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 We