor anderen Weftera.. Statt mir Fechner grosses Gewicht darauf zu legen, dass die Formel dem Schwellenphimomen in jenem einzigen Falle [i.e., in that of the RL] gerecht werden kann, muss man vielmehr uber eine so singu- liire und dadurch sellsame Leistung slutzig werden" (47 ff-)' Ebbinghaus then works out the analogy of the tangent galvanom- eter, sharply separates the fact of the DL from the lav of cor- relation of o c and R, and remodels the logarithmic formula. In his paper on Die Gesetzmassigkeit des Helligketscontrastes (St- zungsber. d. Berlin Akad., I Decr. I887, oo6ff),Ebbinghausdescrlbes an experiment with grey papers. ,, Ich habe ein Gebiet yon Helhgketen, welches alles umfasst, was uns in gewohnlichem Leben bei diffuser Tagesbeleuchtung yon Helhgketen vorkommt, in 7 moglichst glelche Thede getheilt... Dm Quonenten yon je 2 auf emander folgenden ob- jectiven Helhgkeiten bildea nun von unten nach oben folgende Relhe: 2 25; 2.I; 2.05; .77;  72;  68;  98. Es gilt also . . ß fur jeden mgsslg grossen Ausschmtt . . der Satz: wenn mehrere Helhgkmten von uns subjectiv als a:quldistant gesehen wetden, so blden de objectiven Helligkeitszahlen annahernd eine geome~ trische Progression.. ß Die Anschaulichkett einer solchen Reihe a:qui- dstanter Helhgkeiten schent mir noch in einer . . principlelien Bezmhung 5/Oll emem gewissen Interesse zu sein. Sie gestattet, Jedermann In verstandlicher Weise zu demonstriren, was eigentlich gemeint 1st mir einer subjecuven Empfindungsdistanz und mir dem Messen solcher Ds- tanzen."  These brightness distances are not apprehended as differences: ,, die Anschauung der Helbgkeitsdstanzen verhalt sich zu derjenigen der einzelnen Helligkeiten sehr ahnhch wie die Anschauung einer rmmlichen Strecke zu derjenigen der einzelnen Orte" 0008). Still, one may regard 1 Delboeuf here has his revenge; for if Stumpf does not mention lnm, neither does Ebbinghaus mention Stumpf ! See pfluger's Arch., xlv., 122 it. õ 6. cconstructzon cxxix them as differences, if one hopes that anytMng will come of such an inter- pretation. "Willlchz. B. the Resultate der oblgen Beobachtungen.. mcht nut in Worten aussprechen, sondern in tone Formel verdmhten, so komme ch sehr lelcht zu emer derartigen Fiction" 0009). Cf. also Pfluger's Arch., xlv., 889, 3, 2 f. We hate already draxxn largely upon the article of 89o Ueber negative Empfindungswerte (Z., L, 320, 463). It will be remembered that EI)bnghaus here brackets the ]eL and the DZ. as Mike instances of the ])L; deprecates Fechner's separation of the two in two different tormula{the Massformel and the Unterschmdsmassformel); and paral- lels the ]PZ with the facts offrlcuon m the galvanometer, so that ,'de Heremziehung der Schwelle m eme Empfindungsformel lrrig st" (477). ttow does he hmself derive the metric formula ? Fechner's formula (see p. xxwli. above) m S:c log. nat. R+ C. Now .S' is not a measurable magmtude To make t measurable, we must make t a sense distance, refer t to some xvholly arbitrary (not necessardylimmal') S O . Then we have the formula (the stroke above the hne being the sgn of distance): .5So=c log. nat. R + C. To determine C, we have recourse to the fact that every isolated S as such, every S compared not with another S but wth itself, =o. Then s03;=o and, if//' 0 be the R corresponding to .S', o:c log. nat. _R0+ C, C=--c log. nat. R 0. Subsaluting, we have for our original formula S.S;=c log. nat. or in other words (see pp. xxvii. f.) R ss0= log . "De Besummung der Einheten, m denen die œ-Grossen R und de 5'-Gr6ssen SS 0 g'emessen wetden sollen, blelbt bier noch vorbehalten; die Wahl der ]?-Emhet st glechgultg fur'le Formel, dutch dm Fest- setzung der 5'*Eraheir wrd k bestimmt" (479- Only in one case can an apparent difficulty arise: m the case that, having to choose a zero-point of the .S-scale n a purely arbitrary way, we should place it at the limmal 5'. Even so, hoxvever, we have but to remember that ,,de logarith- mlsche Formel ftir klelne Werte der objecuven Reize notonsch ungiltig ----------------------------------------------------------- cxxx Jntr, oduction ist und langst, ehe die Reize dem sog. Schwellenwert nahekommen, aufgehort hat, auch nut annAbernal ein Spiegel des sztchlichen Verbaltens zu sero. x.¾as daher f0.r kleme R-Werte uberhaupt und speziell fur den R-Schwellenwert aus hr folgt, mt sachhch volikommen bedeutungslos, es ist eine rein analytische Konsequenz" (482 f.; of. 47z). See further Psych., i., 6x if., 488 if., esp. 509 if.; Wundt, P. P., i., I893 , 405; I9O2, 549. With G. E. M0.ller, Z., x., 80 n., cf. Ebbinghaus, Psych., 494- f. James in 89o endorses Stumpf's idea of distance measure- ment. "When we take a simple sensible quality like light or sound, and say that there is now twice or thrice as much of it present as there was a moment ago, although we seem to mean the same thing as if we were talking of compound objects, we really mean something different. We mean that if we were to arrange the various possible degrees of the quality in a scale of serial increase, the distance, interval or dz#'ereuce between the stronger and the weaker specimen before us would seem about as great as that between the weaker one and the beginning of the scale. It is these relatio:s, these distances, which we are measur- ing and not the compositions of the qualities themselves, as Fech- her thinks... Introspection shovs, moreover, that in most sen- sations a new kind of feeling invariably accompanies our judg- ment of an increased impression; and this is a fact which Fech- ner's formula disregards" (Psych., i., 546 f.). The discussion enters on a new stage with the work of Meinong (z896). We have so far taken it for granted that ' distance' can be measured. We have sought to save the principle of mental measurement by setting in place of Fechner's S Delboeuf's ' degree of sensible contrast '; not the former, but the latter, is the divisible and therefore the measurable mental magnitude. Are we, how- ever, right in calling distance (separation, apartness, distinction, diversity) a measurable magnitude? A magnitude it unquestion- ably is: but a divisible magnitude ? Meinong decides without hesitation that distance is not divisi-  Cf. ch. vi., esp. 58 if. Since James will not quote the dreadful Fechnerian literature, even in a footnote, one mght expect that he would be particularly care- ful to cite the authors who have been active in the work of reconstruction. Yet he gives no reference to the Delbycur essays of 877 and z878; to Wundt'a remarks of 88o anal 887; or to Ebbinghaus' paper of x887. õ 6. Reconstruction cxxxi ale. Think of two space points: the path or way that lies between them is divisible into parts; not so their distance. "HMt man also Distanz und Strecke wohl auseinander, dann erkennt man reit unmittelbarer Evidenz, dass eine Verschiedenheit, eine Distanz, in Verschiedenheiten teilen ganz denselben Ungedanken bedeutet, als die Tonstarke in Teile zerlegen. Distanz ist eine unteilbare Gr6sse."  But how can we measure a magnitude that is not divisible ? We are familiar, in physics, with the distinction of direct and indirect measurement: we are measuring directly when we lay the metre rod upon the object of measurement, indirectly, when we tell the time by reference to the space-units of the clock-face. Besides these two forms of measurement, which may be termed measurement proper, we have, however, what we may call surro- gate measurement or measurement by deputy. "Bei Messung der Distanz wird eigentlich nicht diese gemessen, sondern die zugeordnete Strecke, bei Messung der Temperatur nicht diese, sondern der Quecksilberstand, bei Messung der Geschwindigkeit nicht diese, sondern eine aus Weg und Zeit gebildete neue Com- plexion. An Stelle des eigentlich zu messenden Gegenstandes, des Messobjektes, . . ist ein Surrogat getreten, das eigentlich gemessen wird; ich stelle daher Messungen dieset Art als surro- gative Messungen den frhher betrachteten als eigentlichen Mess- ungen gegenfiber." = The sanction of surrogate measurement lies in the fact that "mit Htilfe des Surrogates die Vorteile, mn deren Willen Teilvergleichung und Messung bei teilbaren Gr6s- sen vorgenommen werden, sich unter giinstigen Umstinden zum gr6ssten Teile auch unteilbaren Gr6ssen zuwenden lassen. "a We breathe again: all that we have to do, apparently, is to stib- stitute Tonstrecke, Farbenstrecke, etc., for Tondistanz and Far- bendistanz; we measure distance surrogatively in terms of path. But wait! "Das anschauliche Erfassen solcher unriiumlicher oder unzeitlicher $trecken," says Meinong, "ist, soweit iiber- haupt ausfiihrbar, nichts weniger als leicht; noch schwerer dfirfte es sein, derlei Vorstellungen zur Grundlage eines praktischen Massverfahrens zu machen, das vor einer direkten Vergleichung der Distanzen irgend etwas voraus hiitte. So hat das Bestehen der x Z., xi., 98.  laid., 243 f. a lard., 245. ----------------------------------------------------------- cxxxii ]ulJ,odze lzon betreffenden Strecken zwar jedenfalls den \Vert, dem Gedanken der halbert oder doppelten Distanz einen resten Sinn unterzulegen: als Messungssurrogate leisten aber Strecken, soweit sm nizht Raum- oder Zeitstrecken sind, welter keine Dienste."  This is a serious cheek. Fortunately, it is of a practical, not of a theoretical nature. In theory, mental measurement is possible. In practice, we meet with the difficulty that "sich zu jenen Operationen, welche der physischen Messung eigentlich erst den Charakter der Exaktheit verleihen, auf psychischem Gebiete keine Gelegenheit finder... Es giebt darum keine eigentliche psych- ische Messung, die unmittelbar ware. und keine surrogative psychische liessung, bei der das psychische Surrogat eine unmit- telbare Messung gestattete." What then is to be done? "Psych- ische Grossen kbnnen nicht anders gemessen werden, als unter Vermittelung physischer Grbssen: die Feststellung des funk- tionellen Verhgltnisses zwischen physischen und psychischen Gr6ssen wird dadurch zum unabweislichen Bedtirfnis,--die gefriedigung dieses Bedurfnisses die unerlissliche Vorausset- zung aller psychischen Messung. TM In a word, we find in the R-Strecke the possibility of surrogate measurement of the S- Distanz. The functional connection of R- and S-magnitudes is given by ¾Veber's Law, which shows that equally diverse .S' corre- spond to equally diverse /?. The logarithmic dependence of the Massformel obtains not between / and S. but between R and S-distinction (Verschiedenheit): so that we have in this formula, as restated and reinterpreted, the required determination of mag- nitude of distance (mental) by magnitude of the distant terms (physical) .a Melnong's mews are expounded n three articles, Ueber die Bedeutung des \Veberschen Gesetzes, in Z., x., x896, 8 if, 230 if, 353 ft. The arncles are not easy reading: partly because of the subtlety of the reason- ing, partly because Memong s more interested m his subject than in hs reader, and makes no apparent effort to say what he has to say m its simplest and brmfest form, partly again because there are many refer- ences, expressed or understood, to previous work either of Meinong himself or of those who think with hm. A good idea of the general situation may be obtained from A. Hofler's Psychologe, x897 , {{ 29, 39.  ]bd., 250 f.  Z&d., 360. 8 Zbd., 374 if. õ 6. Reconstruction cxxxii[ A popular account isgven byG F. Stout, Manual ofPsych, 899, 9) ff ;of. 3. Meinong's summary, 399 if-, should be read over two or three tmes before the reading of the whole s attempted. On dmtance and path (Dstanz and Strecke) see pp 98 f., 239 f., 245, 247 f., 250 f., 264, 277, 356 , 37o, 376, 379; on the interrelation of the various forms of measurement, 244; on the continuity ofS, 249 f., 365. For characteristic statements of Mmnong's own position, see I27 if., 255 f., 359, 396. Memong has nothing to say of the psychologmal significance of the j?Z. According to Hofler (236), his wev is "dass eine nur eben merk- lich gewordeoe S nmht ihrerseits auch noch den Nullwert der 3', sondern schon eme endhche Grosse darstelle ": so the proportionality of 2? and S is saved. H6fler adds on hm own account (248) that it is not necessary to assume "dass allen R von der 2?-Schwelle bis hinab zum absoluten '-Nullpunkt noch S entsprechen mtissen" [for physiological reasons ?]. The L is thus assamdated to Stumpf's Urtefisschwelle (Tps., i., 33 f-) and Wundt's Aufmerksamkeitsschwelle (P. P., ii., 893, 272 ). In his sec- tion on the DZ. (x 20 if.) Meinong remarks: ,, was verschieden erschemt, istauch verschieden; was hingefen verschieden ist, erschemt als ver- schieden nur bis zu einer Grenze, jenseits welcher der Schen der Gletch- heir eintrtt. Dm Grenze hmsst bekanntlich .DZ.." He then emphasises the epistemological importance of the uncertainty of ' equal ' judgments; but offers no psychological explanatmn, further than to say that Fechner has overestimated the factor of 'zexthch-raumliche Nicht-Komcidenz' (P.S., iv., x92). H6fler (248) ascribes the /9/. to a "Mangel der Unter- scheidungsfthigkeit," and refers again (as does Meinong) to Stumpf, Tps., ., 33. We find, then, that in one form or another, in whole or in part, with more or less of consistency and of agreement in details, the view of mental measurement as distance measurement has found advocates in Delbceuf, Wundt, Boas, Stumpf, Ebbinghaus, James, Meinong, H6fler, Stout, and G. E. Mhller.  It is a good omen for the future of quantitative psychology that men of such varied training and tradition should set about the work of reconstruc- tion in substantially the same way. It is, perhaps, unnecessary to say that there are still psycho]ogmts of the first rank who have so far wthheld their assent to the doctnne of mental measurement here advocated? It should, however, be expressly  Z., x., x897, 25 f., 35.  Thus it is worth noting that Jodl, whose Lehrbuch (x896 , 2xo ff ) gxves a long ----------------------------------------------------------- cxxxiv ;ntroduction stated that there are some whose systematic teaching is incompatible wth it. We may refer, in particular, to certain authors whose names have figured n previous dtscussions. (t) Kulpe remarks (Outlines, 45 f.): "We cannot measure S by refer- ence to or by means of other S. Netther can we, as things are, measure them by their functmnal relations to bodily processes .... But the objecttons which hold against the measurabfilty of S, at any rate at the present time, fall to the ground when urged against S. and D.S." He therefore confineshimselftothe measurement ofsenstvity. The author regards this posttton as needlessly conservative. In the Outlines, Kulpe does not attempt to decide between the phys- iologmal and the psychologmal interpretations of Weber's Law; he therefore leaves the nature of the lxmensundetermined: 65 ff. In the article of I9OI ([Ve Congras nternational de psychologie, Compte rendu, I62, 67 fi), he accepts the psychologtcal interpretation, and explains the limens in terms of attention (Merken as Konstatieren, Augassert, Beuro teilen). (2) The position taken by Mtinsterberg, in his Neue Grundlegung der Psychophysik,  is in effect a compromise between the view of Fechner, that and well-considered account of psychophysms, makes no mention of distance measurements, and does nol: even cte (744, 746) the relevant articles of Delbceuf and Ebbinghaus. Jodl's criticism of the metric formula (-ø28 f.) meets Fechner on his own ground. Renouvier, again, is unable to see any essential difference between the mental measurements of Fechner and Delbyear: Critique philos., va., I, I878, I83, 86. Cf Foucault's critmism, Psychophysique, I9ol , 248 fl.  Ct. Fechner, El., i, 45, 54. Kalpe, in effect, returns to the standpoint of Weber and Vierordt, who were also concerned wxth the measurement of sensitivity, not of sensation,--wlth capacity, not with process. More recently, this position has been represented by F. Gaiton, in England, and by the French and American psychologists who have taken up the subject of 'mental tests.' The following are some of the more important references. F. Galton, Inquiries into Human Faculty, I883, 34 if., 37o, Anthropometnc Laboratory, Notes and Memoirs, i., 189o; Journ Anthrop Inst., May, i889, 4oi if.; J. McK. Cattell, Mind, O. S., xv., i89o , 373; Cattel1 and L. Farrand, Psych. Rev., m., I896 , 618; H. Munsterberg, Centralbl. f. Nervenhefik. u. Psychiatr, xiv, I89i , i96; J. Justrow, Chicago Exposition: Eth- nology, Section of Psych., 893; E. Kraepehn, Psych. Arbeiten, i., I895 , I (with several artroles, by various hands, in the same periodical); J. A. Gilbert, Stud. Yale Psych. Lab, it., I894, 40; A. Binet and V. Henri, Annie psych., ix., i896 , 4II if. (wth other articles); S. E. Sharp, Amer. Journ. Psych., x., I899, 329; J. McK. Cattell et al., Psych. Rev., iv., 897 , i32; v., I898 , I76; vi., i899 , i74; viii., 9oi, 65; L. W. Stern, Ue. Psych. d. individuellen Differenzen, 9oo (with bibliography). It is, perhaps, needless to say that one may both recognise the value of ' mental tests ' and, at the same time, push beyond sensitivity to a measure- meat of mental process.  Beltrage z. exper. Psych., Heft 3, I89ø. õ 6. Reconstruction cxxxt all S may be regarded as sums of S-increments. and the views of wrtters hke yon Krles, who deny the posstbthty of mental measurement. Mtinsterberg mststs, at the outset, that, mtenstve 'dtfferences of ,5' are dfferences not of degree but of kind. "-/fir mussen unbedmgt daran festhalten, dass dm starkere und die schwchere S zwei ganz verschmdene einfache Bewusstseinsmhalte sind, yon denen wit zungtchst mchts anderes aussagen konnen, als dass sle verschieden, d. h. nicht ideatisch sind."  "Dm stgrkere S ist nicht gleich der schwacheren S plus einem Zuwachs, sondern beide sind v611igverschiedene Bewusstseinsmhalte, genau so wie zwei quahtatv verschledene S. Es list] damit die Trennung zwlschen qualitatvem und mtensvem Unterschied aufgehoben. " It would, however, be premature to argue from this fact that S and S-differences are unmeasurable. "Es wire ja vielmehr denkbar, dass bei den Inten- sitatsanderungen zu den )-Wahrnehmungen noch irgend etwas zweites hinzukame, was bei den Quahtatsanderungen mcht vorhanden ist, dass also die Trennung auf Grund eines accessorischen Elementes entritt und somit einerseits in der That nmht auf den S-Unterschieden selbst beruht, und anderseits dennoch, alle Erfahrung vorangehend, naturgemass uberaI1 emtreten musste."* The accessory element required is found in the muscle sensation. "Alle physikalische Messung beruht auf der Konstatmrung resp. HerstelIung gleicher Muskel-S; meiner Ansicht nach ruhr auf genau derselben Grundlage alle Messung der psychischen Grossen, der S-intensittaen, und eben well die Grundlage dteselbe ist, kommt der psychischen Intensitgttsmessung auch rileselbe Berechtigung zn wle allen physkahschen Messungen."  The muscle sensation m quahfied for its task in two ways. (x) A Spannungsempfindung is a constant accompaniment of change in S-intensity. "Jeder 27 lost reflektorisch Muskelspannungen aus, deren Stirke yon der Starke des )g abhangt. Jede N-Aenderung ruft demnach eine Spannungsanderung hervor und these trttt als Spannungsempfindung ins Bewusstsein . . . Wit nennen enen S-Unterschied gleich einem anderen, wenn in beiden Fgdlen glelche Spannungsanderungen vorliegen."s (2) The muscle sen- sation is a Fechnertan sensutton. "Den MuskeLS kommt eine volhg exceptionelle SteIlung zu, die schwache Muskel-3' ist in der That in der starken enthalten und betde stud mcht quahtativ yon emander verschieden, sondern nur dutch ihre zeithche Dauer und rgumliche Ausdehnung."  I N. G., 5, 9 I, 98 f.; cf. Psych., i., 9oo, 263 f., 271 , 281 f.  hr. G., 4, 56; Psych., i., 373. a lff. G., 3, 17. - N'. G., 23 f. .5 lq'. G., 92, lO 9; Psych., i., 284.  ]. G., 22 f, 3 O, 32, 34, 56, 92; Psych., i., 282. ----------------------------------------------------------- cxxxvi f ntrodu ctwn It follows that the single 3', though itself a qualitative datum prompt- ing merely the comparative ludgment of 'like' or 'different,' Is by indirection a measurable magnitude, in so far as the correlated muscle-S, a simple more or less of content, has a determinate place upon atrue quantitative scale. S becomes indirectly measurable by way of its con- stant muscularaccompamment.  It follows also that any sense distance cau be measured, xvhose hmiting terms are correlated with muscle-S (so intensive d,stances, distances of tonal pitch); and that equations can be set up between distances taken from different sense departments. Direct distance measurements are as impossible for Munsterberg as direct .%measurements are for Delboeuf; o_ S-measurements are as easy tor him, by way of muscle, as they were for Fechner by help of the theory of S- increments. This theory is repeated, with all its details? in the Grundztige der Psych., i., I9OO, except that Mnsterberg wfil nov hear nothing of mental measurement, whether direct or mchrect. He declares that ',dasPsychische alssolcheslmletzten Gronde.. uberhauptnicht quan- titativ bestimmbar sei. " Fechner's system is tintenable, for the reason that it makes the S-difference an "addlerbare Grosse ,,s Measurements of the D.S. may be made, and may be valid; but that is because "in den abgeleiteten Wert mcht S, sondern R, also physsche Grdssen, als be- stlmmende Faktoren eintreten. " Ebbinghaus' distance measurements are not measurements at all. "Das Raumhche, das dm Naturwlssen- schaft zu messen hat, sind... gar mcht 'Ortsverschmdenheiten' oder ,Ortsdistanzen,' sondern zwischen den Olten hegende Objekte. Die 'Ortsverschiedenheit'ist tone Gestaltquahtat... Thatsichhch blmben Hell,glreitsdmtanzen wie Ortschstanzen untmlbar, wahrend physlkalische Objekte, yon denen allera die Naturwmsenschaft handelt, tefibar und deshalbmessbar sind... Die Lehre yon der Dlstanzvergleichung 1st sicher ein sehr entwickeluugsfahiges und wichtiges Gebmt der Psycho- logie; sie steht abet pnnzipiell m denkbar sch----------------------------- cxxxviii ]ntroduc/ion value of R Since the S-series is discrete, and the R-values are con- tinuously variable, it follows that the ordinal numbers m, n of S will cor- respond not only to the , normal ' R-values Rm, R,, but to these values +their DZ. 2 Ve have, now, to distinguish two empirical cases. (a) If the absolute .DL s constant, we get the equation R,--R,=2(n--m)DL: the differ- ences of the ordinal numbers of any pair of S are directly proporttoual to the differences of the corresponding R-values? (b) If, on the other hand, the relative D r- is coustant, as s in general the case with inten- sively graduated S-series, xve get the equation n--m:k (logR,--Iog R,)- the differences of the ordinal numbers of any pair of S are directly proportioual to the differences of the logarnhms of the corresponding R- values; or, more general]y, equal differences of the ordinal numbers ot S correspond to equal quotients of the correlated R-values.* Finally, if we rlte re=o, we have n=k. 1ogR,: the ordinal number of S increases proportmnallyto the logarithm of the corresponding R-value? This is Fechner's law, freed from objections. Not S is regarded as a mathemat- ical lunction of 2½. we cannot write S, for n in our last equation: but the ordinal number of S, its numerical place in a series, is brought into functional relation with measurable R-values. This deduction is, wthout doubt, ingenious. It cuts all the difficulties. It is, e.ff., in many respects identical with the doctrine of distance meas- urements: but, whereas the distance-psychologist has to face the ques- tion of the equality of the j. n. d., Llpps can shelve this question altogether; the difference between the ordinal numbers  and 3 is the same as that between 8 and 2o, whatever be the psychological telarran ofthej. n. distances -=,-3, x8-x 9 and9_=o. If, then, we could re- main poised in psychophysms, as the "Grenzwissenschaft zwischen der Psychologie und der Physik (ira weitesten Sinne des Wortes),"- without slipping over into psychology or physiology, we might be tempted to accept Lpps' formulae But, alas ! we have--Lipps himselfhas--psychologicallytoexplain Web- er's Law. This means that we have to account both for the existence  Ibid., 45 if. The psychophysical problem is similarly envisaged by C. Henry (Comptes rendus, cxxii., 896 , 95, I39, t283)- Henry, however, more cautious than Lipps, makes no attempt at nterpretatmn--Ct. the Fechnerian formula of C. Wiener (Wied. Ann., xlvii., 1892 , 66 0: "the measurement valne [Maasszahl: not Ordnungszahl, numro d'ordre] of an .-intensty is given with the uumber of weaker .qntensites that can be interpolated, wth just noticeable dstinguishable- ness, between the given S and the absence of all S,lus one." "lbd, 47 if-, 5 ø- albzd., 5o- 4lbxd, 52. Ibxd, 53' lbd, 7. Reconstruction cxxxix and for the relative constancy of the D.L  Now (a) when we speak of the ' intensity ' ot a mental process, we have m mind its hold over us, ts power to absorb or occupy us. The greater thspower, the stronger, of course, must be the stimulus that can dintract us, that can noticeably m- crease thegven ' intensity'. ,, Demgemass trtt m der DZ nichts anderes as de Intensitt der Szu Tage, uud man wrd dm Intensitt als um so grosser anzusehen haben, jegr6sser das zu der S gehongeR-Intervall st... Zwe Empfindungen S und S der Reihe Sx, S,Sa, . . . mir den -Intervallen ]? DZund RDL verhalten sch hnsichthch firer Intensitt wie DZ,: DL."  Again, (b) "de physmche Energe des R st deobjektive Grundlage fur de subjektv empfundene Intensetat. Da man nun beistetg und glechmassg smh nderndemRemestetgund glemhmssig sich gndernde S vorauszusetzen hat, sowrd auch theR- Energie der S-Intensitt proportional zu setzen sem."a In other words S: S as R: R?Putting the txvo results together, we have DZ,: DL=R: R m, and therefore ..... Herdurch wrd abet dm Gltigkeit des Weberschen Gesetzes gefordert. "* Yes! and herewith are precisely those old difficulties rained which the psschophysical de- ductran had avoided.* It remains, now, to answer certain questions and to meet cer- tain objections that arise in face of Delbuf's theory of mental measurement. The first question is this. () Can we in strict- ness speak of a mental measurement, when our quantitative result is not sanctioned by introspection ? Suppose that we have divided a sense distance a into four equal distances, ab, bc, cd, de. Have we any right to say at =4  when an introspective exami- nation of the two distances would not reveal the fact that tbe one is the fourfold of the other ? This question is answered, by implication, in Fechner's defence of his principle of mental measurement (El., i., 56). "Die S theilt sich nicht yon selbst in gleiche Zolle oder Grade ab, die wit zghlen und summiren konnten. Abet erinnern wit uns class alas bei physischen Gr6ssen nicht anders ist. Zahlen wit denn die  Ibid., 54-  Ibrd., 54 f- a ]bid., 48, 55; cf Jodl, Psych., 229.  Ib2d., 56.  ]bd., 56. It should be sad that Lipps is here writing with all possible brewty, and that hs two principles of explanatmn are avowedly popular.  Lipps' position is now worked out, m greater detml, in his Die Massmethodea der experlmentellen Psychologm, 9o4; Arch. f. d. ges. Psych, iii., 123 if. ----------------------------------------------------------- Zeitabschnitte direct an der Zeit ab, wenn wir die Zeit rnessen. die Raumabschnitte direct an dem Raton ab, wenn wit den Raum roessen? Vielmehr wir legen eine ausserlichen Massstab an... Dass man doch das Mass des Psychischen iraruer im reinen Gebiete des Psychischen gesucht hat, mag ein Hauptgrund sein, dass man es hisher nicht finden k6nnte." It is, indeed, clear that all measurement would be superfluous, if we could tell beforehand and without the procedure of measurement how many times our unit is contained in the gven magnitude. The equa- tion œ:_x is the result of measurement. "Beim Messen kommt es Y gerade darauf an, den eigenthumlichen MXngeln menschlicher Ver- gleichungsfihigkeit nach Thunhchkeit nachzuhelfen" (Meinong, I23). We gve below, p. cxliv., references to the topic of measurement in geu- eral. The reader may now of., on this special point, Zeller, Abh d. Berhn. Akad., 88, 6 ; Sitzungsber., I882, 298; Wundt, P.S., i., 465; Ebbnghaus, Z., i., 327; Psych., i., 507; Sitzungsber. d. Berlin. Akad., 887, 1oo7; Delboeuf, llments, esp. I25; Jodl, Psych., 225. The ob- jectran is stated very clearly, in Fechnerian terms, by Wahle (Das Ganze d. Phfios., 86 if.). "Wenn das Bewusstsein mcht weiss, dass eine .q zwei, zweimnhalb, dreimal so gross ist, als elne andere, oder dass se um ein bestimmtes &Quantum gr6sser ist, als ene antiere, so kann so etwas auch nicht in die Psychologe eingefuhrt wetden... Soltte die Ent- schedung fiber em Vielfaches der S-Stgrke nicht mehr in dem Bereiche der menschlichen Beurtheilungskraft hegen ? Das ist doch mcht zu glauben." Cf. F. Boas, Pfl. Arch., xxxin., 1882, 573 f. (2)Hoxv does the S-distance come to consciousness ? What is the material of the distance-judgment of equality, or of ' greater ' or ' less '? We will take the authors in order. For Fechner, ths question did not arise. Fechner's sensed difference : dfference sensation = contrast sensation is a true sensation, for ' sensed difference' means smply ' sensed .S-increment' or , partial sen- sanon ' (see E1 , iL, 83; cf i. 48, 75;, etc.). There are, it is true, passages in Fechner's writings which could hardly be reconciled with this inter- pretauon, but there can be no doubt that, on the whole, it represents Fechner's oplmon2  See footnote, p. lhi., above.  The ' Bewusstsein einer Beziehung' is, for Fechner, a conscious act of a higher order than the mere ' Auffassung einer 3' '; El., ii, 86. Since the compar- ison of two ..g falls under the heading of a ' Vergleich zwschen einer Mehrheit õ 6. Reconstructian cxli Nor did the question arise for Delboeuf. Since sensation at large ,, provient d'une diffreuce ou d'un contrasic," it s the most natural thng in the world that change orSshould consist in change of sensible contrast. See esp. Examen, 93, lt7, 43, x$4 L Stumpf, t wfil be remembered, defines the distance between two S as the inverse value of their degree of sirerarity. Direct judgments of equality of distance (equal degree of dissimilarity)--judgments ,, rein auf de beztiglichen Empfindungen, Quahthten, Intensxtaten, etc.,gestiitzt "- are theoretically probable and practically possible (i., 122 fl.; Qt. 97). "Ist es zur Schatzung einer Distanz notwendig," Stumpf goes on to ask, ,' dm 5', welche zwischen den belden die Distanz bfidenden Sliegen, oder den Uebergang in der Phantasie vorzustellen ?" Iu that event, com- parison of distances would resolve itselfnto comparison of the magnitude of 'Uebergangs-&' Now this magnitude may mean either the timethat the transition takes, or the number of S that are passed over. The time is variable, and must therefore be ruled out. As for the number of S: ,,z[h/en k6nnen wir nur Unterschmdenes." If the discriminated S are the j. n. d. S, then our comparison of two dmtances involves a very large number of extremely difficult judgments. If more wdely separated Sare chosen, then these must themselves be placed at equal dmtances,--and our task is muluplied. And if small distances can be drectly compared, why not large dstances ? ,,Ein Uebergang mag im Bewusstsein in manchen Fallen in con- tmuirlicher Form statbqnden; es mag auch oft nulzlich sero, eine gege- bene grosse Dlstanz m mehrere kleinere zerlegt zu denken; abet mner- halb einer jeden yon diesen ist dann der Uebergang zum anderen nicht unbedingt und allgemein zur Distanzsch.tzung notwendi; er geh6rt nicht zu den essentiellen Bedingungen des Distanzurteiles. Zu diesen gehort mchts weter als 3 oder 4 S emer gexvissen Gattung." We ought, therefore, to be able in some measure to estimate distances of S, in cases where intermediate S either do not exist or at least have never been ex- perienced. ', Bei Geruch und Geschmack durfte des sogar wlrklich vielfach zutreffen"(i., 126 if.; cj e. 62). Ebbnghaus does not scruple to employ the term , Dlstanzempfindung ' interchangeably wth' Empfiadungsdmtanz.' "Dm raumlichen Bestim- yon S', this 'higher act' is involved in the apprehensmn of a sensed dfference. There is, no doubt, a certain obscurity here .of. footnote, p. lxiii. above. Fechner, as we have often resisted, was not a systematic psychologist. 4ever- theless, hm msimcave use of Empfinduug in place of Merkhchket is sound and sane. While, therefore, the author agrees with Augell in his polemic against the term ' difference S ' as employed by later writers (P.S., vii., 47; cfi i., I. M., 378), he regards Fechner's usage as (for Fechner) correct. Ct. Langer, Grundlageu d. ?sychophysik, 1876, 17; Grotenfelt, Das Weber$che Gesetz, 1888, 57 f. ----------------------------------------------------------- cxlii Introduction mungen bilden wie Farben, Tone, u. s w. eln eigentumliches Empfind- ungsgeblet und mchts anderes" (Z, i., 325); so that one may speak ot , Raumempfindungen ' (328). This usage may be condoned, ff one has it at heart to emphasse the immediacyø the drectness of the distance judgment. In strictness, it must be condemned: for a tone-distance is a mental formation of a different order from the tone, and the colour- distance a formation of a different order from the simple colourß Eh- binghaus himself, when he is writing within a psychological system, talks not of 'Empfindungen' but of ' Anschauungen.' Distance con- sciousnesses ,,gehOren dahin, wo man de Raumanschauungen unter- brmgt"; so that the Anschauung of brightness distances stands to that of the separate brightnesses very much as the Anschauung of a spatial dis- rance (Strecke) stands to that of the separate positions torre): Sitzungsber. d. Berlin. Akad., x887, ;008. Even here, an objection may be raised: for is there an Ortsempfindung, comparable with the Helhgkeitsempfind- ung ? Or can we, in strictness, speak ot a Helhgkeitsanschauung ? In the Psychology, a distinction is made between the ' spezifische ' and the ,gemetnsame Eigentumtlchkeiten' of S. Colour-tone and brightness are specific properties 'of wsual S, pitch differences of auditory, warmth and cold of temperature S. Spatial extent, on the other hand, is com- mon to the S from eye and slain, temporal duration to all S ahke (t , I68 f.). The two groups of properties are discussed in two different chapters (69 if, 409 if.). ,, Haben wit S behebiger Art," says Ebbinghaus (4;;), ,'so kommt uns an lhnen ausser den... spezlfischen Elgentumhchkeiten ohne weileres utd nvermitlel dzrch Reflexion noch vielerlei anderes zum Bewusstsem ' . . riiumliche Bestlmmungen; . . zeitliche Bestimxnungen; ß . Vergtnderung; Mehrhelt und Einhet; Identitgtt, Aehnlichket und Verschedenheit." The specific .5' have, as a rule, several of these gen- eral properties attached to them, and can be cut free only by a process of abstraction. Conversely, the general properties never occur alone, but alxvays in connection Wlth specific S. The properties themselves are Erleh]Isse, Inhalte. As there is no general name for them in current psychology, and no generally accepted theory of their origin (Meinong's phrases 'consolidated contents' and 'ideas of higher order' mply a special theory), Ebblnghaus borrows for them--without theoretical im- phcatlon--the Kantian term Anschauung. He then points out that the Anschauungserlebnisse--what shall we call them: recepts ?--may be approached, psychologically, from two different directions, may be met  If the term must be translated, ' recept ' would seem to be a better word than 'mtultlOn,' although Romanes, who first employed it, would hardly have sanc- tioned the usage: see Mental Evolution in Man, I888, 36 if. õ 6. Reconstruction cxliii by one or other of two psychological attitudes . those of geness (412 ffl and of nailviSta (418 if.). He himself decides in fayour of a nauvistic view (esp. 420 f.).x We should, now, expect to find the S-Dstanz (Stufe, Intervail, Abstand, Grad tles Abstechens gegen einander: 64) mentioned in the section on Aehnhchkeit und Verschiedenheit (474ff). As there snosuch refer- ence (anti as Stumpf's  6, not  7, is referred to: 474), we must suppose that Ebbmghaus is reserving the topic for further treatment. Besides the passage quoted from the Sltzungsber, we have the fact that in the Psych. (502) anti in Pfiuger's Arch , xlv, t3, the S-Dstanzen are termed S-Verschedenhelten. There can, then, be no question as to their place in Ebbmghaus' system. James thinks that, in equating distances, ,, we mean that f e were to arrange the various possible degrees of quality in a scale of serial in- crease" the interval or difference "between the stronger and the weaker specmen before us would seem about as great as that between the weaker one and the beginning of the scale" (i., 546). This is measuring Distanz by Strecke: cf. Stumpf's criticism, above. James' remark need not be taken hterally, since he has, in his feelings of relation (i., 243 if.), an adequate nativistic basis tor direct distance comparisons. Meinong's treatment in the articles before us is largely epistemo- logical: the reader, may, however, c.f. [6, o4 if,  o, 4 if., and the footnote, 358,--this to be taken in connection with Dittenberger, Philos. Monatshefte, ii., x896, 82 f. For Meinong's psychology of relations (" Distanz ist eine Relation:" 98) see the references given in his intro- ductory sections, 8I if., and I. M. Bentley, The Problem of Mental Ar- rangement, Amer. Journ. of Psych., xlii., 9o2, 269 if. Finally, we may call attention once more to Lipps ' Logik, I2. "The magnitude of the qualitative distance between two colours, say, red and green, or the degree of their dissimilarity, IS determined primarily, for my immediate consciousness, by the certainty with which I keep them distinct even with slight energy of application (Festhallen) or slight at- tention to their particularity." Here is that theory of, mental work ' to which we have referred above, p. lxxxiv. n. "The iame. . . degree of dissimilarity is also determined conceptually, and therefore indirectly, ß . . by the number ofj. n. d colours Into which the total distance divides for me." Here is indirect measurement in terms of Strecke. "The absolute measure of a given . . . S, that s, the degree in which ß . it itself is given, consists in the number ofj. n' d. into which the quali- tative distance of this S . . from its zero-point dvldes." Here ve have justice done to the Fechnerian distinction of S and S-difference: c.f 1 Cf. Lipps' criticism, Z, xxwfi, 9o, I66 if. ----------------------------------------------------------- cx!iv œJttroduct fol above, pp. xxxvi., xhx., lxw. ', Qualities and qualitatxve differences [' in- tensities' and ' intensive' differences included] are measurable as such; only one must remember that measurement m this case is never anything else than the becommg-conscmus of numbers of the just noticeable."-- The whole passage, { 0.39, offers an admirable essay subject. There are, then, various xvays. of answering our question, according as one inclines towards a ' genetic ' or towards a ' nati- vistic' theory of mental function: or, again, according as one lays the greater stress upon introspective or upon logical analysis. In any event,--and this, for our present purpose of reconstruction, is the important point,--the current psychological systems are all alike able to meet the question without difficulty. õ 7- lgotes to }õ x-7 of lhe Text; --The following notes cover points that have not been raised, or at least not raised in the same context, in the foregoing Sections. { . i[easurement.--On measurement in general, see Helmholtz, Zahlen u. Messen, in Philos. Aufsatze E. Zeller gewldmet, I887, x7; W. S. Jevons, The Principles of Science, 887, bk. iu.; Fechner, El., i., 45 if., 56; P. S.,iv., 27 L; Delboeuf, ]lements, x, x34; Examen, 99; Wundt, P.S., il., x885, o; Loglk, ii., x, x894, 403 if.; li., 2, I895, 79; yon Kries, Vjs., Vl., x882, 257; M. Radakowic, iid., xiv., 89o,  fl.; Mtns- terberg, N. G., x89o, 4; Ebbnghaus, Z., i., 89o, 325; Mmnong, Z., xi., 896, 232, 237, 239; E. W. Scripture, The New Psychol., 897, 3 ø; B. Russell, Mind, N. S., vi., 897,326; T. Lipps, Logk, 893, x2o fl. Especi- ally interesting, in psychological regard, is Meinong's statement (Z., x., I7): "[es] schelnt mr das qualitative Moment nittends deutlicher erfassbar als beim Raume "; of. H6fler, Z., x., I896, 223 If. To avert misapprehension, it may be said that the deftration of the umt of mechanical energy on p. xx. is phrased to suit the exposition, and differs from that usually offered. Energy is ordinarily defined either in terms of mass and velocity or in terms of the equivalent amount of work. Where the energy is kinetic, it is made = « my , and its unit (the erg) is defined n ternas of the work done by unit force (the dyne) in moving a body through a distance of i cm. We set out with the expression r47_---fs, where 47 is the work,/the force, and s the distance through which the force acts. Slncef=ma, where m s the mass of the body moved and a the acceleration produ.ced, õ 7. Notes to õõ x- 7 of the Text cxlv we have the equatmn =mas. Here s=« at ; so that Pgmay be writ- ten -- = (Cf. the statement of the dmensons of work or energy, vj _4 3 p. xxhi.) Smci, again, the absolute v is = 2s, and therefore ----, we may put 4/= « my : this is, as was said above, the usual expressran for the kinetin energy. { 2. J[ental .½IeasuremenL--See esp. Fechuer, El., i., ch. wi. (quota- tion, p. 6o) and Wundt, Die Messung psychischer Vorgange, in Essays, x885, ;54. The statement that sense differences were early remarked and utilised refers to the classificatmn o tiae stars by visible magnitude: Fechner, P.S., iv., x887, z8z. On units of measurement, see the art. \Velghts and Measures, by W. M. F. Petrie, Encyc. Brit., 888; on the qualitanve dlssimfiarity of groups of mental processes, see Wundt, Logik, ii., 2, 895, 79 f. (of. P. S., li., o if.); HOfler, Psych., 897, 236. Fechner gives two reasons for the tardy advent of a quantitative psy- chology: (z) dass man das Mass des Psychischen immer im renen Gebiete des Psychischen gesucht hat; (_o) dass (so to say) ungleiche Abtheilungen des Massstabes gleichen Abthefiungen des zu messenden Gegenstandes entsprechen: El., ., 56, 62. For Kant's position, see the Metaphysische Anfangsgrunde der Natur- wissenschaft, ;786, x. f.; and c.f. the author's artrole on Psychol. in the 9 Cent., Internat. Year Boole, x9oo, 978. Those who are interested m the matter from the standpoint. of Kant's own psychology should of. J. B. Meyer, Kant's Psychologie, z87o, az4 if., =67 if.; G. Itelson, Philos. Monatshefte, N. F., fl., 89o , 285 f.; M. Dessolr, Gesch. d. neueren deutschen Psych., i., I9o2, 366 f. On Herbart's 'theory,' cf. Wundt, P. P., 874, 6; i., x9o2 , 7: "dem Unternehmen Herbarts, Mathematik auf Psychologie anzuwenden, kann, was man uber seinen sonstitch Inhalt urtheilen moge, das eine Verdienst mcht bestritten werden, dass es dm MOglichkeit einer Anwendung mathematischer Betrachtungen in diesera Gebiete deutlich n's Licht gesetzt hat." Onhs'fact,'cf. ibid., x874,798; i., x893,486: ,,treffend sagt Herbart selbst yon selner Psychologie, sic construire den Gemt aus Vorstellungsreihen, ghnlich we die Physiologie den Leib aus Fibern. In der That, so wenig es jemals gelingen wlrd, aus der Reizbarkeit der Nervenfasern de physiologlschen Functonen zu erklaren, so lruchttos ist das Unternehmen aus dem Drucken und Stossen der Vorstellungen de nnere Erfahrung abzuleiten." For a special instance, see Stumpf, Tps., fl., 85 if. A popular account of Herbart's psychology s gven by T. Ribot, German Psych., x886, 24 ft'. { 3. Mn Analogy.--For the tangent galvanometer, see W. 5Vatson, ----------------------------------------------------------- cxlvi œntroduction Text Book of Physics, i899, 684; fuller treatment xwll be found m A. W0.11ner, Lehrbuch d. Experlmentalphysk, m., x897, 579; E. Mascart et J. Joubert, Leqons sur l'lectricit et le magn6tisme, i., I897, 213. The precise behaviour of the galvanometer needle will, of course, depend upon the nature of the mechanical restraint under which it suffers. The Analogy presupposes that the neettle is not free, but restrained by a considerable friction. The conditions are perfectly reahsed m certain instruments of an older pattern: modern galvanometers are practmally so free that those accustomed to their performance wfil, perhaps, fail to get the point of the illustration until they reach the end of the . Again: if we have a galvanometer which 'sticks,' but whose construction is such that the needle becomes entirely free when the friction s overcome, we find that the needle swings by the proper point, instead of following the increasing current, and perhaps sticks again at some too high a reading. But these and similar objections mean simply that the analogy is no more than an analogy, useful tip to a certain limit, and not to be pressed beyond it. Non-mathematical students are sometimes puzzled by the statement that the needle will never make au excursmn ot 9 oø. Since lan 90ø= oo, it is clear that nothing short of an infinite force will produce the deflec- tion. Or again: since the movement of the needie is always the resultant of the pulls of the current in the coil and of the earth's magnetism, the influence of the latter wfil always be apparent with anything but an infimte amount of current in the coil.  4. Three ?roblems.--Some of the instances of this  will be familiar to the student from vol. i. Many of them wall be discussed in the course of this vol. In the meantime, the following references may be useful for lecture purposes. For the DL of tones, E. Luft, P.S., iv., I888, 58; a9L of colours, P. Mentz, P.S., xid., x898, 538; extensive JgL, Helm- holtz, P. O., 896, 256, 374; temporal ]L of colours, A. Kunkel, Pfiger's Arch., x., x874, v-19 f. See also KCfipe, Outlines, } 5, xS, I9, 24, v. 5, 56, 65. "Sensation . . . is a continuous function of stimulus." The author has taken the truth of this proposition for granted through- out his discussion. For one thing, it seems (apparently) to the majority of present-day psychologists to be more probable than its opposite; for another, it affords, true or false, a perfectly good working hypothesis. Nevertheless, it has not found universal acceptance; and we must here consider some of the arguments brought against it. õ 7. Notes to õõ x-7 of the Text cxlvii In his Metaphysik (884, 53), Lotze asks the question "why a continuous curve of increase of/?-intensity is not followed con- tinuously by the more slowly ascending curve of S-intensity; why there rather remains an interval, during which R increases without effect, producing a noticeable change in S only with the attainment of its final value." He proposes three answers, of which the first appears to be the most satisfactory. () "It is not an insoluble task for mechanics, to construct a system of material parts in such a manner that a continuously impelling force can still, by reason of internal checks, exert its effect only with intermissions, at determinate moments; on this analogy we should have to think of the nerve as so constructed that, -what- ever the degree of excitation from which we start, a certain further accumulation and increase is required to produce a move- ment that can serve as stimulus for the arousal of a new sensa- tion... However, we have not the remotest idea of how such a mechanism should be conceived and where in the nervous system it should be placed." (2) Less probable is the hypothesis that makes E proportional to and continuous with R, and seeks the ground of discontinuity "in der Natur des Empfindens "; "eben in dem Begrifle des Empfindens liegt Nichts, was reit Wahr- scheinlichkeit die bier unm6gliche Zwischenmaschinerie ersetzen konnte." (3) Nor is it allowable to make a distinction between Empfindung and Wahrnehmung, and to say that the former is continuous with R and E, "aber die Vrahrnehmung bringe die wirktich gewachsene Intensit/St der S in anderem Verhiltniss und unstetig zum Bewusstsein."--The fact that we have a discrete series of S-intensities over against the continuous curve of R- intensity is due, therefore, not to anything intrinsic to S itself, and not to the processes of discrimination and comparison in- volved in our estimates of S-intensity, but rather to the discrete character of E, of the nervous substrate of S.--Cf. the less posi- tive discussion in Outlines of Psych., x886, 9 f- Funke (in Hermann's Hdbch., iii., 2, 88o, 358 f.) admits that Lotze's physiological conception is possible, and cites as parallel the intermittent innerration of the nerves of inspiration that goes along with continuous stimulation of the respiratory centre. He thinks, however, that the hypothesis in the present ----------------------------------------------------------- cxlvifi Introduction case is by no means probable: we cannot imagine the nature of the inhibitory mechanism required, and the fact of the DE is more readily explained "aus der Unvollkommenheit des Auffas- sungsverm6gens fur verschiedene S-Intensitaten" (ct. 349)- Moreover, there are two counter-arguments. If the hypothesis be correct, then () continuous increase of R must give in con- scionsness an intermittent increase of S; and (2) at a certain lower limit of rapidity of the R-increase, the corresponding S must show pauses, interruptions of continuity. Neither of these consequences is realised in fact. Stumpf (Tps., i., 35 if-) points out that the second of these arguments is not binding. While R proceeds from a to b, E might remain at a; while R goes on from b to c, E might stay at b: and so forth. The first argument, again, is valid only on the assumption (common to both Lotze and Funke) that "any the least change in o e must be perceptible." If we reject this assumption, then the R-zone a--d, corrosponding to a j. n. d. of S, may really give rise, say, to the four S a, b, c and d,--these S being discrete. but so little different that their difference cannot be perceived. "Lotze's view is, then, possible and defensible,-- but only if one gives up the principle from which its necessity would follow." Stumpf, it is needless to say, does not accept the principle. He is, nevertheless, non-committal in his conclu- sion: "mir scheint einstweilen weder pro noch contra ein trif- tiges Argument m6glich." In his discussion of quality (83 if.) Stumpf remarks that the Helmholtz theory of audition favors a discrete tone series. He also suggests (himself employing Funke's second argument) that an extremely slov R-change might even render the discrete nature of the S-series perceptible. As for the continuity of tonal idea (as distinguished from tonal sensation), that might be real enongh; xve might fill out the breaks in sensation "dutch Acre unwillkdrlich productiver Phantasie": c[. the blind spot of the eye. A similar "unwillkfirliches Hinarbeiten der Phantasie" is possible in the case of intensity (353). So Stumpf leaves the question. It is one that peculiarly suits his somewhat scholastic temperament: and if he does no more with it,--iœ he leaves it in this way, with merely academic pro õ 7. Jkbtes to õõ I- 7 of the ]'cx! cxhx and co,--we may ourselves, wthout hesitation, choose the ortho- dox view. x Readers who desire to pursue the topic farther may consult: Aubert, Phys. Optik, I876, 595; Preyer, El. d. reinen Empfindungslehre, 877, 6, 62 f. (these writers think that we are "inclined a priori to attribute continuity to objects, and to hold fast to this assumption for so long as sensation and perception do not directly contradict it "): Wundt, P.S., ii.. x885, 7; P. P-, i., 893, 325, 458, 484 f.; i., I902, 441; Hofier, Psych., 242 ff : G. E. Muller, G., 38o f.; Z., x., 79 if.: Delboeuf, Examen, I27 if. I35 f.; Stout, Manual, 899, 203; C. Renouvier, Critique philoso- phique, vii., , 878, 8o f.; A. Stadler, Philos. Monatshefte, xiv. 878 , 2 9 if.; F. A. Mhller, Axiom, ;882, 23; J. Ward, Mind. O. S., i., 876, 46I f.: A. Elsas. Psychoph., 886, 38 ff.: A. Grc- tenfelt, Das Webersche Gesetz, I888. x69 fl.; C. S. Peirce and J. Jastrow, Mem. Nat. Acad. Sci., ifi., , 884, 75, 82: Jastrow, Amer. Journ. of Psych., i., 888, 277; P. Tannery, Rev. phi!., xvii., 884, 22, 25 ff.; xxv., 1888, 94 ff: A. Kbhler, P.S.. iii., I886, 583; A. H. Pierce, Journ. Ph. Psych. Sci. Meth., ii., 9o5, I50. { 5. Technical Terms--The term SchNselle appears to occur for the first time in Herbarr's Psychol. Bemerkungen zur Tonlehre, 8I ; Werke, ed. G. Hartenstein, vti., $$9, o. C.f. the Lehrbuch zur Psych., 816; Werke, v, 886, I8; and the Psychol. als \Vmsenschaft, 1824; Werke, v., 341. The term Unterschedsschwelle was introduced by Fechner, apparently n I86O (E1.,'.,239). For Rmzhohe, seeWundt, P. P, 874, =82. A humorous critic has remarked, tl propos of experimental psy- chology, that "the success of a modern science depends largely, if not wholly, on the elaboration of a technical terminology and the generous provision of instruments for a laborators:." The remark raises the smile that it was meant to raise: but it may be taken seriously as well. For both instruments and terms are necessary; and yet we meet with a sort of contempt for both, even within the science itself. We are often told, for instance. that 'the best work has always been done with the simplest in- struments,'  and that we are in danger of making our labor-  Fechner, El., ii., 84; P.S., iv., 172 if.  The idea is sanctioned by no less a psycholocal authority than J. McIC Cartel1: see Psych. Rev., v, x898, 658. ----------------------------------------------------------- cl _Introduction atories too pretentious, and losing sight of the end in our interest in the means. But this is mere nonsense. The best work has always been done by the best men; and the best men have, all too often, been forced to content themselves with poor instruments. Their work would have been still better, had they had adequate appliances. The most reliable investigation into the differential sensitivity for visual sensations that we possess--the work of A. K6nig and E. Brodhun, Sitzungsber. d. Berl. Akad. d. Wiss., 26 Juli 888, 97; 27 Juni x889, 64t--was made with an extremely elaborate and expensive dioptrical apparatus. The more gener- ously we are supplied with such instruments of precision, the better shall we work.  Similarly, the importance of a good terminology can, from the point of view of teacher and student, hardly be overestimated? A rose by any other name would smell as sweet; but we do not teach botany by smell. The teacher of psychology is required, in a very limited time, to bring his pupils within the circle of the science; to start them psychologising, to train them in method, to give them facts and uniformities. How much of his success must depend upon his choice of words, and how completely is the beginner at the mercy of his phrasing ! Experimental psychology was, in origin, a German science; and the German technical terms must be translated. One great difficulty is that the terms already current in English psychology --the psychology of 'associationism': see i., I. M., 404, 49-- are all surcharged with functional meaning; they refer to mind in use; whereas the characteristic terms of experimental psychol- ogy avoid functional reference, and imply nothing more concern- ing mind than its existence. Take, e.g., the word Unterschieds- empfindlichkeit. It is tempting to reduce this to familiar Eng- lish by translating it 'sensible discrimination.' a But--' sensible 1 Provided, that is, that we are already psychologists ! Cf. i., I. M., vii. a Ct. Scripture's remarks, New Psych., 39,- in which naivetd would seem to reach its limit. a As, e.., the author did in his translation of Kulpe's Outlines, 895. Sully and James use the phrase 'dscrimmative sensibihty,' Human Mind, i., I892 , 89, Psych., i., x89o, 533; Stout and Baldwin recommend ' sense discrimination,' Dict., i., 9o, 284; Foucault uses ' sensbilitd diffdrentxelle,' Psychoph.,  . õ 7. Notes to õõ 1- 7 of the _Text cli discrimination ' is rather the equivalent of sinnliche Unterscheid- ungsfahigkeit, or Unterscheidungsf/ahigkeit im Empfindungs- gebiet; and the student of psychophysics is called upon to distin- guish sharply between Unterschiedsempfindlichkeit and Unter- scheidungsfahigkeit. Nothing remains but to take the ugly col- location ' dfferential sensitivity,' and to make it passable by the abbreviation D. S. It would be wearisome to follow out, in this way, the history of every technical term employed in the book. And it would also be useless: for technical terms, however good the reasons which prompt to their suggestion, must fight their own way in the world, and stand or fall by their own merit or demerit. The author may, however, quote the most important maxims which have guided him in his choice. () The first rule has been negative: that one should not try to satisfy the requirements of psychology at large, but be content with terms that ' work ' well in experimental psychology. For psychology is a vast subject, and its departments are as yet imperfectly co-ordinated. It is out of the question to secure, as things are, terms that shall serve interchangeably, say, in the genetic psychology of Stanley Hall and Baldwin, in the functional psychology of James and Stout, and in an experimental course. Contexts, even postulates, are xvidely divergent. Ultimately, we may hope, there will be a rap- prochement of the various psychologies. In the meantime, it is the part of modesty and of common sense to let each psychology work out its own verbal salvation. (2) A good terminolo should be absolutely transparent, letting the facts be seen through the words. Constructive thought runs its course, for the most part, in symbols, which mav be arbitrarily defined; though the story of the Kritk der rei:ez Erfahrulg shows, clearly enough, that arbitrariness may go too far. But the beginner thinks imi- tatively, not constructively. For his use, technical terms should do more than svmbolise the facts: they should. so far as possible, suggest, recall, indicate, relate. clarify, quicken the facts. It fol- lows that the terms chosen for use in experimental psychology should cover. as literally as may be, the corresponding German terms to which the student will be constantly referred. Almost all ----------------------------------------------------------- clii Introduction of the classical literature is in German, and very little has been translated.  It follows, further, that the terms chosen must neither be familiar terms which would bring with them misleading asso- ciations, nor terms so unfamiliar that their assimilation would it- self be difficult. Sometimes it is possible to take a current word, and to change or restrict its meaning, for scientific purposes, with- out loss of the warmth and intimacy that go with its use. Some- times one must have recourse to a neologism; but then one must see to it that the novel term is not wholly novel, but exists already in some derivative or cognate form. And it follows, finally, that the terms chosen must be terms that fall naturally into groups, that allow of adjectival formations, that lead easily to or from other terms and groups: in a word, that they must be both ade- quate and self-consistent. So much for rules. Having formulated them, let us admit frankly that they cannot be strictly followed, that every working terminology is a compromise. Technical terms are a matter partly of individual authority, partly of organic growth, partly of inertia of attention, partly of accidental factors,--training, association, chance likes and dislikes. They are too important to neglect: but he who meddles with them should be endowed with a vast deal of patience and a plentiful supply of humour. Cf. F. Tonroes, Mind, N. S., viii., 1899 , 289, 467; ix., 19oo , 46; Bald- win's Dict. of Phil. and Psych., l., 29Ol , vi. f.; fl., i9o2, 677 if.; Titch- ener, Arner. J. of Psych., vii., 2895 , 78; viii., I896-7, 584. 6. Quanlzlative ?sycholoffy.--On contrast measurements, see A. Lehmann, Phil. Stud , iii., 1886, 497; H. Ebbinghaus, Stzungsber. d. Berl. Akad., xh., 1887, 995 (our filustration is drawn from this paper: for the law of contrast darkening, of. ibid., and Psych., i., 223); . Kirschmann, P.S., vi., 2890, 427; C. Hess and H. Pretori, Arch. f. Ophthal., xl., 4, 894,  ; H. Pretori and M. Sachs, Pfl. Arch., lx., 895 , 71 . On the law of the fortune morale, see D. Bernoulli, Comment. Acad. scient. imp. Petropolit., v., I738, 77, 8I f.; P.S. de Laplace, Theorie analytique des probabfiits, (1812) 1847, 87, 432; of. the Essai philoso-  It is to be hoped that we shall some day have an Englished series of psycho- physical classics, in which such things as Weber's Tastslnn, the constructive parts of Fechner's Elemente, Hering's Lichtsinn, etc., will be accessible to all Englishø speaking students. õ 7. Notes to õõ -7 af the Text cliii phique (2814), trs. by F. W. Truscott and F. L. Emory, I9O2, 22 if., 89; S. D. Prosson, Recherches sur la probabditq, etc., 837 , 72; Fechner, El., i., 65, 236; fl., 549 f-; I. S., 59; Wundt, Betr.ge, 862, xxx. f ; P. S., i., 1883, 252; P. P., I874, 434; ., 188o, 469, 494; i., 887,52,537; i., 1893, 563, 59  ; fl., 9o2, 317 f.; A. Grotenfelt, Das V, rebersche Gesetz, x888, 87 if.; F. Krchner, Psychologie, 2883, 47; J- Merkel, P. S., v., 1888, 591; G. A. Lindner, Psych., 88o, 3o, 34 f.; F.C. Muller, Arch. f. Physiol., I886, 311; Delboeuf, Examen, 42 f.; H6fler, Psych., 48 fi; Jodl, Psych., 2I 3 fi, 394; Zeller, Abh. d. Berl. Akad, 188, 2 if.; J. Ward, Mind, O. S., i., 876, 457 f.; A. Lehmann, Hauptgesetze d. menschl. Gefiihlslebens, 1892, 256 if. The first quantitative determnatton of an optical illusion was made by H. W Knox and R. Watanabe (Oppel's hnes: i., S. M., 157), in A. J. ofPsych.,w., 1893-5,43, 509- Since this time thequanntative method has been xvidely used. ooe of ts latest applications wfil be found n A. H. Pierce, Studies m Auditory and Visual Space Perception, 9o, 224. Stout re[ers to it (Manual, 1899, 32 f.) as one of the standard il- lustrattans of quanntatve work in psychology. For the memory formula, see H. Ebbmghaus, Das Gedachtms, 885, lO6; H. K. Wolfe, P.S., hi, 886, 554. Quantitative work on memory has continued, almost wthout interruption, down to the present; but interest has also attached, in recent years, to the quahtatve questions o[ the mechanics of association and reproduction, and of the course ant[ employment of the memory-image. Cf. the bblmgraphy pubhshed by I. M. Bentley, A. J. of Psych., xl., 899-19oo, 4 if- A good account of current doctrine is given by Ebbinghaus, Psych., i., 19o2, 606 if. It is now becoming possible to combtne the quahtatxve anti quantltatlx'e pro- cedures: c./. G. M. Whipple, A. J of Psych., xfi., 19o2, 4Ol; xfii., 19o2, 2I 9; and the introspective records m Malllet and Plzecker, Ged.chtmss, 19oo. See, further,  4 below. The Instructor must recognise, at the outset, that method work is, to the average student, very much more difficult than qualita- tive xvork. A parallel has often been drawn between qualitative and quantitative work in psychology and qualitative and quantita- tive work in chemistry. In the main, and so far as analogies are accustomed to go, this analogy holds: but elementary quantitative work in psychology is, in the author's judgment, relatively much harder than the corresponding work in chemistry. This fact alone, quite apart from the difference in mental attitude involved, justifies the separation of the two fields, and the putting of quality ----------------------------------------------------------- cliv Introduction -before quantity in a psychological training course. The average student, on entering the laboratory, is simply not competent to do quantitative experiments. And more than that: it will happen, time and time again, that even one's best students, after the full- est directions and the most careful explanations, will hand in results of a laborious experimental series which---owing to some slip in method, some irregularity of procedure, some too facile interpretation, some unforeseen and undetected prepossession, some lapse of attention--are altogether worthless from the stand- point of the experiment. A method is not an easy thing to grasp: the Instructor, who has gone over it hundreds of times, step by step, bringing out and insisting upon the psychological import- ance of each determination, has it ingrained in his mental consti- tution: but the student must assimilate it, by a sustained effort of attention. Practice in method work itself can alone give the surety of manipulation and the discriminating judgment that method work requires. We can, however, shorten the term of practice by giving a preliminary training on the qualitative side. Hence the author cannot agree with those psychologists who advise that qualitative and quantitative experiments be intermin- gled, from the first, in class work.  In his own experience, the result of such mixture is that the qualitative experiments are slighted as rough and indeterminate tests, which ought by rights to be made quantitative; while the quantitative experiments are performed--largely through sheer ignorance of their true diffi- culty-in a slovenly and intermittent fashion? It is well, of course, to throxv one's qualitative exercises, so far as possible into quantitative form: that ensures accuracy: but it does not turn quality into quantity. On the other hand, there are a few really quantitative experiments that do not take much time, and that can be performed roughly, in a sort of qualitative way, with- out prevmus training: so the determination of certain RL, and the sorting into groups of given weights or brightnesses. But these are the very experiments that should be used as an introduc- tion to quantitative work. Their tendency to slip into 'quality' I See, v'., J. Jastrow, Science, xifi., o May x9o , 742 f.; O. Kulpe, Z., xxx, I9o2. 436 . g Cf. 5th thin vol. i., I M., xx. if. õ 7. %tcs lo õ -7 of the fcxt clv of the wrong kind makes them admirable warning examples; and their comparative easiness does not at all disprove the diffi- culty of quantitative work at large. Moreover, even they are meaningless to the student unless prefaced by a pretty full ac- count of the aims and limits of quantitative psychology. x Over and above the greater difficulty of quantitative work, we must keep in mind the change of mental attitude which it de- mands. It is not easy for the student to turn, in qualitative work, from experiments upon sensation, which require the keenest at- tention, to experiments upon affective process, which require a passive, as it were a listless frame of mind. It is not easy, again, for him to turn from sensation or affection to perception, where the problem is far more complex, and where he is called upon, so to say, to drive several observations abreast. The change from qualitative to quantitative work is greater than either of these changes. The student is conscious that, once an experi- ment is started, there is no release. The series must be gone through with, or the time xvill have been just wasted. To put the matter in simile: the student is not now rehearsing a set speech, but arguing to prove his case; and if there be one weak spot in his argument, the whole case breaks down. He is not playing the part written for a single instrument, but directing the orchestra; and if he make a slip, the whole performance is thrown into confusion. He is not working out an illustration to a known mathematical rule, but going through an elaborate set of computations; and if he make a mistake, the whole work will be to do over again. Or, to phrase it more directly: the student becomes, by practice, a manipulating machine, making a long series of adjustments at regular intervals and with great accu- racy; at the same time, his attention ranges ahead, he has the  The proof of the pudding is in the eating; and the author writes from sad experience. If it is objected that other people may do better,--that quahtatlve and quantitative experiments have, e.g'., already been intermixed, vnth good result, in Sanford's Course, hy, let Sanford Mmself supply the answer. "Most of the experiments," he says (p. iv.), "are demonstrational in character, and axmed at quahtative rather than quantitative results, even where for couvenience they have been given a quantitative form. Precautions necessary for results of the latter sort have therefore been lightly touched upon." Besides, Sanford puts at the end of the Course his special chapter on XVeber's Law and the psychophysmal methods. ----------------------------------------------------------- clvi ]ntroductio whole course of the method in mind, he is quick to note lapse or error on the part of O, he decides promptly on doubtful points, he is alert to the total ' situatxon.' As O, he is required to make a succession of maximal efforts of attention; to judge quickly and accurately, relapsing into passivity as soon as the judgment is passed; and, at the end of the series, to give account of his manner of judging. Indeed, there is no need to search for sim- iles. If method work were not intrinsically difficult, if it did not demand its oxvn special mental attitude, the greater part of the literature of psychophysics, constructive and destructive, would not have been written. It is, then, even more important here than it is in qualitative work (see i., I. M., xx.) that the Instructor shall teach from first-hand knowledge of the methods. One error may ruin an experiment, and the possibilities of error are legion. Yet if ad- vice and criticism are to be helpful, they must be definite, de- tailed. Fortunately, the Instructor acquires, after a few years of teaching, a sort of instinctive familiarity with the methods: so that he can, as a rule, lay his finger accurately upon a weak point of procedure, and say: "Here your pauses must have been ir- regular," or "Here you were getting inattentive, and the habitua- tion error came in." As a rule,--not invariably; for students and methods are slippery things. However, the human mind is mainly impressed by positive instances, and the student, after a few such criticisms, gains a wholesome respect both for the methods and for the Instructor. This is the reward of first-hand work. But if the Instructor does not know how precisely to shape his directions, so that E and O shall understand just what they have to do; and if he is not able to check and control the re- sults handed in to him, so that E and O shall realise the psycho- logical importance of the method they have employed: then psy- chophysics becomes as foolish and worthless as its worst enemies could desire. And if the student, after all, go wrong,--as, in the light of this somewhat pessimistic discussion, he may almost be expected to do? Has he then wasted his time ? Not at all: there is nothing like making a blunder to keep one straight in later work. It is always better to have worked wrongly--if you know afterwards õ 8. Qucstzons and E'ssay Subjects clvii where your mistake lay--than not to have worked at all. In the present case, it is not seldom better to have worked wrongly than to have worked rightly at the first attempt; the reconsideration of the method stamps its psychological necessity more firmly on the student's mind; the problem becomes luminous; the difficul- ties, now fully realised, are seen to be surmountable. Cf. i., S. M., xv.-- So far, then, as training is concerned (the author is not speak ing of original work), quantitative experiments are far more diffi- cult than qualitative, and should be postponed till some general practice has been had in a psychological laboratory; while the attitude of mind in the two cases is so widely different that a beginner will find it impossible to turn successfully from the one to the other. { 7. Questions.--(x) See ,V. S. Jevons, The Principles of Science, x887, 85 if. (2) Answer from { 2. (3) Ansivet from pp. cxlvi. if., above. (4) Ansver from { 4 (). (5) Answer on the hnes of {6 of the text. (6) An- swer from { 6. (7) Answer on the hnes of Ebbinghaus' formula, { 6. p. cxxix. above. (8) Answer from { 4 (3) and references there given. (9) Answer from { 4 of the text. The second part of the question is not set in order that the Instructor may strike a decision, but rather that he may hold the balance between two equally important departments of psychology. The interested student will ' take sxdes; ' just as, when one begins the study of hterature. one is very sure that lyric poetry s of a hgher order than dramatic, or vice versa. If he is for psychology and nothing but psychology, he vill cry up the mental measurements; if he is an enthusiast tot natural science. he will find no sure ground outside of physics. In either case, the Instructor is m opposxtion. õ 8. uesti.ms ad Essay Subjects.- The following are sug- gested as essay subjects. Materials for their treatment will be found in the foregoing discussions and references; a few new references are here added. The essay should. whenever the subject allows, be both historical and critical. It is advisable to assign a topic to each pair of stude:'.s, at the beginning of the quantitative laboratory work, av, d to allow a considerable time (say, two months) for its study. The Instructor will decide whether reports of progress are to be handed in separately by the students, and privately discussed with them, or whether a number ----------------------------------------------------------- clviii nroduc œon of topics shall be dealt with in informal seminary meetings. As the essays approach completion, it will probably be worth while to have them read and discussed in seminary. (I) The doctrine of mental measurement. This topm may be subdwded m various ways: e.ff., (a) Fechner's view of mental measurement (the Elemente and the Massprincipen); (b) the difference between the teaching of Fechner ant] the Reconstruc- tion (say, Fechner's Massprincipien and Ebbmghaus' ?sychologi:); (½) physical and mental measurements: their resemblances and differ- ences. The field may, again, be narrowed by the assignment of special books or artroles ior cnncal review: thus, (a) Fechner's EI., i., chs., i ii., iv., vi., vii.; (b) selected chapters of the :Elemente with Delbeeuf$ :Examen or Ebbinghaus' articles m Z., i.; (c) Cattell, Philos. Rev., ii., 893, 316 if. wth Scripture, The New Psychology, x$97. A good deal of psychology may be learned by a critical study of some author who gives, m brief compass, a ,personal,' perhaps a heterodox statement of the psychophysical problem and its solution: z.ff., (d) Munsterberg, Beltrage, Heft iii.; (e) Tarde, Rev. phil., x., 85o, 5o, 264 (restricts measurement to belief and desire); (f) Foucault, ?sychophymque, ch. vi. (the "quantt qui est en jeu dans les mesures psychophysiques" is "la clart des perceptions "). () The doctrine o Merklichkeit. Wundt, P. P., and Meinong's criticism, Z., xi., z4 if. A good text for this essay may be found m the following sentences (C. Wener, Wed. Ann., xlvii., x89, 66I). "[Es] drangt sich uns als Maasseinheit der Zunahme der .-Stlirke und damit der .-Stlirke selbst de deser Zunahme auf, sodass wit sagen, zwei .-St.rken stud um eine S-Emhmt verschieden, wenn lrUnterschied gerade bemerktoder emp- funden (!)wetden kann . . . Die .S'-Emhet 1st also gegeben dutch die eben merkbare Unterscheidbarkeit (!) zweier ." Or, again, in these words (W. Dttenberger, ?hfi. Monatshefte, N.F.,iI., I$96 , Io): ',der Unterschied zweier appercpirter Empfindungsintensititen ist psycholo- gisch betrachtet yon der Merklichkeit des zugeh6rigen Reizunterschiedes grundverschieden." It is interesting to compare Wundt's doctrine of Merklichkeit wth Foucault's doctrine of clart. (3) The sources o Fechner's psychophysics. This essay has two parts: (a) the course of Fechner's own thinking (El. il , 553 if), and (b) hs relatmn to predecessors (especially Herbart), and contemporaries. õ 8. Questions and Essay Subjects clix (4) The relation of Fechner to Herbart. Fechner owed to Herbart three things: the general idea of mental measurement, i.e., of the apphcaton of mathematms to psychology; the concept of the hmen; and the ideal of mental analysis, for vhich the proved to be so effecnve an instrument. On the two former counts, see Wundt, G. T. Fechner, 9o, 66 f.; P. ?.,  , I9o2 , 7 n. On the third, Wundt, Logk, n, 2, 895, 62, P. P., i., 9o2, 357; L. W. Stern, Z paed. Psych. u. Path., n, 9oo, 334- It s possible, too, that Fechner's preponderant interest m sensanon was clue, in part, to the ' mtellectual- istm ' trend of Herbarr's psychology. (5) The relation of Wundt to Fechner. A text may be found in O. Ki21pe, Arch f. Gesch. d. Phfi., vi., x893 , 83; or n G. F. Lpps, Massmethoden, 9o4, 5 f., 33; Arch. f. d. ges. Psych., ilL, x67 f., 85. (6) The sources of the ' new ' psychology. Thss essay would include a review of Lotze, of whom we, have said very little. Lotze is, indeed, indefinitely less modern (on the purely psy- chologmal side) than those who know him only by his theory of local sigus would be apt to suppose f. Stern, loc. oil., 345; and n., p. cxl above. (7 The question of 'mental work' and 'mental fatigue.' This essay should connect with Hofler's definmon of attennou (see S. M., x7; Psychologe, 263) and with his article on Psychische Arbet, Z.,,vfii., 895,44, x6L Seeabove, p. lxxxiv. . Hofier's dscusslonsmay be taken together with Lehmann's criticism; Die k6rperL Aeusserungen psych. Zustande, ii., x9oI, x92 if. (8) Psychophysical parallelism. This is an exceedingly dfficult topre, and should not be assigned with- out especial reason. Usually, wth enthusmstm students, there s spema[ reason: men take sides, as if temperamentally, with parallelism or interactionism. It is then best'to give them something solid to bite on. The best popular accounts known to the author are: for interaction, James, Psych., i., ch. v. (of. 67 if.); ii., 584, 591 f.; for parallelism, Ebbinghaus, Psych., i., 7 if- Good essay texts are: (x) Fechner, El., Enlmtendes, i., iL; (a) Fechner, Ueber die Seelenfrage, I86; (3) F. Paulsen, Introd. to Philos., (x892) x898, 74 if.; (4) C. Stumpf, Eroff- nungsrede, in Bericht u. d. III. rotemat. Congress f. Psych., 897, 3 if. (for interaction); (5) G. Heyroans, Zur Paral]ehsmusfrage, Z. xvii., I898 , ----------------------------------------------------------- ½1 x Intou(tio 62 if.; (6) O. Kulpe, Ue d. Beziehungen zw. korperlichen u. seehsclen Vorgangen, Z. f. Hypnotismus, n., 898, 97 ff ; (7) W. Wundt, Dm psych. Causahtat u. d. Prmcip d. psychophysmch. Parahehsmus, P 5, x., t894, 47 if.; (8) A. Riehl, Der phfiosophishe Kritizmmus, n., 2, 887, 76 if. (eptstenmlogcal); (9) J- Rehmke, Allgememe Psych., 894. 35 if. (polemic against parallehsm); (to)J. yon Kries, Ue. d. matersellen Grundlagen d. Bewusstseinserscheinungen, 898; (U C. Hauptmann, De Metal'hysk in d. Ph_xsmloie, x893; (-) C. A Strong, Why the Mind has a Body, 9o3 . The literature of the subject is very wide, and of all degrees of value (9) The teleological significance of the logarithmic law. For Feebrier, .I J. Muller, Bet. d kgl. s0.chs. Ges. d. Wiss., math.-phys. C1, xxii , x87o, 328, against lum, Herrag, Sitzungsber. d. kais. Akad. d. Wss zu Wlen, math.-naturwss. CI., lxxi., 875, 3x$, 32t if-, 33 g if. See also Fechner, [. S., 57, 75; G. E. Mailer, G., 878,403 if., 408 if.; A. Grotenfelt, Das Webersche Gesetz, I888, 28 f.; P. Langer, Grundlagen d. Psychophysik, x876, 5 f-, 27 if.; J. Delbceuf, Examen, 5 f., 63 f.; J. yon Knes, Vjs., vi., x882, 287 f.; A. Gruenhagen, Physiologie, i., 856, 28 if.; A. Memorig, Z., xi., 896, 387; H. Ebbinghaus, Psych. i., 19o2, 512 ff; Kulpe, Outlines, 68; A. Elsas, Phfios. Monatshefte, xxv., 885, 49- (o) The doctrine of relativity. See esp. Stumpl, Tps., ., x883, 3 if., 76 if.; Ward, Mind, O. S., i., 876, 457 ff.; Grotenfelt, Das Webersche Gesetz, 76 if., t74 if.; Memorig, Z., x., 383 if., 398; Ebbmghaus, Psych, i., 58 if.; Wundt, P. P., ., 893, 393 if., 397, 399, 46, 59 ; i., I9o2, 541 fl., 55I; in., 9o3, 784, T. Lipps, Sltzungsber. d. kgl. bayr. Akad. zu Mdnchen, phil.-philol. KI., 19o2, 3 if-; Leitfaden d. Psych., 9o3, 74 if. Stumpf, Grotenfelt and Wundt give many further references. ( I ) Fechner's psychology. A general sketch in Wundt, G. T. Fechner, I9OI, 133 iT. Special crucisms wdl be found scattered in the literature: thus, on Fechner's psychology of ,sensation' see %Vard, Mind, O. S., i., 876, 464 if.; Her- ing's letter quoted by Fechner, I. S., 49 f.; Delbceuf, Examen, 43 f., 87, to be taken with I. S., 6I z. and El. i., 15, ii., 336; Foucault, Psycho- physique, x9ox, 9 f., x75 if., with refs. to Fechner, 2:29, 269; Lipps, Mass- methoden, 9o4, t5; Arch. f. d. ges. Psych., iii., 67. () Wundt's psychophysics. Two things should, in the author's opinion, be emphasised: () the development of the doctrine of apperceptlon on the basis of that of un- õ 8. Questions and œssay Subjects clxi conscious inference (see, besides refs. already gven, Stumpf, Tps., i., 9 ø , n.), and (2) the essentml smllartty of \Vundt's Merkhchkeitsgrade to the'distances' and ' contrasts ' of the Recoustruction. (3) Stumpf's psychophysics. This essay requires a careful study of the first three t of the Tps., i. Stumpf sets out from the fact of the universahty of the sensory judgment: ,,dem Erwachsenea bmtet sich keine Sinnesempfindung, de mcht m einem gewissen Masse beurtefit, in rgend elner Bezlehung aufgefasst wCtrde" (7): "das Vorhandensem emer Sim Bewusstsem 1st fast aus- nahmslosmitgewissen Urtefieu uber firVerhgltms zu anderen Vorstel- lungen verbunden" (22). Moreover, these'judgments, apprehensions, apperceptions'can, if not alter the contents of S, at least bring about a confusion between apresent Sand other contents not now sensed. This effect of judgment s, then, Stumpf's point of departure. By the reliability of a judgment is meant the degree of confidence that may be placed by others in the truth or accuracy of the judgment as expressed. Snce, in general, objects are judged along with their sensa- tions (c_f. our discussran of the ]('-error), we may speak of the objecttee reliabzlily of judgment, in cases where "mt den S zugleich Objektives" or "uber S als Zelchen ausserer Vorg.nge beurtefit wird" (23). Ques- lions accor(hngly arise as to the factors which conditiou obj. tel., and as to methods of measuring it. Betore answering these questions, Stumpf distinguishes two classes of judgments. The first class consists of those inwhIch every one of the possfi)leanswers toaglven question may (accor(hngto circumstances) beetther rghtor wrong. For instance: "How many tones do you now perceive?" ,,Which of these two different tones is the higher ?" The second class contains judgments in which the affirmatmn is always rght and the negation always wrong, or wce versa. For instance: "Isthis tone the same as that you heard just now?" "Isthisnterval pure?" (24). The obj. rel. ofjudgmentsof the first class is dentical wth their degree ofprobabilzly, i.e., the ratio of the chances for the rghtness and wrongness of the assertion made; that of judgments of the second class s identical wth the degree of accuracy of the affirmative statement (hkeness or purity), or vth the degree of its approximation to the truth, --this being determined by the j. n. orjust unnotmeable unhkenessor impurity (26 f). Objective rehability, noxv, is conditioned upon two generaI factors: 1 We omit the dscusson of the law of relativity, on which see Question (0). ----------------------------------------------------------- cl xii Zntrotuctivn (1) sensiliwty, the degree in which our Scorrespond to the adequate R which arouse them; and (2) subjective reliabiltty, the rehabthty of a judgment with regard to the correct apprehenston of sensations as such, and without regard to their correct reference to external objects (28, 3I). In general, defects of sensitivity are responsible for errors in judgments of the second class, and defects of subj. tel. for errors in those of the first class (38). Passing to our second question, we find three things to measure: obj. rel., and its two factors, sensitivity and subj. tel. (I) Obj. tel. may be measured directly, without reference to (or even knowledge or) its factors. "All 'psychophysmal' experimental series furnish, as direct results, measurements of this kind. They telI us what the difference or ratio of two )? lnUSt be that shall call forth, under certain deftrote condi- tions,judffments of a definite degree of probability (first class) or of ac- curacy (second class) . . . The means to this end are xeries of judg- ments, from which we calculate the ratio of the right to the total number of answers, or the average error of the wrong statements" (43 f.). (2) IVleasurement of subj. tel. is "usually accomplished by examination of a series of judgments taken from the same O with constancy of adequate external  and with the introduction of circumstances that may affect the judgment. Judgments of the first class are here the more useful, since they show more plainly the effect of the dtsturbxng ctrcum- stances" (45). (3) "Measurement of sensitivity presupposes knowledge of subj. rel. It can be based only upon O's statements, and these are dictated, tn the first instance, not by hts .S'but by his apprehension of them. Sensitivity ttself is given, when we have subtracted from obj. tel., which alone is directly measurable, everything that should be laid to the account of subj. rel. Here, judgments of the second class are the more available, since they gtve the greater prominence to senstttvlty" (49).-- This is the framework of Stumpf's argument. It is clear that his psychophysics is Fechner upstde-down. Fechner began with sensitivity, and looked upon differences of subj. rel. as disturbing factors that should, so far as possible, be eliminated. Stumpf begins with th obj. tel. of judgments, and in so doing sets subj. rel. in the forefront of interest; the measurement of senslttvity thus becomes a ' Restproblem,' a remalntter of work that is left us when we have taken the one of our known quanti- ties, the subj. rel., from our total, the obj. rel. "Die Psychophyslk tritt so ihrem ganzen Inhalte nach als em Capitel und zwar, was den Lauf der Forschung betrtfft, als das letzte, in eine messende Urteilsleltre ein" (54). Here fs material in plenty for the exercise of the student's critical acumen! What are we to say of this doctrtne of the Sinnesurthed? õ 8. Questions and Essay Subjects clxiii Whence did Stumpf get tt ? What is tts validity? Is it true that we never haveasensattonwithout at the same tme'judgmg'it? What is the psychological mechamsm of ' apprehendmg in connectton,' of 'judg- ing about relatmn to other ideas'? What precisely does Stumpf do (i.e., what does he do for psychology) m measunng obj. rel. ? What ts the measurable magnitude (or what are the magnitudes) involved ? What is the psychological value of hs discrtmination of two types of judgment? Can the same distraction be couched in terms of directton and preparation of attention ? What are the psychological factors that make up subj. rel. ? Are they measurable ? Can Stumpf's position be worked out in associatonist terms ? The position has extreme value as a reasoned statement from premtsses the direct opposite of Fechner's: has it positive, permanent value on its own account ? In detail: are Stumpf's definitions clear-cut, ' workable'? are the methods which he suggests themselves reliable ? does he offer us a deftrote programme of work ? ts there any close connectton between his psychophysical prin- clples and his doctrine of distance measurements ? is he consistent in his view of psychophystcs (of., e.g., the definition, 54 n. wtth 55, last paragraph ) ? All these queries are to be answered, primarily, on the basis of the first three {{ of the Tps. A complete answer demands, of course, famtl- iarity with the whole of Stump['s psychophysical work. See also Wundt, Lectures, I x 5 if.; P- P', ill., 9o3, 579 if.; H. Bobmet, Die physiol. The- orie d. Smneswahrnehmung vom Standpunkte d. Psychophysik, 865, 355 if-; A. Riehl, Der philos. Kritlzlsmus, n., x, 879, I87 if.; James, Psych., i., x if.; Jodl, Psych., 896, t78 if. (t4) The doctrine of negative sensations. Fechner, El., if., 39; I. S., 88; R., 206; P.S., iv., 218; Preyer's Wiss. Briefe, 89o, I; Z., i., 9, o8 (also in Preyer's Wiss. Brtefe); Delboeuf, llements, 2o, 77; Examen, 37, 1o5,154; Langer, Grundlagen d. Psychophysk, 876, 49; Psychophysische Streitfragen, 893, 2; G. E. Mailer, G., 368; G6ttingische gel. Anz., 3 Juli 1878, 835; A. Nitsche, XXX. Programm d. k. k. Staats-Gymnasiums zu Innsbruck, I879, 22; C. Gutberlet, Natur und Offenbarung, xxvi., 88o, I 4; A. Elsas, Ue. d. Psychophysik, 1886, 47; G. Tarde, Rev. phil., x., I88O, 162; Wundt, Lectures, 42; Vn., 1897, 47; P- P., i., I893, 402, 406; i., 19o2, 498, 5ox; A K6hler, P.S., fit., i886, 588, 598 , 65; W. Preyer, El. d. reinen Empfindungslehre, I877, 2o, 43, 45; letters tn Wiss. Bnefe, 189o; H. Eb- binghaus, Z., i., 89o, 320, 463; Psych., i., I9o2, 5II f.; IV[. Foucault, Psychophysique, I9oi,  50; F. Jodl, Psych., I896, 28 f. ----------------------------------------------------------- clxiv Introduction (5) The physiology and psychology of Wundt's doctrine of appercepton. This essay mvolvesa comparison ofP. P., i., i893 , 230 if., wth 398 f. and n., 275 t.; or of i., I9o2 , 324 if., vith ibzd., 552 f. and il , I9o3, 34I. The lbrmer comparison has been made, in detafi, by W. Dtten- begel, Phfios Monatshefte, N. F., il., I896 , 97 if- Dttenberger's dscus- son may itself be taken as text for the essay. (6) The relation of Fechner's psychophysics to his experi- mental aesthetics. A text wfil be found in Lipps, Massmethoden, 22; Arch., ifi., 74. The student should read Fechner's Zur expenmentalen Aesthet,k, i. (all pubhshed), n Abh. d. kgl. sachs. Ges. d. Wiss, math.-phys. C]., ix., no. w., 87, 564 if, and portruns of the Vorschule d. Aestheuk, 2 vols., 876. (7) G. E. Mhller's psychophysical axioms. See Z., x., 896 , I if. Cf. Ktilpe, Z. f. Hypnotmmus, vii., 898 ,  4 if. The classical literature of psychophysics abounds in mathe- matical discussions. To the early workers a quantitative millen- nium seemed near at hand; even in 879 Fechner could say to Wundt, a propos of the founding of the Leipzig laboratory, "Wenn Sie die Sache so im Grossen betreiben wollen, dann werden Sie in ein paar Jahren mit der ganzen Psychophysik fertig sein. "x The present generation tend, on the contrary, to fight rather shy of mathematical formulations: at any rate, the author has not found among his students any considerable interest in this aspect of the science, and it is hardly probable that his experi- ence is singular. A few essay subjects which imply mathematics are, hoxvever, subjoined. The points involved are, in every case, points of psychophysical, not simply of mathematical importance. () A criticism of Fechner's use of the 'mathematical aux- iliary principle,' El.. ii., 6 if. See W. Dittenberger, Phfi. Monatshefte, x896 , 78 f.; A. Elsas, ibid., xxiv., I888, I33 if.; A. Stadler, ibid., xiv., 878, 219 f.; M. Radakowic, VJs., xlv., I89O , 7 if. (2) A criticism of Wundt's formula S----k-, where is "eine eben merkliche oder gleich merkliche Aenderung der  Lasswitz, G. T. :F½chner, 896 , 9 o. õ 9. The ])rob/eros of Sensitivity clxv S," k is a constant, and ,R is the "Zuwachs, der zu einer cen- tralen Sinneserregung R hinzukommen muss" in order to effect a /kS. See P. P., i., 887, 382; 1., 893, 4oo; i., 9o2,497; P.S., ii., 885, 6; A. Elsas, Ueber d. Psychophysfiq 886, 7 f., 7; Phfi. Monatshefte, xxiv., I888, I32; W. Dttenberger, ibid., 896, 80; A. K6hler, P. S.,ili., 886, 585; Fechner, ibid, ix'., 887, 67, 2o,227; A. Grotenfelt, Das \Vebersche Gesetz, 888, I7 h; A Hofler, Vjs., xi., x887, 355 if. (3) "The most important ameliorations of Fechner's formula are Delbceuf's in his Recherches sur Ia mesure des sensations, x873, and Elsas' in his pamphlet Ueber die Psychophysik, x886." --James, Psych., i., 89o, 539- Give a critical estimate of the mathematical xvork of Delbceuf and Elsas; note the points (if any) in which it marks an advance upon Fechner; compare Del- bceuf and Elsas as mathematical psychophysicists. Delbmuf, llments, 32 .; qt. 64 if., and Examen, 5t, 14o if.; Elsas, Psychophysik, o ff; rf. Phil. Monatshefte, xxiv., x888, 3I if. Fechner replies to Elsas in P.S., iv., 887, 65 if., and to Delbceuf in I. S., 27 if., etc. G. E. Muller heads { I24 of the G. (400 if.) with the words: "auch. Delboeuf's Correctur der Fechner'schen Maassformel muss far eine wenig gltickliche erachtet werden" (xv.). See also Kohler, P. S, iii., 1886, 6o4 if.; F. A. Miller, Axiom, 882, I29 if.; M. Foucault, Psychophysique, 9oI, I97ff.; A. H6fler's remev of Elsas, in Vjs., xi., 887, 35I if. (4) Criticise, in the light of the Reconstruction, Stadler's proposal of a Massformal that shall recognise the fact of the DL. A. Stadler, Phil. Monatshefte, xiv., 878, 220, 223. (5) "Fecbner's Unterschiedsmassformel . . . widerspricht [der dritten Ableitung der Massformel] geradezu." Criticise this statement, and estimate the psychophysical importance of the Unterschiedsmassformel. M. Radakoxmc, Vjs., xiv., 89o, 9 f.  9- The Problems of Sensitivity.The author has avoided, in the text, any mention of ' that blessed word ' Sensitivity. The student will soon run against the word, or some English or for- eign equivalent, in his reading of the literature; and it is advisable to give a lecture upon it, early in the present Course. But the ----------------------------------------------------------- clxvi Introduction term is probably better out of the way in a first introduction to quantitative experiments. What does Sensitivity--Empfindlichkeit--mean? "One and the same R," says Fechner (El., i., 45), "may, even if applied in the same way, be sensed more or less strongly by one person or one organ than by another, or by the same person or organ at different times; and contrariwise, R of different magnitude may, according to circumstances, be sensed equally strongly. We then attribute to the one person or organ, or to the given person or organ at one time, a greater or less sensitivity than to the other, or to the same at another time." "We regard sensitivity as in- versely proportional to the magnitude of the R which evoke . . . an S of equal magnitude" (46). "In general, the term sensitivity covers the same ground as the terms stimulability, excitability, sensibility" (5). "The measure of sensitivity is. as measure of mere capacity of 3', not to be confused vith a measure of 3. itself. Nor does it, as thus understood, presuppose any such measure, but only the observation of equal cases of 3', partly under the same, partly under different conditions of stimulation" (54). "Since sensitivity is variable, we need not seek for any hard and fast measure of it; but we can determine (1) its limit- ing values and (2) its mean values; we can investigate (3) the dependence of its changes upon circumstances; and we can (4) establish laws which remain valid through all its mutability" (ibid.). Fechner thus regards Sensitivity, response to stimulus by sen- sation, as a property of organised matter, of the living individual. In measuring it, we are always measuring R, not S (54): we de- termine what R are sensed or not sensed, what R or R-differences are sensed as same or different. It is, however, the necessary basis of 3.-measurement (46, 59 f.)- The three metric methods of the Elemente (just noticeable differences, right and wrong cases, average error)--methods for the measurernent of sensi- tivity, not of S---furnish the data upon which our measurement of 3' depends (i., 71; ii., 191 ). Fechner's views of 3.-measurement have not found acceptance. The concept of sensitivity has, however, taken a permanent place in psychophysics, irrespectively of what may lie beyond it. And, õ 9. T/re Problems vf Sensitivity clxvii like many other general terms in psychology, it vacillates between two meanings, or two aspects of meaning. It is employed, on the one hand, to denote a psychophysical function, the organism's capacity of sense-response to stimulation; it is employed, on the other, as the logical representative of a great group of facts, statically taken,--as the Inbegriff of all determinations made by the metric methods. In vol. i., I. M., xxi., the distinction between qualitative and quantitative work was drawn. for convenience' sake, in functional ternas. Fechner undoubtedly thought of sen- sitivity in this way: so do the ' mental test ' psychologists. Kulpe, who dispenses altogether with 3.-measurement, at least in the present stage of our knowledge, and accordingly makes the meas- urement of sensitivity the be-all and end-all of psychophysics. defines liminal sensitivity as "the bare capacity of experiencing and communicating 3.," and differential sensitivity as "the in- trospection of different contents and the report of their differ- ence" (Outlines, 31 f., 33). Here we seem to stand halfway between the functional and the logical definitions: the word ' ca- pacity' emphasislug the former, while the warning against the assumption of a 'faculty of comparison' (3) suggests the lat- ter. Wundt. who measures not 3' but degrees of 3.-Merklichkeit,   (more generally, defines sensitivity, formally, as  orz in the second instance, as the inverse value of the R-change neces- sary to a determinate change of 3'): P. P., i., 893 , 333 f-, 336; i., 1902 , 468, 470. Stumpf, who regards psychophysics as the final chapter of a 'messende Urteilslehre,' defines sensitivity as "the degree to which our 3' correspond with the adequate R which arouse them" (Tps., i., 28, 54)- This last is, in the au- thor's judgment, the best, because it is the least committal defini- tion. We may classify the departments of sensitivity, at least pro- visionally, as follows: I Liminal sensitivity (L. S.); Modal sensitivity (M. S.): . .. Terminal sensitivity (T. S.). Differential sensitivity (D. S.): Differential sensitivity (D. S.); Sectional sensitivity (S.S.). These forms must be briefly discussed. ----------------------------------------------------------- clxviii Introduction We measure L. S. by determining the least value of R (quali- tative, intensive, spatial, temporal) that can arouse an S. We measure T. S., similarly, by determining the highest value of R that can still arouse an S. These two measurements, therefore, give us the RL and TR of the text. We measure D. S. (in the narrower sense) by equating and differentiating two supraliminal S', and noting the R-values xvhich correspond to sensible equality and to j. n. difference. We obtain either the DL, or some value which is conditioned upon the DL. Finally, we measure S.S. by equating and differentiating two supraliminal sense distances, two sections cut from the whole sense conmnuum. We obtain a sectional DL, or some value that is conditioned upon it. It is clear that. in the last two cases, there are eight part-problems (equa- tion and differentiation for all four S-attributes). We must go into a little more detail as regards the M. S. (x) Fechner distinguishes between S. for absolute R-values, which he calls Absolute S., and S. for R-differences, xvhich he calls D.S. Absolute S. is measured by the inverse value of the R-mag- nitudes which arouse an S, liminal or supraliminal, intensive or extensive, of the same magnitude. Apart, then, from supralimi- hal and extensive R, it may be said that Fechner's A. S. corre- sponds to our L. S. and T. S., although Fechner is naturally pre- occupied with the L. S. (El., i., 45, 50; of. 3o if., 238 if., 254 ff.). (2) Wundt's terminology is different. The 'minimal' o e corresponds, for him, to the RL, whose value is an inverse meas- ure of R. S. (Reizempfindlichkeit). The 'maximal' o e corre- sponds to the TR, whose value is a direct measure of R-capacity (Reizempfanglichkeit). The portion of the R-scale lying be- tween RL and TR is the range of R (Reizumfang). Its inves- tlgation is a matter of the D. S. (P. P., i., 893, 334 ff-; i., 9o2, 468 ff. Tb.e terminology is worked out onlv for intensity: cf. ii., x893, 6 with i.. 45 o, 483). Wundt's R. S. and R-capacity thus correspond to our L. S. and T. S. Whether or not his range of R be included in the M. S. is a matter of definition; the usage of the different authors differs. (3) Stumpf uses the term M. S. (Umfangsempfindlichkeit) for "the extent of the S-sphere as compared with the sphere of R." It includes our L. S. and T. S. In the case of the partial series of vision (R-G, B-Y, B1-W), its , 9' The Problems of Sensztivity clxix investigation is, in practice, identical with that of the D. S. In the case of taste and slnell, where we cannot arrange the S in seres, ve determine the M. S. by listing the R which do and do not arouse S (Tps., i., 28 f.). (4) Khlpe distinguishes M. S., "measured by the number of S given with or possible to a par- ticular sense," from 'sensibility,' "measured in terms of the attributes predicable of the separate S." M.S. is thus partly con- cerned with the determination of upper and lower limits, our L. S. and T. S. (though these cannot be determined save in terms of the S-attributes !), and partly with the work which properly fails to the D. S. In two special cases, Kulpe's distinction seems to lead him into error. The M. S. of the skin, he says, is determined when we have counted up all the possible cutaneous S. But these are not qualities of a single sense: they proceed rather from four senses. Further, it"would be a test of quahtative senstbfiity to enqmre how many air ribrattans are necessary for the perception of the pitch of tone to which their period corresponds." But this is a determination of a temporal tone limen. The R]. of pitch are the wbration rates correlated with the highest and lowest audible tones: see Stumpf, Tps., i., 28; Fechner, El., i., 25;8; Ktilpe, Outhnes, 33 f. The ambiguity of usage and, the crossing of definitions are in- telligible enough when we remember (a) that the DL is a fact of 'friction,' and as such strictly co-ordinate xvith the RL, while (b), on the other hand, there is evidence that the least sense dis- tances correlated with the DL may be regarded as equal, and thus taken as the units of S-measurement. The DL is called upon (as we noticed in the text: p. xxxvi.) to play two different parts. Since we have ourselves decided to look upon all j. n. d. of S as equal distances, it seems best to take the DL from the sphere of the M. S., and to make this simply a collective name for the L. S. and T. S. The statement of the qualitative M. S. for tones xvould then be: "About 4 to 5o,ooo vs." The statement of the extensive M. S. for a certain blue would be: "Nasal, 53 ø, temporal, 37 ø, upper, 5 xø, lower, 24 ø ": together with a table of its minima visibœ1ia in direct and indirect vision. And so on. And now what of the two sorts of j. n.d.? Are we justified in bracketing together, as D. S. in the wider sense, the D. S. ----------------------------------------------------------- t:Ixx Introduction proper and the S.S.? Let us take some instances. In the one case, perhaps, we seek to determine the grey which is j. n. lighter than a given grey; n the other, to find a visual point-distance that is j. n. larger than a given point-distance. In the one case we seek to equate the brightness of a point, directly seen, with the brightness oœ a point shown in indirect vision: in the other, to equate a tonal distance in the bass with a tonal distance in the treble. x In all such experiments we obtain œormallv like results: a j. n. d., or some error value that is conditioned upon the j. n. d. May we bracket the two sets of determinations, differential and sectional, under a common heading? There is only one assumption upon which the bracketing is justified: the assumption that txvo sensibly equal distances of the S.S. contain equal numbers of least sense steps (intensive, quali- tative, etc.). The truth of this assumption is, of course, by no means evident. The decisive appeal lies to experiment: but, as we have seen, such appeal has been made in very fexv instances, and then under conditions that are not wholly free from objec- tion. 2 In the absence of direct experiments, it xvill, however, be rendered probable, if we find that the R-distances which are equated in sensation differ with difference of the DL,--beino smaller where the DL is smaller, and larger where it is larger; if we find, e.g., that a small tonal difference in the middle region of the scale (small DL) is the equivalent oœ a large difference law in the scale (larger DL); or if we find, conversely, that a given space distance (separation of compass points) is sense:l as larger on a part of the skin where the DL for space distance is small, as smaller on a part where the DL is large. Since this is what we actually do find. the assumption may be regarded as entirely rea- sonable. Stumpf, Tps., i., 60 if. It is, nevertheless, impossible to identify the D. S. and the S.S. For nvestigatons of D. S, only txvo R are employed; for those of S.S., at least three The conrhttons m the latter case are, therefore, more cora- l Here belong the experiments made by Fechner's method of equivalents, and referred by him to the A. S.: the equation of pressure intensities, e', at different parts of the skin, or of visual distances (Fechner's extensive J') in different regions of the retina.  See above, p. lxxxiv. õ 9' The Problems of Scnsztzvity clxxi plicated; the danger of judgment by secondary criteria is much greater. Moreover, we have said in the text that, m certain instances, the general condmons of judgment are (hfferent as we pass from determination of the Dœ to comparison of S-distances (Ebbinghaus, Psych., i., 504 f.): in these instances there can be no argument whatsoever from the D. S. proper to the S.S., or conversely. So, on the whole, our classification may stand. Like most classifications of complex material for pedagogical ends, it is a compromise. Things are put together, from one point of view, which from another should be kept apart: so the L. S. and the T.S. Things are set apart, from one point oœ view, which rom another would be brought together: so the L. S. and the D. S. But the schema will serve, at any rate, for lecture purposes, for giving the student his bearings in the vast tangle of facts that constitutes psychophysics. Essay Subject.--A complete programme of the investigation of S., showing the method to be employed for every attribute of S in every S-department. Ths essay may most profitably be written after the student has gained a general knowledge of the methods and oftherinterrelaton (see pp. 93 if., below), and understands the sigmficance of tle test-vaiues winch they furrash. The lacuna in the programme are especially instructive, and the reasons for thmr existence should be fully discussed. Some hints are given by Stumpf, Tps., i., 57 f. Muller, at the opening of the M. (I f.), says that the applications of the metric methods tiusserlich betrachtet are fourfold: to RL and Dr_., and to equal-appearing R and R-differences. An advanced student may be asked the question:What, then, are the apphcations, innerlich be- trachlet ? Does the doctrine of sensitivity furrash a satisfactory 'inter- nal' point of view ? ----------------------------------------------------------- CHAPTER I IRELIMINAR¾ ]XPERIMENTS My desire and aim are to arouse interest as well as toimpart instructton. Labour is not to be shirked m the study of a great questton, but it may be lightened m two ways: first, by the &mmu- tiou of its absolute amount, and, secondly, by calhng forth an energy whtch shall dimfresh it relatively. The true teacher, with the discipline of his pupil in view, wtll, I apprehend, always revoke the post- tire in preference to the negative force--TYNDALL. EXPERIMENT I õ Io. The ualitative RL for Tones; the Lowest Audible Tone.-- M^TERi^LS.--The dimensions given for the lamella are those of the author's instrument. Zwaardemaker (Z.. vii., I894, 2o) makes the strip 42o mm. long and 2 mm. wide, and the cloth ring 15 mm. broad; the range of rs. is the same.  The metal disc is always pulled from above; so that, in course of time, its lower edge works away from the strip. When this happens, it is apt to rattle for a moment after the lamella has been released. The fault is easily corrected by the mechanician. But if the accident occur in the course of an experiment, a wisp of cotton wool should be introduced between disc and strip. ADJUSTMENT OF APPARATVs.--The distance between lameflu and ear should be determined as the least distance at which the lamella, making the maximal excursion required by the series, fails to strike O's ear or head. 1 According to a note in Vrundt, P. ?., i., 893, 45 o, the lainella was described by A. Appunn in a pamphlet published in 859 (Ueber Wahrnehmung tiefer Tone: Hanau). The author has not seen this paper. Neither, as may here be remarked, has he been able to procure the papers by G. [and A. ?] Appunn in the Wetterau. Ges. Nat. Ber., I863-7, 73 if.; I887"8- B I ----------------------------------------------------------- In all demonstrations of the use of the lamella that the author has seen, the instrument is clamped to a high support, and 0 stands sidewise to it,--holding himself erect, or bending his head, in such a manner that the disc is always directly opposite the opening of the meatus. This arrangement answers well enough for a quick (say, a two-series) determination of the RL. For a methodical determination, it is not advantageous. If 0 keep his eyes open, he is apt to connect the appearance or disappearance of the tone with a certain length of the lamella. If his eyes are closed, and his head is brought into position by E, he is apt to connect the appearance or disappearance of the tone with a cer- tain set of head and shoulders. Judgment is thus passed, not in terms of hearing, but in terms of sight or of 'muscular' sensa- tion. Moreover, O's attitude soon becomes fatiguing, and the distance between his ear and the lainella may vary within pretty wide limits. Some laboratories will, doubtless, possess a stand, which can be raised or lowered without noise. Where this is the case, the lainella should be clamped to the stand, and its height varied as the experiment demands. But the monev required to build such a stand may be more profitably invested in a set of wire forks. Those xvho are unfamfimr with psychophysmal work may be inclined to underestimate the danger from ,secondary cnterm' of judgment (sght, muscularsensatmns, etc.). It is, however, alamentable fact that the human mind shoxvs in ths regard an unfafiingngenmty. Even the trained worker is constantly surprised by the protean forms which the secondary criteria may assume. One may give. definite instructions; one may have an honest, fairly practised and entirely well-intentmned 0; one may hedge the ,ntrospectons about wth all sorts of conditions: yet, fthere s awayoutor axvayround, that way will sooner or later be taken. \V,th a practised O, the secondary criteria w11 also, sooner or later, make their appearance in the introspectwe reports. Wth a comparatwely unpract,sed O, there is no guarantee that they wfil ever be recorded. The psychology of the matter looked at in the abstract, is somewhat as tolloxvs. 0 is called upon to gve a series of maximal attentions to an unfamdmr and ,ntnnsically uninteresting/. The outcome of this series of attentmns ,s to be a quantitanve d&termmaton. 0 is therefore on his mettle; he wshes to pass stable and accurate judgment. He is also õ o. The Quahtaive RL for Tones 3 anxious: for he has no means of knowing how accurate atd stable hs judgment really is,--he has nothing to 'go by.' If, then, there is any half-way constant or famfi,ar concomitant of hs first few judgments (a vmual pattern, a muscular set, or what not), he almost mstnctive!y takes adwmtage of it, and uses it as a standard of reference m later judgments. Brief as fins statement is, t may serve to shoxv the naturalhess and, ff one may say so, the reasonableness of the recourse to secondary criteria. No abstract statement could do justice to then' insidiousness and umver- saliW. The author has known a student to compare &stances, on MmJsterberg's apparatus for arm movement, by noting the place at whmh hshand struck his thgh as he dropped ,t from the finger-carri- age !--and thts was done qmte innocently, xxthout suspmion that t was wrong or even unusual. Nothing, indeed, seems too far-tetched or im- probable to serve as secondary criterion of judgment m psychophyscal method work. The Instructor should collect and classify instances, as the experiments proceed.  must be very caretul always to release the disc by the same move- ment. Otherwise, the sound of the pluck may be made the critermn of judgment. As the disc of the lamella swings to and from the ear, air-vaves are set up, whose impact upon the concha produces distinct sensations of pressure and temperature. Some 0 &sregard these accessory sensa- trans; others are distracted by them; still others make use of them, often unwmingly, as secondary criteria of judgment. The author has made experiments, on a sngle practmed O, to determine the effect (a) of interposing a thin Bristol-board screen between ear and dmc, and (b) of allowing the lamella to play past (instead of ,nto) the opening of the auditory meatus. In both cases, the A'L was sh,fted only  v.: ,n (b) it lay one v. higher, in (a)--curiously enough--one v. lower, than m the regular experiments. The particular results must be regarded as ac- cidental: but the fact seems to be estabhshed that such a change of experimental conditmns does not materially affect the position of the hmen. It would be worth whfie to make comparative tests in some numbers. An objective source of error in the lamella, under the prescribed con- (litions of usage, s that the mtlal amphtude of vibration increases as the rate of vbration decreases. Zwaardemaker suggests a numerical correctran of the results (o/. oil., 2). It would also be possxble to reg- ulate the amount of pull from test to test, say, by means of a vemcal rod hinged to the table. But the author doubtsffether procedure s worth w}nle. For one thing, the dfference m amphtude s msgnmcant over the crmcal portran of the scale, which (m the author's experrance) rarely ----------------------------------------------------------- ]relznzzary E:cerz'ments covers more than 3 vs and usually hes in the region x3 to 17 vs. For another, the strp s not uniformly elastic; tt warps and bends, robrating much more freely from some pomts thau from others. It should, of course, be pulled as often in the one direcnon as in the other (it may be changed about after every sertes); but even so this source of error is inewtable. As a rule, the cloth ring serves sxtisfactorily to cut off the overtones. Occasionally, however, by some accident or by careless manipulation, a shrill overtone will be heard. It need not nterfere wth O's judgment. For the temporal regulation of the series, a noiseless metronome may be constructed. Ascrew-eyeisturnedntoawooden upright, or into a bloclt of wood fastened to the wall; and a pendulum is made from a length of cotton thread and a weight. The thread s adjusted to the re- qmred frequency of oscillation by the help ot a stop-watch. An instru- ment of this kind s useful for many laboratory purposes. On the value of practice and ' warnting-up ' experiments, see Mtiller, M, 33- MEror).--The method is Mhller's Method of Least. Differ- ences as applied to the determination of an absolute L. It will be discussed in detail later. The following points may now be noted. O) lnlerrufitions of series--Any single test may be nulltried by a lapse of attentmn, an outside nmse, the pt;esence of an overtone, etc. The questran then arises whether the series shall be continued, or the test in question repeated The answer depends upon circumstances. If the test come at the beginning or end of a series, no notme need be taken of ts fafiure; ff t occur at a critical part of the series, t must be re- peated. In ether event, /' must face the situation in a perfectly matter- of-fact way; he must not allow O to be dtsturbed. In the former case, e.ff., E might say- 'All right ! Makes no dfference ! Now.t'; n the latter ß ,All right  Take t again * Wow !' The repetitton should be noted in the record, but the series may be counted in wth the rest. The mportant thing is that the full 20 series be worked through, evenly and steadily, xvithout departure from the plan of arrangement. (2) Zenffh of series.--A , moderate' seres has 6 to 8 steps. A. long series should not go above t2; a short series should not fall below 4. (3) Order of series.--If 0 has attained a fair constancy of judgment in the preliminary experiments, the order of the series (as well as the length of successive series) may be determined by' chance. (4) O's atti/ude.--The chtefsubjective sources of error in this method õ o. The Qualztative RL for ]'ones are two: expectation and habtuation. The effect of the latter is seen m a tendency on O's part to go on judging as he has been judging. e.ff., after he has said ' Tone ' a few times, to go on saying ' Tone ' beyond the point at which a change of judgment would normally occur. The effect of the former is usually seen n a tendency toxards a too early change of judgment: Oknows that the RLis coming nearer at every step, and therefore grows tncreasingly expectant of a marked change n the char- acter ol the R. In this form, the error of expectatmn makes against the error of habtuation. Sometimes, however, the two play into each other's hands. 0 knows that the steps are small. Hence, if the given J is a clear tone or a clear noise, he may. expect that the following R will be equally clear as tone or noise. This expectation may also carry hm beyond the pmnt at whtch achangeofjudgment would normally occur, and so reinforce the error of habttuatxon. In mew ot these sources of error, O should be carefully instructed to judge every R ndependently, as it is presented. If hs series show signs of a subjective error, the nature of the dangers to whmh his judgment is exposed should be pointed out to htm. If they do not, the discussran of these sources of error may be postponed. (5) Size of stes.--In order not to introduce too many vartables in a first experiment, we have kept the steps constant at x v. If, however, the method is to be strictly followed, the size of the steps as well as the length of the series should be vaned. There are two principles of variation. (a) The steps may be madelarger at the beginning ofa senes, where judgment is prompt and certain, than they are towards the end, when we are approaching the limen. Thus, a 6-step series might have the form 3, =, , ,ø.5, o.5. Theoretmally, no objection can be urged against this principle of series formatran. Practically, the principle cannot be carried very far, f we are to keep to the rule of correspondence between 4/and , seres A 4/series with constant steps may be matched, within a step or two, by an ' series. But t s very difficult to construct an , series that shall match a 4/ series with variable steps. Hence t would seem better, on the whole, to keep to a single step xwthin each series. (b) On the other hand, the absolute sze ot the steps should vary trom series to series. The lamella, e.ff, can easfiy be scaled to half-vs. We may then employ umts ofo.5 v., I.O v., and .5 vs.,in differentsertes. O should be left n gnorance of the size of the step used from one series to another. It need hardly be said that every unit must be taken as often in a 4/ as in an ,[, series. It is not necessary, however,--t is not even ad- visable,--that the two members of a paired series be always taken in immedmte successran; the dstribution of series may be planned before- hand, or may be left to chance. ----------------------------------------------------------- 6 ]>reliminary a:periments RESULTS.--The following Table shows the complete results of an experiment taken under the conditions laid down in the text. x Vs. 24 + 23 + 22 + + + 2I + + + + + :o + + + + + + 19 + + + + + + + + 18 + + :+ + + + + + + I7 + + + + i+ + + + + + t6 + + +'+I+ + + + + + + + + ? I5 + -- + + + + + + + + --:-- + 14 ?-- ? + ? -- -- -- 13 II IO 6 -- 5 -- 4 -- Notice, in the first place, that there is a fair degree of correspondence in the length of the 4 and { series. If we tabulate the series, in order of length, we obtain the following figures: 4 It 9 8 7 7 6 6 5 5 4, ' I2 9 8 8 7 7 6 6 5 4. 10 had worked through the experiments of Pt. i., but had had no special prac- tice beyond the prehmmary experiments. Ihs left ear was stimulated. The unused ear was open. õ to. The Qualitative RL for Tones 7 Now for the calculatmn ! Summing up the final terms of all series, and dividing by 20, we find RL=14.85 vs. Summing up the dfferences between this average 2L and the separate determmatmns, and divxdmg by 20, we find M'V'=.595 v. This m as far as the text takes us. We may, however, make the results the basis of various other computatmns. () In our determmatton of the arithmetical mean of the numerical re- suits (the average Rœ), we have accepted the figures yielded by the Table. Fhese figures it must be remembered, represent limts,--limts of steps of 1 v. Suppose that, ina4, senes, Osays'Tone'attsand'Nøtøne' at I4. The value I4 is entered in the Table. In reahty, O mght have said 'No tone' at any point between the limits 5 and I4. Hence the fairest value from whxch to calculate is not I4, but 4.5- Suppose, again, thatman,lxsenes, O says , No tone, at t3and,Tone'ati 4. The fair- est value to record xs I3.5. Wherever the change ofjudgmenttakes thin positive form, we should add -5 to the final terms of the 4' and subtract ß 5 from the finalterms of the ' series. Under such conditions, our aver- age L would be dentical wtth the 2L as determined above: we add as much to the Io 4' series as we subtract from the o  series. The MV would be a little smaller: -555 instead of .595- There is, however, a slight complication, due to the fact that the final term of some 4 serms corresponds to a ?, not to a--judgment- In these cases, the recorded figure may stand. If O says ,Tone'at t5 and ,Doubtful' at I4, we may assume that he would say ' No tone' at 13. The fairest value to calculate from is then I4. On this basra, we deter- mine our RL as I4.72 4- .54 rs. Ths is a more accurate value than the I485+.59. (2) We may calculate (from the revised figures) the separate values of the 2L 4' and the RL . For the former we find I4.75 4-.6; for the latter, 4-7 4-.48. The difference is xnsignificant. (3) We may ' fractionate' the experiments, and calculate the Rœ for each separate group of 5 determinatmns. Using the revxsed figures, we find: Rœ()  I4.6 4. .36 , RL(2)  14-I 4. -32, RL(3): I4.9 4. .44, L(4)  I5.3 4- .44. The differences are slight. It is, however, noteworthy that the steady ascent of the RL from (2) to (4) tallies wth O's introspectmns. O de- clared that he had given his best attentmn in group (2), and that he be- came increasingly tred and inattentive tn (3) and (4). He even doubted whether the values of group (4) could be counted in wtth the rest of the determinauons. ----------------------------------------------------------- ]rcliminary xpcvtnents (4) We may give a graphic representation of the results by construct- ing what is called a ' surface of frequency.' If we turn to the Table, we see that the value 14 occurs 7 times, I5 " 9 " 16 ,, 4 times. If, nov, we represent the values I4, 15, 16 each by a distance ofo. 5 cm. marked off along a horizontal line, and if we represent each time that the value occurs bya height of  min. above this line, we obtain a figure which shows at a glance the magnitude and variability of O's RZ. Rules for the construction and interpretation of surfaces of frequency are given the student under Exp. XXIV. (simple reactran). (5) A set of measurements may be represented by many other single values, besides the average or arIthmetmal mean. One of the most portant of these values is the median (Zenlralwer, I4,erlmille). The mediau is, literally, the middlemost value of a series. It may be defined as the magnitude above and below which one-half of the results appear, when they are arranged in ascending or descending order. Like the aver- age, it need not coincide xwth any one of the actual results. Indeed, it is nearly always an interpolated value. In long series, however,--senes of one or two hundred upwards,--the difference betxyeen the middlemost determinatmn and the median is nsignificant. We may determine the median, from our revised figures, as follows. We have 20 determinations. Grouping them, we find: Result 3.5 4 4.5 5 5-5 x6 Frequency of its } occurrence x 3 9 x 5 The median value (the value above and below which xo determina- tions occur) evidently lies among the group of 14.5. Now there are 4 values below 14.5. This means that there are 6 more values to be taken before we reach the median. The value 14. 5 itself occurs 9 times. Ac- cording to the simplest principle of interpolation, then, we have to take - of the interval covered by the value 14.5, and to add t to the lower limiting value of that interval. The interval is 4 25--4.75. If we add or .66 of this interval (i.e., of 0.5) to the lower limiting value i4.25, we obtain 14.58, the value of the median. The calculatmn may be reversed, and our result tested, in this way. There are 7 values above 4 5. Thin means that there are 3 more values to be taken before we reach the medmn. We must therefore subtract of the interval covered by the value I4.5 fi-om the upper limiting value of that interval. And 4-75--.I 7 is, again, 14.58, the value of the median.--  IO. T/I' Ouahtative RL .for Tones 9 This procedure may be formulated as follows. Divide the results into three lots: those less than the m(ldle class, whose tot.fi humher is a; those of the middle class, b; and those greater, c. Then a+b+c:n= the whole number of results. Let /':the lower, and/"=the upperbmt- mgvalueotthemddleclass. Letx=the distance ofthe median above/' or below l", according as x is positive or negative. Then:  l" -- ----a: b=x: l', when x Is positive; 2 ---c: b:x:/"--/', when x is negative. Grouping our 20 determinations, as the rule requires, we have: Below middle Middle class Above middle 4 9 ? The first equation reads, accordingly: o--4:9 =x ß 4.75--14-25, x= 33 Simfiarly, the second equation reads: o-- 7: 9 = --x. 4.75--14.25, --x:.I 7. Hence the median is 4.25+.33 or 14 75--.7, œ e, 4.58. (6) Yet another representative value of a series of measurements is found in the mode (dichlesler I4er, Dichlg/celsmll), which is the commonest single value, the single value that appears most frequently in the records. The mode of our ]L determinations is, evident]y, 4.5: this is the value that appears most frequently (9 times) m the rewsed figures 1 Putting these results together, we have: Average Median Mode 14.72 14.58 4 5 ø rs. (7) As with the representative value, so with the measure of variability: we are not by any means confined to the 2kF. We may, e.g'., determine what is called the standard deviation or error of mean square. This is the square root of the average of the squares of all the individual differ- ences between the final A'Z and ts separate determinations. Iu other words, it is the dfference whose square is the average of the squares of all the differences. If v represent the single differences (residuals), and n be the number of determinations, then the formula for the standard  This is, in reality, only the empirical mode, or mode as determined by inspec- tion; it corresponds roughly to the determination of the median as lying within the group of 4-5. The precise calculation of the mode is more laborious than that of either the average or the median. We need not enter into details here: see Fechner, Kollektivmasslehre, 897, x82 if. ----------------------------------------------------------- IO Prehmtnary Ea:periments deviation is / n ' When, however,--as in the present case,--the number of determmatmns ts small, it is customary to introduce a cor- rection by writing n-- for n in the denominator of the fraction. The formula thus becomes: , :( Let us determin the staudard deviation of the average 14.72. The individual differences or v are as follows: Dfference .22 .28 .72 .78 1.22 1.28 Frequency of occurrence 9 The sum of the squares is therefore .o484 + .4884 +  6384=8.238. The fraction E(v) or .238=.4335. Then n--  19 1/.4335, approximately .66, is the standard deviation required. Theoretmally, and practically in series o[ sucient length, the  of the average stands in a constant numerical relation to the SO, as follows: JVor O: SD=I: 1.2533, or AD=o.7979 SD. (8) Another measure of variabfiity xs given by the , probable error' of the representative value. In any series of errors, the probable error has such a value that the number of errors whmh exceed it s the same as the number which fall short of it. In other words, it ts an even wager that an error taken at random wtll be greater or less than the probable error. For a discussion of it, see p. 52 of the text. The formula for the probable error of the mean = is: 1 It may be noted, for the benefit of the student, that the terminology of ' errors ' and ' dewations ' is somewhat confused. The term ' mean variation ' has become established in psychophysics, English and German alike. It is identical with the 'average deviation' of statistics and the ' mean error' of physical science. The 'error of mean square' is called by Merriman (Least Squares, t9oo, 204) the ' mean error,' by Sanford (Lab. Course, 359) the ' average error.' This phrase is a translation from the German (of. Kulpe, Outlines, 67, and the German text-books generally). In statistical work it is known as the 'standard deviation.' On the other hand, the terms ' average error ' (Fechner, E1, i., 72), ' average crude error,' ' average variable error,' when they occur in discussions of the metric method of average error, often (perhaps usually) denote ./l/'V's of one sort or another. C./; Cattell, art. Errors of Observation, in Dict. of Phil. and Psych., i., 34o- 2 Notice the implication of the formula: that the trustworthiness of an average is proportional, not to the number of determinations made, but to the square root of that number. Other things equal, an average of $ determinations is five times a.s trustworthy as is the single determinatxon. õ o. The Qua/ztative RL for J'ones lI SD .PE, =o.6745 or, in full: .PE:o.6745 / (-) In our own case, ths becomes: =o.67456, or o In other words, =o o99. For general purposes we may use, instead of the above formula, the approximate formula: _ ø'8453.M In our own case, this becomes: 4.30 In other words, (9) Lastly, there s, of course, a ' probable error' of the single obser- vanon, as well as a probable error of the mean. Its formula is: PE=o.674 or PE=o.6745 SD. In our owu case, it amounts to o 44. Calculated from series of suffictent length, PE: g: SD=: .8: .48. Even with our few results and approximatxve determinations, flus ratto gves 0.44: o 52: 0.65. (o) Putting all these results together, and adding some new determi- natrons on the same lines, we have Merae 4 72 vs. SO= .66 Y= 5.5 o 3[edian 4.58 rs. SD=  .67 dlF=  .47 3od 4.5o rs. SD= .7o PE= ß .44 P= Z .ø99 (xx) It is needless to say that many other things may be done with the figures. Thus we may determine the reed,an erroro[ themedmn: rather by the method given above, and now applied to res,duals instead of to determinatmns, or simply by arranging the determtnatmns in order. writing the residuals under them, counting off a quarter of the residuals from either end, and averaging to obtain the median. In our own case. the median errors o 5- XVe may then determine the probable error of the ----------------------------------------------------------- 12 2>reliminar y 2xperiments o5 roediana itself as  or o I I. Again, we may determine the uncer- l" n tamty (the probable error) of the _Pœ. Or, once more, we may calculate (by the ad of Tables in the mathematical text-books) the relative chances that the true average of our measurements hes within certain, contin- ually widening hmits. And so on. Now all these determinations are valuable in their own place. But it is foolish to run to extremes, and to make a fetish of numericaI valnes.2 .The statistical treatment of variations is very much, in the air ' just now, and there is a temptation to carry it too far. For all practical purposes, it is enough in these experiments to know the values of the average and the F(M611er) or the values of the average and the E (Scripture)? It would be well if every student of quantitative psychology understood the KollektlvmassIehre; occasions arise when 0 finds a knowledge of the meaning and computation of the ordinary measurement values ex- ceedingly useful, if not indispensable. But it must be remembered we shall have more to say upon the matter laterthat ideal curricula cannot be mposed upon undergraduates. And the student who desires to gain a limited acquaintance wth psychophysical methods and quan- titative results should not be burdened with a mass of prehminary work which he will forget as soon as he leaves the laboratory2 Vith graduates the case is different. INTROSPECTONs.--With unpractised O, there can be no ques- tion but that it is best to take extra, separate series for the introspections. It is essential that the series run smoothly; and the introspective requirement means continual interruption.5  One of the disadvantages of the median is that it is a more uncertain value, for a given set of determinations, than is the average. It is necessary to make 249 determinations to secure the same accuracy for the median as is given by H4 determinations for the average.  Cf. what is sad below of the treatment of reaction-time results. pp. 362 if. a Scripture slmpl ties cd. culatmn by writing - for the factor o6745. Yale Studies, iv., 896 , 9  ff t The author was glad to run across a somewhat similar remark in Muller (M, 62). After discussing various values derived from the method of constancy (right and wrong cases) with a full series of F's Muller says: "Es gibt naturlich noch zahlreiche andere Operationen, die man reit den.. Resultaten Vornehmen kann .... Abet die Mltanwendung weiterer Operationen--man kann hier das ganze Rustzeug der Kollektivmasslehre hervorholen--wird im Grunde nichts lgeues yon Wesenheit zutage fbrdern." It is true that Muller knows his Kol- lektivmasslehre, while the average student of psychology does not ! * It may mean a total change of mental athtude. Take an unpractised O, in  o. The Quahtative RL for Tones Something may be done in the pauses. But E has his coming series to arrange, and O has only his memory to rely upon. Still, O should be encouraged to volunteer remarks at the end of the series ;E's attention may thus be called to sources of error, factors in judgment, etc., which wonld otherwise escape notice. With practised O's, the qualitative and quantitative procedures may be combined to an extent that the older psychophysics would have deemed impossible. Even so, however, it is in general safer to duplicate the series. See Muller, M., 33 if. IsruTs.The following are the most available instruments for un- dergraduate use. () Lainella. This is the cheapest and simplest instrument for the work. Its defects have been discussed above: cf. also F. Bezold, Funktionelle Pruf- ung des menschlichen Geh6rorgans, x897 ' x3 ¸. According to Zwaarde- maker (Z., vii., 3) it was first described by A. Appunn in 887-8; Wundt (P. P., i., 893, 450) dates Appunn's paper x889. (2) Giant fork. Helmholtz and Wolf worked with a giant Koenig fork in 87ø' and Preyer with Appunn førks in 879- The Koenig fork (Fig. 3) is still listed bv L. Landry (Koenig's suc- cessor) and by Kohl. The specimen in the Cornell laboratory gives, by means of sliding weights. the tones 6 to 25 es. The fork may be actuated by pinching with the gloved hand. or by Fro. 3- striking with the two fists or with rubber-faced mallets. It is a good demonstration instrument, but not very satisfactory for the sense of this book, and determine the/œ () by a paired series without and (2) by a paired series with step-for-step introspectmns. The discrepancy in the results is startling. ----------------------------------------------------------- I4 ]>reliminary xpcrimvnts laboratory purposes. If no resonance box is made, the accom- panying noises and overtones are confusing. The resonance box itself fills up the whole side of a room (Preyer, Ak. Unt., 4). (3) Edelmann fork. Bezold's set of instruments for a 'con- tinuous tonal series' contains a low fork of  to I8 vs. The fork is light enough to be held before the ear with the hand. This and the fork next above it could probably be bought separately: the au- thor has not worked with the Bezo14 instruments. See Z., xiii., 897 , I62. (4) ffire forks. The Appunn wire forks (Fig. 4) were apparently intro- duced by S. Moos (Z. f. Ohrenheilk., xxiv., i893 , i5i ). They range from 8 to 24 rs., by 2 rs. intervals; higher forks, of 32 , 48, 56 , etc., rs. are fur- nished for practice work. The material is a wire (4 min. in diam.) of soft steel or of some alloy; the weights are brass discs. There are no perceptible over- tones. The author greatly prefers these forks to the lainella; though it should be said that they are brittle, and soon break in two at the bend. He has had the set reproduced in medium .grade (spring Bessemer) steel wire. The new forks give shrill overtones, which must FIG. 4. be damped by cloth rings sewed round the xvire. QUESTmNS.--() A discussion of this point will be found in J. Venn, The Logic of Chance, 3d edn., I888. 444 f., 448 f., 460 f., 474 fl. The student may also cf. W. S. Jevons, The Principles of Science, 9oo, 357 ff. (2) The student may be referred to Venn, Logic of Chance, chs. xviii., xix.: K. Pearson, Grammar of Science, 9oo, 38 if.; C. ]3. Davenport, Statistical Methods, 899 (an extremely useful õ m. The Qualitative iL for Tones little book for practical purposes); M. Merriman, A Textbook on the Method of Least Squares, I9OO, esp. 41 fl., 208 fl. (the book is admirably clear, and may be understood in good part even by the non-mathematical reader); E. W. Scripture, Yale Studies. 894 ,  if. (an unnecessarily technical paper, and not to be fol- lowed in all of its conclusions); E. L. Thorndike, Educational Psychology, 9o3, 3 if-. 66 if.; Mental and Social Measurements, I9O4, esp. 7  ff.; F. Galton, Natural Inheritance. I889, 35 if- (median); J. McK. Cattell, art. Errors of Observation, and W. R. F. Weldon, art. Variation, Statistical Treatment of, in Dict. of Phil. and Psych.. i., ii.; Fechner, Ueber den Ausgangswerth der kleinsten Abweichungssumme, Abh. d. kgl. sachs. Ges. d. Wiss., math.-phys. K1.. xi., 878 ,  if. (esp. for the median); Fechner, Kollektivmasslehre, ed. G. F. Lipps, 897, 8, 7, I6O if. (average); I3, 7, 65 if- (median); 2, 7, I7ø if-, 82 if. (mode); 4, I72 if- (other representative values); 8 if., 92 if. (measures of variability). The student should be led fully to realise what it is that the various representative values represent. He should, e.g., under- stand why it is that the average is the best representative value of the experiments that he has just been making. It is a good plan for the Instructor to have a collection of examples, so chosen as to indicate the relative importance for different purposes of the three values discussed above. The collection may easily be formed from the literature. (3) A good answer to this Question implies a psychological theory of the method. Some few points (mostly in relation to sources of error) will be brought out by an intelligent student. The Instructor may discuss these, and may anticipate the histori- cal and critical discussion of the methods (pp. 99 ff-) so far as he judges advisable. Hints of theory should be thrown out as early as possible in quantitative work: on the other hand. it is bad pedagogy to load the student's mind at first with too much detail. (4) Introspection ends when the series end. Psychology goes farther: for the RL, though an ideal value, lying midvay between the final introspective data of corresponding ( 4, and ' ) series, is  On these two works, see p. 9 8 below. ----------------------------------------------------------- 16 Prehminary œxperments a psychological value. Calculation thus begins for psychological purposes, and for those only. Once begun, it naturally follows the rules peculiar to it as a special mathematical operation. The student must clearly understand that the calculation is psychological calculation. It is a common mistake, at first,- and it may be reinforced later by interest in the calculafive pro- cesses for their own sake,--to suppose that there is a sharp divid- ing line between the psychological work of the experiment and the mathematical work of calculating its result. If that were true, the calculation might be dispensed with. (5) In the Exp., as made, every 4, and every  series has given us a single RL-value: the 4, series, the value of the first or just unnoticeabte R; the ff series, the value of the first or just noticeable R. If we represent these values in two typical series, by the letters b ands', our average RL (as determined from any paired series) is a'+b + I + 4, + + ? I - It is clear, however, from inspection of the series, that they fur- nish two other values, whose average has an equal claim to repre- sent the RL. These values are a, the last noticeable R of a series, and b', the last unnoticeable R of an ' series. The aver- age of the last ' noticeable ' and the last ' unnoticeable ' is as truly a liminal value as the average of the first ' unnoticeable ' and the first 'noticeable.' In other words, RL may be made=a+b Or, if we combine all four critical values, RL 4 MEwaor).--As thus employed, the method is Higier's exten- sion of Mhller's Method of Least Differences. It will be dis- cussed in detail later. In the present instance, precisely the same õ Io. The Qualttatzve ]qL 5r Tones 7 series may be made the basis of either mode of calculation. The extension of the method becomes of importance only when we apply it to the determination of the DL. Nevertheless, it is worth while at this stage to call the student's attention to the sgnifi- cance of the values a and b'. RsuL:s.--Instead of working out the combined /L froin our former Table (p. 6), we may take another set of results. The following Table shows the complete results of an experiment made under the conditions laid down in the text, except that 2 (not 20) series were taken3 SERIES I 2 3 4. 5 12 Vs. 23 + 1 22 q- 2I 20 + + 19 + + + + 18 + + + + + I7 + + + + + + 16 + + + + + + 15 q- q- q- q- q- I+ q- q- q- q- q- 4 + -- + -- + -- ? ? + ? + ? 3 i2 i0 7 -- 6 --  0 and conditmns as before (p. 6). The table shows the effects of increastng practice. C ----------------------------------------------------------- 18 Prehmznary œxpcrzments The series correspond, fairly well, as follows: 4' xo 8 7 7 6 , xo 8 8 7 5 4. The separate averages, as drawn [rom the Table, are: a last noticeable 4 2 ñ.3; b first unnotceable 13.2ñ. 3; a' first noticeable 15.o4- o; b' last unuotmeable 24.o4- o. The )?.L, calculated as b+a'=4.x4-.92; 2 ,, a+b'--t4.4-. 7 ; " a+a'+b+b'--14.oSñ 53. 4 If we undertake a revision of the figures of the Table (see p. 7, aboveL we find (0 that m all but one of the 4' series a and b coincide. Thus, in series t, the last noticeable and the first unnoticeable fall with equal probabdxty upon I3.5. Only m series 7, a falls upon I4.5 and b upon 4.o. Again, () in the first 3 ' series a' and b' coincide. In the last three, we must put a' at 4.5 and b' at 4- Averaging all values, we obtain Rœ= 14 4- .4 '2' The determination of other representative values and measures of variability may be assigned tothe student, if the Instructor see fit, as an exercise in computation. If the student fail to answer the Question, he may be asked to criticise some bt of work in which Higier's method (or an approximation to it) has been employed. Higier's own account is to be found in P.S., vii., 892 , 265 if. If it be thought too difficult, take Scripture's Exercise on the Threshold of Touch (Yale Studies, iv., 896 , 92 if.). The following criticisms will occur to the reader: (a) It is not advisable to place the hand on the knee. Apart from the fact that constancy of position cannot be guaranteed, complicating press- ures are introduced which may distract the attention. (b) The interval between the ready-signal and the application of )? is to be "about 2 to 5 sec." It should be kept constant at a short 2 sec.; otherwise, O's attention may lapse and xvander. It is advisable to vary the conditions of an exp.; it is oftentimes advisable to vary them irreg- ularly. But the degree of attention is the very last thing that should vary in a limlnal determnatmn ! Notice that nothing is sad in the õ m. The Qualitath,e I?L/or Tones 9 Specimen Record of the times elapsing between the Ready ! and the ap- plication of R. Some of the more startling irregularroes in series 4, 7, io may be due to their variation; although () errors of manipulation play a large part m any exp. with the touch- weights. (d) The exp. is performed only in the  direction. The series have all the same length and all the same size of step. (e) The value chosen to represent the' lower' hmen (our Rœ)is a'. This is correct, although in strictness  mg. (halfthe unit interval) should be subtracted from every recorded value before the average is drawn. (f) Another value (,,the number of the chsc beyond which all were felt ") is selected to represent the ' upper' hmeu. This may suggest to O the possibility of determining upper and lower limiting limens  or LL, in addmon to the ]eL proper; or--since he knows nothing so far may suggest to him the use of the value a in the J/ (and therefore also of b' in the ,l x) series for the determination of the Z itself.  At any rate, the procedure is so different from our own as to set him thtnking.  The authorproposes this term for the German ' Schwelle der Unentschiedenheit ' and' obere Grenze der zufalligen Werte der A'/'..' The former, according to Muller (who is speaking of the Raumschwelle der Haut), "ist dadurch charakter- isiert, dass jedes 29, das kleiner ist als die S. der U., den 'Endruck der einfachen Beruhrung erweckt, hngegen jedes ]9, das grosset ist als dieselbe, entweder das Utter ' unentschieden ' zufolge hat oder den Endruck der Doppelberuhrung her vorruft" (M., 44)- The definition may be applied, mutatls mutand, to the deter- minatmn of any absolute œ. The latter is "der genngste yon allen denjenigen ])-Werten, die stets das Urteil ' doppelte Berihrung ' ergeben" (:bzd.) ß the defini- tmn may be similarly extended. It m this upper ZZ. that Scripture seeks to deter- mine. While, however, the lower ZZ may be ascertained, the value of the upper ZZ. is always very dubmus; see Muller, n loc.; Ebbinghaus, Psych., i., x9o2 , 492. What holds of the/fœ in thin regard holds also of the ]gZ: see Muller, M., 44, 55; and of. hm crmque of Fechner and Volkmann, G., 56 if. There may, of course, be exceptional mrcumstances which suggest the determinatmn of the upper Zœ: of. Meumann, P.S., ix., x893 , 277 if.; xii, z896 , xS: fl.--These /.Z must be sharply dzfferentmted from the overlimens or OZ. "Man kann neben der oberen und der unteren /)L uoch eine obere und eine untere Ueberschwelle unterscheiden, welche dadurch charaktensiert sind, class /nur dann fur viel grosset bezw. viel kleiner erklS. rt wird als ]];, wenn der Unterschied zwischen //und far din obere bez,. untere Ueberschwelle hberschreitet": Muller, M., 55, 7 z; E. Mosch, P.S. xiv., 189, 542  Muller remarks (M., 84) that Scripture noted "bei dem aufsteigenden Ver- fahren neben dem ersten merkbaren )?-Werte afich nodh den letzten unmerk- baren." This would represent the ascending half of }llgier's method What Scripture really does, however, is to record the disc first felt (the fist notretable /V) and the disc beyond whxch all were felt, At., the upper hmitmg value of the as- cending J?œ. The 'last unnoticeable ' does not appear at all in his directions. ----------------------------------------------------------- 2O Prchmbtary Experœmetts (6) For sources of error, see the discussion of the method, PP- 4 f.-- In some cases, the effects of expectation, habituaton, suggestibility, etc., are so great as to prevent the determination of the limen by the serial method. Thus Kiesow, in his determi- nation of the qualitative RL for taste. found it impossible to em- ploy the 4 series: P.S., x., x894, 358 f- Stratton devised the method of 'serial groups,' for the determination of the visual movement-limen, because "certain excellent though suggestible subjects" proved refractory to the method of minimal changes; they "persisted in seeing the light move on every occasion, whether there was any actual movement or not ": Psych. Rev., ix., I9o2, 444 if. Miiller, in determining the limen for the visual sensation aroused by electrical stimulation, repeated his R 5 times at every step, and averaged the R-values at which the five-fold perception was ' still just possible' and ' just no longer possible ': Z., xiv., 897, 372: c[. 364, 367- Gamble gave up the 4, series for smell, as Kiesow had done for taste: "it is often impossible, on account of adhesion in the tube or in the nasal passages, or on ac- count of memory after-images, or cumulative stimulation, to move from a point of intensive stimulation to a point at xvhich sensation entirely disappears." O was allowed to move to and fro, back and forth, about the first final point of an ,1, determination: A. J.. x., x898, o6. Some instance or instances of this sort will probably be suggested to the student by his qualitative work. (7) The student should think of certain perception limens (limens of movement, visual, cutaneous, articular, etc.; the two- point limen of the skin) as well as of the RL proper. (8) The student will almost invariably suggest modifications of the serial method, i.e., ways of varying the R so as to bring out the same judgment of ' just noticeable.' This gives the In- structor an opportunity to introduce the idea of the method of constancy (right and vrong cases), where the R are kept the same and the judgment of O varies under the influence of acci- dental errors. As was said above, theoretical hints of this kind cannot be thrown out too early in quantitative work. õ I I. 7']lt Qualitative RL for Toncs 21 EXPERIMEN II õ  . The (lualitative RL or Tones: the Lowest Audible Tone. Alternative Experiment.--Ti.e method is a form of Nraepelin's co:rib.ned method of limits and differences (i.e., of min. ch. and right and wrong cases): see P.S., vi., z89 , 499 f. The object of the haphazard order of the R is to avoid the errors of expecta- lton, habitnation, etc., incident to the former method. On the score of psychologmal analyss, it may be doubted whether the results of thin and of the first method are ever strictly comparable. For one thing, (a) the standard or criterion of judgment is]lkelytodlffer m the two cases. In the method ol ]east dfferences (method oflimts),the standard is fixed by the character of the series. 0 begins every new series with the knoxvledge that 'this s a tone; ths is the sort of t}ing that a very low tone m,' or that ,this is a nose; this is the sort of thing one hears hefore one reaches the tonal hmit.' He need not trouble to memorise tone or noise; he s constantly remiuded of what tone and noise 'sound hke' In the combined method, on the other hand, he has notMng to help him but hm memory of the prehminary experiments. As the severalRare presented, he has to askhmselfafresh: Is there tonal- ity in ths impression ? does thssound hke a low tone? If he has a standard, it s either an ideal, memory standard, or a standard m- prowsed from themmedmtely preceding experiments. In both events, t is hkely to vary from series to series, even from one part to another of the same seres. Again, (b)--perhaps as a result of this dfference of cnter,on--there is apt to be a marked dfference in degree of attention. In the method of least dfferences, O, after a very httle pracuce, inchnes to take thmgs easily for the first few stepsofasenes. In the combined method, attenton is stramed to the utmost at every step; so that t is, at tinies, almost comic to note the rehef wth whmh the judgment ' Nothing' s passed on an R of 6 vs., or the judgment , Tone ' on an R of 22. The combined method is thus by far the more fatgmng of the two. Besddes, (c) the method of least dfferences has its own pitfalls of expectat,on, etc., which the combined method ams to avoid. Despite ths difference of psychological motivation, the quantitative results yelded by the two methods in laboratory practme are, to all intents and purposes, the same,--equal degree of practice being presup- posed. The RL is a varmhle value: variable not only for different 0, at thfferent stages of practice, wth dfferent degrees of attention, but intrin- sically variable. Nevertheless, the results of the two methods tally surprisingly well. Hoxv are we to explain this fact ? ----------------------------------------------------------- 22 ?reliminary Ea:periments We might, perhaps, shelter ourselves behind the roughness of our work. O is not an investigator. And we know, from the analogy of physical weighings and measurings, that the rough determinations are those most hkely to agree. With a better instrument, with smaller steps, with more refined introspections, the variability of the RL would come out more plainly, All this is true. It is also true, however, that the representative values of the ]?L for tones, as determined by different methods, agree very well even under the most accurate condotrans of observation. This can only mean that the A?L corresponds to a real and definite change in the character of the sensations aroused by the instrument employed. There are certain 27œ whose position is so masked by physiological and psychological disturbances that their determination, whether by the method of least differences or by the combined method, is out of the question. But the )?œ lot tones, the ideal dividing line between tone and no-tone, the first critical point upon the tonal scale, is so clearly marked for retrospectran that axe find it (within certain closely drawn limits of variation) by whatever psychologmal road we approach it. No liminaldeterminatmn is easy, but this particular determination is cer- tain. It is for this reason that the experiment s well fitted to serve as introduction to quantitative work in psychology. REsuLrrs.--The following Table x shows the complete results of an experiment taken under the conditions laid down in the text. Vs. 8 9 o  2 3 4 5 16 x7 x8 9 2o Series  + + + -- + + + + + + ,, 2 + + + + + + + " 3 + -- ? + + + + " 4 + + + + + + + + " 5 + -- + ? + + -- + + + ,' 6 ? + + + + + + + + " 7 + + + + + + + + + " 8 + + + + -- + + + " 9 + + + -- + + + + ,, lo + + -- + ? + + + +  O and conditions as before, pp 6, t7. O has now reached his first steady level of practice. A renewed determination by the method of least differences gave A'œ:t 3, with_ an J/r/,- of less than 0. 5. It is possible that further practice would reduce this value by a vibration; but, according to the author's experience, it is not probable. õ  r. The Qualitative ]L for Tones 23 () The first question that arises is the question of the treat- ment of the ?-judgments. Muller thinks that "bei der etwas prekgren Beschaffenheit" of these judgments, their R should not be counted either as perceptible or as imperceptible (M., 85). He is, however, evidently thinking of results in which (owing to the smallness of the unit) ?-judgments are quite common; for his immediate problem is, whether the arithmetical mean of all the ?-R can be regarded as a 'characteristic value representing the RL.' In the case before us, ve have only one ?-judgment to consider: that of series 6. This series is quite regular; and there is no reason to think that the ?-judgment stands on any other level than that of the b of a 4, or the b' of an ß 1' series (method of least differences). We may therefore assume that the critical values of series 6 are 3 and 4, not x2 and 4. (2) Since the R have been given in haphazard order, the in- terval covered by any value y is not the interval y--z, but the in- terval .v. 5--y. 5. In other words, we may calculate our averages from the figures as they stand, without revision. (3) The iregularities of judgment which occur with this method are always a little puzzling to the student. In some cases we may, of course, suspect an objective source of error. Thus the two- under 8, and the two? and one -- under 7, may with some show of reason be attributed to a warp of the lamella, which prevented its oscillations attaining their full amplitude or main- taining their normal duration. Unfortunately, the instrument was not examined at the conclusion of the experiment. It should, however, be said emphatically that irregularities of judgment are characteristic of the method; they are due to all sorts of acci- dents, which the keenest observation will be unable to identify in detail. It will be remembered that the determination of an upper LL is vitiated by their occurrence. An experiment that gave only regular series of the type of series 6 would be open to the sus- picion either that its units were far too large or that 0 had not judged in terms of audition. (4) If we average the last unnoticeables, we find RL:2. 5 :k 0.8; if we average the first noticeables, RL=3.5 + 0.8 If we take the average of both values, we have RL:x 3 4- o.8. ----------------------------------------------------------- 24 Prelimtnary ]z'xperiments It is possible to treat the results by the procedures of the method of constancy (right and xvrong cases). Such a course is, per- haps, hardly advisable at this stage; though the Instructor may take the results as a text in answering Question (8), p. 20 above. (5) Muller (M., 185) recommends the introduction of blank experiments. With the lainella, hmvever, they are usually fail- ures. The strip must be plucked, or O will miss the sound of actuation. If, now, the lainella be arrested immediately after the pluck, O misses the impact of the air-waves upon his ear and hair. If a screen be interposed between lamella and ear, the im- pact is again cut off, xvhile supraliminal tones are still heard. On the whole, therefore, it seems best to dispense with the blank experiment in this particular case. õ 12. Determinations of the Lowest Audible Tone.--The fol- lowing Table brings together the most important historical state- ments. A fexv other references are given in the Remarks appended. I. PROPER TONES OF VARIOUS INSTRUMENTS. (I) (2) (3) (4) (5) (6) (7) (8) (9) (lO) (1i) (1) (13) (14 (15 Observer Date Sauveur Chtadm Brat Wollaston Sayart Despretz 17oo 18o2 7187 182o 831 1845 40 it. pipe 12. 5 32 ft. ppe About 16 Stretched string About 16 32 ft. pipe 16 Weighted string 16 (Organ) Below 33 Rotating spoke 7 or 8 Rotating spoke Between 16 and 48 Helmholtz Wolf Preyer Elhs McKendnck Wundt Melde Cuperus Bezold 1863 I87O 871 (187o) I876 1879 1877 I878 1887 1893 I902 1891 \Veighted string Koemg rk Koenigfork Loaded reeds Appunnfork Loaded reeds Appunn fork Appunn lamella Wire forks 1894 1897 Appunn lamella Edelmann fork 37 28 to 30 28 16 to 24 About I8.6 15 or 16 About 3 ø 14 or less 8 to lO Below 16 4 IO.I to 12.9!{ I I or less õ 2. )9etermtna/ws of the Lowest Audible Tone II. DIFFERENCE TONES. 25 (16) !Wundt (17) Pre,er (18) Schkefer 1874 1876 1899 Large pipes Reeds Edelmann Galton whistles, forks, blown bottles 8 18 to 20 30 or less (once I4) III. INTERRUPTION TONES. (19) Schaeter 1899 Sren discs, wood 16 and metal REM^RKS.--I. Proper Tones of Farious Instruments. (1) J. Sauveur, Histoire de l'acadmie royale des sciences, Annie MDCC. A'qec les mmoires de mathamatique et de phys- ique, pour la m&me annae. Tires des Registres de cette Acad- mie. 2 edn., Amsterdam, MDCCXXXIV., 9 o. Second Paris edn., I76I , 134. The account is not from Sauveur's own hand. (2) E. F. F. Chladni, Die Akustik. Leipzig, 83 o, 2. Unver- iinderte Ausgabe. The preface is dated 18o2 (so Preyer, Gr. d. Tw., ). With the stretched string, "wird man ungefghr yon 32 (einfachen Schwingungen) an eine Wirkung auf das GehSr bemerken." The 32-ft. C of 16 vs, is "der tiefste Ton yon dem man Gebrauch zu machen pflegt" (27). Again, experience shows that "bei den tiersten T6nen, von denen man Gebrauch macht, wenigstens 3 ø (einfache) Schwingungen in einer Secunde geschehen" (230). (3) J- B. Biot, Pr&is ddmentaire de physique experimentale, 3 d edn., 1824, i., 344, 356. "Cette limite . . . n'est au reste qu'une indication approche qui n'est point susceptible de rigeur." The first edn. of the Prcis appeared in I817.--The same limit, of I6 vs., is accepted by K. Vierordt, Physiol. d. Menschen, I877, 365 . (4) W. H. Wollaston, Philos. Trans, for the year 182o. Pt. ii. London, 182o, 313 . Wollaston writes that the lowest note of the organ (by which he means the contra-C of 33) is distinctly per- ceptible by most ears. But (3Io) "there does not seem to be any ----------------------------------------------------------- 26 Preliminary Experiments strict limit to our power of discerning low sounds... We may doubt at what point tones suited to produce any musical effect terminate; yet all [normal] persons... continue sensible of vibratory motion, until it becomes a mere tremor, which may be felt and even almost counted." (5) F. Savart, Ueber die Grenze der H;Srbarkeit tiefer T6ne, Pogg. Ann., xxii. (xcviii.), 283I, 596; Ann. chim. phys., xlvii., I83I, 69. Sayart cut down his toothed wheel to a single diameter, i.e., to two spokes. At the extremities of the diameter he held two cards or thin boards; these were laid close to the ends of the spokes. in a plane at right angles to the plane of the wheel. As the spokes drove by, a "series of little explosions" was pro- duced. A low tone was heard when the strokes came 7 to 8 times in the 2 sec. Sayart assumes that this tone is directly due to the stroke, and that each stroke represents 2 complete vibra- tion.--Criticised by Despretz, 444; Helmholtz. Sens. of Tone, 75 (also in Lehre yon d. Tonempf., 2863, 266); Wolf, Sprache u. Ohr, 244; Preyer, Gr. d. Tw., 3 f. Wundt (Phys. Psych., 874 , 362) gives an erroneous description of the instrument. In I83 o (Pogg. Ann., 3o) Savart reports that a wheel with a single tooth, rotated against a card more than 32 times in the  sec., gives "a peculiar steady tone, whose pitch rises with in- crease of the number of revolutions." There is no indication that Savart is here seeking to determine the lowest audible tone, although Preyer (3 I) so interprets the passage.  (6) C. Despretz, Pogg. Ann., Ixv. (cxli.), 845, 442 if.; Comptes rend., xx., I845, I214 ff. Despretz used Savart's instru- ment, and also a similar apparatus in which the spokes revolved between four pairs of boards. At I6 strokes in the  sec., he heard no tone; the lowest tone given by either instrument was the contra-G of 48. He remarks that the apparatus gives a number of tones and noises, and that neither Marloye nor Cagniard- 1 Whtch has been othem'ise unfortunate ' Sayart says that, if the toothed wheel be struck against the card, we hear a tone -- of a quality altogether different from the quahtles of the tones produced by two or more teeth -- which does not vary, however rapidly the single stroke be made. Whereupon Poggendorff remarks that, if two single strokes follow each. other as rapidly as the successive strokes of the two-toothed wheel, we ought the hear the same tone. Of course I But Sayart is speaking of one (quick or slow) stroke. õ 12. Determinations of the Lowest Audible Tone 2 7 Lotour had referred the low tone heard in Savart's experiments to the shocks of the rotating rod. See Preyer, 4. (7) Helmholtz (Sens. of Tone, 76) used a thin brass piano wire, weighted with a copper coin, stretched over a sounding box. The string was chosen because it had only high harmomc over- tones, which could not be confused with the fundamental. The contra-D gave "a very weak sensation of tone, and even this was rather jarring"; at the subcontra-B) "there was scarcely anything audible left." Helmholtz' statements concerning the vibration-rates of his string vary somewhat: see Preyer, Akust. Unt., 9 f.; Schaefer, Z., xxi., I899, I6. Subsequently (87o) Helmholtz obtained two Koenig forks, giving the tones from 24- to 35, and from 35 to 6, respectively. "For 3 ø vs. I could still hear a weak drone; for 28 scarcely a trace." In his Popular Lectures on Scientific Subjects, Helmholtz re- marks that the contra-C of 33 is "very nearly the limit of audi- bility," and that for the subcontra-C of 6 "the ear can scarcely separate the tone from an obscure drone." The lower limit is finally set at "about 20." See PopuD. re wiss. Vortrige, x865, Heft, i., 64; I876, i., 64; Pop. Lect. on Sci. Subj., New York, 885, [First series] 64, 69; new edn., London, 2884, st. ser., 56, 6. The lecture was first printed in I857. (8) O. Wolf, Sprache und Ohr, 872, 24- 5. "Bei grosser Anstrengung und Aufmerksamkeit konnte ich noch [einen Ton] yon 28 Schw. unterscheiden." The observation was made in Helniholtz' company, with the forks mentioned under (7). Wolf also describes an Appunn ' lower limit apparatus,' consist- ing of 4 reed pipes: the lowest reed, with variable weight, made 4 vs., the second 8 vs., the third x6. the fourth 32 in the  sec. (op. cit., 245 if.). The third reed gave an overtone of 32 vs., and ' einzelne Luftst6sse.' The fourth ga. vea clear fundamental. Why there were no reeds between 6 and 32--in the critical region--Wolf does not explain. The contra-C of 33 is heard as continuous tone from a i6-ft. stopped labial pipe. (9) Preyer used an Appunn 'fundamental tone apparatus,' a series of loaded harmonium reeds, giving the vibration-rates 8, 9, o .... 32, 34, 36, 38, 40. The fundamental was heard as the ----------------------------------------------------------- 28 2Prelimœnary œxlpcriments reed rang off. See Table. Gr. d. Tw., lO f. Criticised by Helm- holtz (who thinks that reed pipes were employed): Sens. of Tone, 176: cf. Ellis, ibid., and Preyer, Akust. Unt., 5 if- Later, Preyer obtained two Appunn forks, the one of which vibrated approximately 18.6. the other 13. 7 times in the I sec. The tone of the former could be heard, xvith or without resonance box; the latter gave no audible tone. Akust. Unt, 1879, 1 J. K. Love (Glasgoxv Thesis: abstract in Journ. of Anat. and Physiol.. xxiii. [N. S., iii.], 1889, 336) accepts Preyer's deter- mination of 5 to 16 rs. "Many ears cannot hear notes caused by less than 24 rs." (lO) A. J. Ellis (Preyer's Akust. Unt., 6 If.; in extract, Helm- holtz' Sens. of Tone, 176 f.) used a duplicate of Preyer's funda- mental tone apparatus. Results: Nominal pitch of reed Actual pitch Introspections 8 7.91 Sishing of escape of wind from reed, and beats from upper partials. 9 to x 5 8.89 to I4.9 Sshmg and beats; faint low tone like a dfferential. Oc- tave of lowest par- tial ? 16  5.9 t ', Quite an organ tone; nothing like a hum or differen- tial; but the slsh and beats remain. I must have heard the lowest partial." (11) J. G. McKendrick, Encycl. Brit., 9th edn., vii., 393- (12) W. Wundt, Physiol. Psych., i., 1887, 423: a large fork by A. Appunn allows the tone of 14 to be heard "vollkommen deutlich." Ibid., i., 1893, 450: the Appunn lamella gives a tone at 8 to lO vs. Ibid., if., 19o2 , 90: the Appunn wire forks give a clear tone, gradually lowering in pitch, down to 14 rs. At 12 to lO rs., 9 practised observers heard a tone, but of indeterminate pitch. Five of the 9 heard an indefinable tone at 8 vs. Some of õ 12. Determinations of the Lowest .4 udzble Tone 2 9 the observers declared the tones from 12 to 8 vs. to be higher than the tone of 4 rs. Xothing is sad of the lainella. (13) F. Melde. in A. Winkelmann's Hdbch. d. Physik, i., 764.--E. W. Scripture (New Psych.. 324) puts the lower limit at "somewhere around 2 complete vibrations." (14) See H. Zwaardemaker, Z., vii., 1894. 21. Cuperus' re- sults are as follows: Age of 0 Average rs. IO to 20 io. IO 20 to 30 io.4. 30 to 40 o.85 4.0 to 50 1I.OO 50 to 60 12.33 Over 60  2.95 The number of O's was 19o. The variability of four-year aver- ages is determined as : see 2t, 23. The error of the instru- ment is that it gives a larger initial amplitude of oscillation for lower than for higher tones: 2t. Moreover, ve do not know how it rings off at different lengths and with different initial ampli- tudes of oscillation: 24. (15) F. Bezold, Z., xiii., 1897, I62, 66. The tone of 1 rs. "wird nut mehr yon einem Theil sonst normalhSriger Gehbror- gane perzipiert." Bezold regards his low forks as free from over- tones: but an argument from pathology is rebutted by Schaefer, bid., xxi., 1899, 164 f.--C[. the earher paper, Z.. f. Ohrenheil- kunde, xxiii., 1892, 254 If.; reviewed by Schaefer, Z., v., 893.356. II. Difference Tozes. (16) Wundt declares (Phys. Psych., I874, 362) that two large stopped labial pipes, sounding the C and D of the great octave, gave a difference tone C =8 vs., "die man sehr deutlich als einzelne Luftst6sse wahrnimmt." Yet very different persons, musical and unmusical. recognised difference tones of 8 to 16 vs. as deeper in pitch than the primaries. The tone of 8 vs. is also heard on large organs. while the two primaries are almost com- pletely annulled by interference, if the pipes stand near together. ----------------------------------------------------------- 30 ?rchmnavy œxperiments In x88o (i., 393 f.) Wnndt remarks that tones "somewhat Iover than 6" can be heard as difference tones from labial pipes. In 887 he accepts the 8, if the vibrations are strong enough. The limit 8 to o recurs in the edn. of 893, i., 45 ¸. In x9o2 (if., 9 ¸) he regards the tone heard as a Zwischenton (96, xo3, x, 29), whose pitch is masked (a) by the general uncertainty of pitch- estimates of ' stossende T6ne,' especially in the lower regions of the scale, and (b) by the subjective impression of greater depth made by these tones as compared with continuous tones of the same objective pitch.- See (7) below, and cf. C. Stumpf, Vjs. f. Musikwiss., 888, 540 f.; Tps., if., I890 , 55 . (I 7) Preyer says (Gr. d. Tw., I5): "I hear plainly the dif- ference tone of 24, but I am doubtful at 8, and at 2 there is no trace of any fusion." The Appunn tonometer, which furnishes beats of 4, 8, I2, . . . in the I sec., gave a "sudden continuity of sensation at 20." Preyer worked with metal tongues, apparently within the limits xoo and ooo. He notes that a deep tone, heard with reeds of 5o0 and 52, is not the tone of 12 vs., but the difference tone of the octaves, xooo and lO24 rs. Schaefer (x66) agrees, and explains in the same way Wundt's difference tone of 8 rs., and an observation of his own in which the tonometer ap- peared to give a difference tone of o rs. (8) K. L. Schaefer (Z., xxi., 899 , x66 if.) sought to deter- mine the limen of perception of difference tones, in the different regions of the musical scale, with primaries that were free of, overtones. At 9000 to IOOOO rs. (whistles), the limen was gen- erally 30, sometimes rather less. From 8000 to 2o0 (whistles, forks, bottles), a difference tone was always found above 3o, "in der Regel schon viel frfiher." In one case (fork of 200 and bottle), it appeared "bereits spurweise bei I4." From oo down, the method became unreliable. III. Iterruption Tones. (x9) Schaefer, op. cit., 7o if. Results: Instrument Principal tone Deepest interruption tone Wooden disc b (247 5) to a  (440) 24, 25 Metal dsc ea (132o) toff[? (152064) 22, 23, 25 Wooden disc d2 (594) tod  r (1237-5) 16, I8 The QuaDrature TR for Tones 3I Four series were taken, in this order, with each dsc,--t2 series in all. The reduction from 25 to x6 rs. may be referred to prac- tice. The author thinks it possible that, under especially fayour- able conditions, the lobvest limit might be still further lowered. It should be noted that Schaefer (6 if.) looks with suspicion upon all the determinations of pt. I. of the Table, since there is no guarantee in any case that "man es nur mit dem Grundton zu thun hat." EXPERIMENT III  13. The tualitative TR for Tones: the Highest Audible Tone.--Ve require for this experiment an instrument that shall give physical 'tones,' beyond the range of hearing, whose inten- sity is at least as great as that of the highest audible tones. The instrument most commonly found in psychological laboratories, for the determination of the upper limit of tonal hearing, is the Galton whistle (Cambridge Instr. Co., I-Iawksley, Koenig or Edel- mann). Many laboratories possess also the Appunn or Koenig series of small forks, or the Koenig series of steel cylinders. The Galton Vhistle.--Galton seems to have first described his whistle in 876: "Vhistles for determining the Upper Limits of Audible Sound," S. Kenstngton Conferences (m connectran with the Loan Exhi- bition of Scmntific Instruments), 876, 6L "I contrived a small whistle for conveniently ascertaining the upper limits of audible sound in dif- ferent persons, which Dr. Wollaston had shown to vary considerably. He used small pipes" (Inquiries into Human Faculty and its Develop- ment, 883, 38, 375; Nature, xxvii., 883, 49 x; c.f.W.H. Wollaston, Philos Trans. Royal Soco London, cx., 82o, pt. if., 3IO, 3x2; Sanford, Lab. Course, 379 if.). Hiffh Forks.--The first set of very high forks was apparently that Fig. 5--Appunn's series of hgh forks, for the determination of the quahtatve T./. The forks are actuated by bowing across the tops of the trees. ----------------------------------------------------------- 3 2 ?relmnary œxcriments made by Marloye, and used in 8451 by C. Despretz (Comptes rendus, xx., 845, 2x4; Pogg. Ann., 3re Refie,v. [c,:h,], x845,445). Koemg made hm first set of high forks m 874 (Wied. Ann , N. F. lxix. [cccv.], 899 , 627). The forks with whmh Preyer worked in 875 were furnished by G. Appunn (W. Preyer, Ueber die Grenzen derTonwahrnehmung, Jena, 876, 20, 23): the pattern-set was kept in the Appunnworkshop (A. Appunn, Wind. Ann., N F. lxiv. [ccc], 898,4t.) Cyltnders.--Koemg showed a series o steal cyhnders at the Pans Exhibition of 867 (R Koenlg, zbid., lxix. [.cccv., 899, 627). These instruments have been thoroughly tested, of late years, by different methods. As their reliability is a matter of great importance, the author here brings together the principal liter- ary references. (t) R. Koenig: Catalogue des appareils d'acoustique. Paris, 27 Quai d'Anjou. 882, no. 47, I889, no. 5 ø . "Srie de r8 dmpasons pour les notes de uh = 892 v. s. &fa = 4369o.6 v. s. [in our notation, c = 4o96 rs. tof ?: 21845 3 vs ] avec tm, et un support en fonte de fer .... Dj& avec les trois derniers diapasons, au-dessus de ut, la production de ces sons et leur observation deviennent assez &fficiles, aussl at-le prfer arrter cette srie aura0, pour qu'on ne pmsse me reprocher d'entrer dans la domame de la phantasie." Cf.. also Quelques expn- ence d'acoustique, Paris, t.882, to8. 889, no. 5 . "Srie de 22 cyhndres en acier pour les notes de uh a utt0 [ca = 4o96 to c a: 32768 vs.] avec marteau en acier" (2) Spezialitaten welche in dem akusttschen Institut yon A. Appunn . . . ange- femgt werden. Three catalogues. (a) No date ß 892 ? No.  5' Elne Reihe yon 33 Sttmmgabetn auf mnem Fuss, 4.3 Octoven Tonletter darstellend yon c  - 2048 bs g-s = 49152 Schwmgungen, zur Ermittlung der hochsten Horgrenze. No. 7. Horprufungs-Apparat nach Professor Kessel-Jena; enthalt H Sttmmgabeln yon 20o0 bis 50ooo Schwingungen. (b) No date': 8947 Nos. 3, 4 as nos 5, 7 above. No. 42. Stimmgabeln nach leder Angabe; Elnstimmung derselben auf jede beliebige Schwingungszahl, mtt Garantm fur absolute Genautgkeit. (c) I898- 99. No. 3 (c). 62 Metallpfeffchen in Etui, eine Tonrethe yon 5oo b:s 5oooo Schwingungen darstellend, aufsteigend yon tlalbton zu Halbton. Unter Garantte fur Rmhtlgkeit der angefuhrten Tonhohen. No. 4 as nos. 7, I4 above. No 42 as no. 42 above. The special set of 33 htghest forks is not menttoned--Other advertised series of high forks and pipes are here omttted. (3) A descriptive hst of instruments manufactured and sold by the Cambridge Instrument Company, Cambridge, 1892. Sec. 28, Anthropometnc apparatus, I9 if., Hearing highest audible note. Cf. F. Galton, Inquiries into Human Faculty,  Not 848, as Koenig says (probably by a printer's error) in Wind. Ann., N. F lxix [cccv ], t899, 626. õ x3. The Qualitative TRfor Tones 33 883, 375 ff "The number of vtbrations in the note of a whtstle may be found by divtding 344o by four trines the depth, measured in nches, of the inner tube of the whistle. This rule, however, supposes the  vibrationsof the air in the tube to bestrictly ] longttudinal, and ceases to apply when the depth of the tube s less than about one and a half times its dtameter" Sanford remarks of the Cambr. Inst. Co.'s form of the Gallon whistle: "All that the instrument can safely show, except when handled wtth elaborate precautions, is the general character of very htgh tones and the fact that some persons can still hear tones N ( that others cannot... It is hardly hkely that [the makers] would contend for a hgh degree of certainty of the values given, especially at the upper end of the scale" (Course in Exp. Psych., 898, 379 ff-)'--See also F. Gal ton, On the Anthro pometnc Laboratory at the late Internatmnal Health Exht- bttion, Journ. Anthropol Inst., tt Nov. 884, xiv., I885, 2x6. (4) Illustnrtes Verzemhniss no. iii der medizin. Praci- sions-apparate . . . yon Dr. M. Th. Edehnann Munchen, 895. No. 31 (x3). Galton-Pfeifchen neuer Construction. Tonum- fang his uberdie obere Geh6rgrenze hinaus. [This is the pipe tested by Stumpf and Me.ver, tt s not the new Edel- mann instrument recommended xn the text for experiment (5) H. Zwaardemaker Daa presbyakustische Gesetz.  Zts. f. Ohrenhefik, xxn,., 893, r. Also: Der Einflus der Fro. Schalhntensxtat auf &e Lae der oberen Tongrenze. 303 . [Gives a subjectxve method for standardizing the Gallon wMtle.] (6) F. Melde: Ueber einige Methoden der Bestimmung yon Schwingungszahlen hoher Tone. Wted. Ann., N. F.h. (cclxxxvti.), 894, 66 , lil. (cclxxxwfi.), i894 , 238. [Melde's two objective methods, the opttcal-graphic and the method of resonance, take him to the cL Appunn's small forks are entirely unreliable. "dm Abstim- mung . . ist . . vollkommen unzuverlassig" (259). Koemg's forks, on the con- trary, are extremely accurate ] (7) C. Stumpf u.M. Meyer: Schwingungszahlbestmmungen bei sehr hohen Tonen. Z&d., N. F. lxi. (ccxcvi.), x897, 760. [Test of Edelmann's whistles, Koenig's