GIFT OF MICHAEL REE^E UBfeARl G THE CONTEMPORARY SCIENCE SERIES. EDITED BY HAVELOCK ELLIS. THE NEW PSYCHOLOGY, -THE NEW PSYCHOLOGY/ BY E. W. SCRIPTURE, PH.D. (LEIPZIG), DIRECTOR OF THE YALE PSYCHOLOGICAL LABORATORY. WITH 124 ILLUSTRATIONS. LONDON: WALTER SCOTT, LTD., PATERNOSTER SQUARE. CHARLES SCRIBNER'S SONS, 153-157 FIFTH AVENUE, NEW YORK. 1897. To THE FOUNDER OF THE FIRST PSYCHOLOGICAL LABORATORY, WILHELM WUNDT, PH.D., LL.D., M.D., Professor of Philosophy in the University of Leipzig ; To THE FOUNDER OF THE FIRST AMERICAN LABORATORY, G. STANLEY HALL, PH.D., LL.D., President of Clark University ; AND To THE FOUNDER AND GUIDE OF THE YALE LABORATORY, GEORGE TRUMBULL LADD, D.D., LL.D., Professor of Philosophy in Yale University ; THIS BOOK IS DEDICATED IN RECOGNITION OF THEIR INVALUABLE SERVICES IN ESTABLISHING A NEW SCIENCE. PREFACE. DURING the last few years a wide interest has been aroused in the growth of a science of mental life which employs methods hitherto peculiar to the physical sciences. The interest has been followed by misconceptions of the most varied character. Some have supposed the new science to concern itself with experiments on thought-transference and clairvoyance ; others have regarded it as a presumptuous sub-depart- ment of the physiology of the senses and the brain ; and still others have treated it as merely a materialistic philosophy in one of its aberrations. Amid such confusion it is no wonder that people ask : " What is the new psychology ? Is it brain- physiology, or spiritualism, or a new kind of meta- physics ? " And the chemist, geologist, or physicist is also inclined to ask : " Is it a science at all ? " My aim in this book is to show just what the new psychology is. I have sought to make clear the funda- mental ideas of the science, and have not attempted to cover the whole fielfl of investigation. Salient points and fundamental methods were chosen rather than a multitude of details. The reader will probably notice a difference in the treatment of Parts II., III., and IV. In Part II. Time, PREFACE. my aim was to illustrate methods of careful experi- ment and measurement in psychology ; in Part III. Energy, I emphasised the results obtained rather than the means ; and in Part IV. Space, I have given a systematic development of principles rather than par- ticulars either of methods or of facts. The development of the standards of time (Chap. V.) from a purely mental standpoint was suggested by Jevons's chapter on time ; the standards of space (Chap. XXV.) were treated analogously. The third fundamental quality, energy, has been placed in a clear light on the psychological side by Ostwald's essays. A consistent treatment, how- ever, would have required more rearrangement of psychological data than I felt it wise to attempt at present ; therefore, after stating the principles regarding energy (Chap. XII.), I have in the rest of Part III. kept to the usual classification according to quality and intensity. It is, perhaps, unnecessary to state that the approxi- mate method of computing the mean error has been used on p. 47 and elsewhere in order to avoid a tedious explanation ; moreover, for most purposes the approxi- mation is amply satisfactory. It becomes my agreeable duty to acknowledge the extensive and varied assistance received from others in preparing this book. I am under special obligations too numerous and varied to be detailed to Professors Wundt, Binet, Sergi, Cattell, Fullerton, Baldwin, Ladd, James, Stanley Hall, .Sanford, Delabarre, Krohn, Lom- bard, and Calkins, to Drs. Dearborn, Bolton, and A. Moore, and to Mr. Lough. Thomas Edison, Esq., of Orange, N.J., was kind enough to send the strip of kinetoscope negative used in Chap. VI. Thanks are due to Leopold Voss, of Hamburg, publisher, for the use of the figures illustrating Heymans's experiments PREFACE. xi in Chap. XXVIII. ; and also to Georg Brokesch, of Leipzig, for the portrait of Fechner. The picture to illustrate the runner's reaction-time was made from a lantern slide loaned by Rector Geo. Fox, of New Haven, Conn. ; the original photograph from which it was made is no longer accessible, and it is unfortunately impossible to assign full credit to the photographer who has unintentionally given such a remarkable illustration of a psychological fact. Figures i, 2, 3, 8, 17, 49, 51, 92, 93, and 1.17, are re- produced by permission directly from the original articles cited in the text ; figure 18 is from a print by Ottomar Anschutz, Posen ; figures 9, 45, 46, 53, 56, 74, 79, 81, 82, 83, 84, 85, and 86, have been newly drawn or cut after the originals cited in the text ; a number of the illustrations are from my " Studies," references being given at the appropriate places. Many photographs of apparatus were received from various American laboratories, but unfortunately only a few of them were so made that they could be used for reproduction by photo-engraving. I particularly regret my inability, on account of late arrival, to use more than a small portion of the manuscript and photographs kindly prepared by Professor Delabarre (Brown Uni- versity), and by Mr. Lough and Dr. Dearborn (Harvard University). To Professor George M. Duncan, of Yale, I owe the deepest gratitude for a careful criticism of every impor- tant point in the book. From Dr. C. E. Seashore, my friend and assistant, I have received many valuable suggestions and much aid in preparing both manuscript and proof. E. W. S. YALE UNIVERSITY, 1897, CONTENTS. o PART I. METHODS. CHAPTER I. PAGE OBSERVATION CHAPTER I!. STATISTICS J 5 CHAPTER III. MEASUREMENT ... CHAPTER IV. EXPERIMENTING ... ... 53 xiii XIV CONTENTS. PART II. TIME. CHAPTER V. PAGE STANDARDS OF TIME 79 CHAPTER VI. TIME OF SENSATION ... ... ... 89 CHAPTER VII. TIME OF VOLITION 121 CHAPTER VIII. TIME OF REACTION 135 CHAPTER IX. TIME OF THOUGHT 155 CHAPTER X. TIME ESTIMATES 170 CHAPTER XI. RHYTHM 177 CHAPTER XII. TIME INFLUENCE 185 CHAPTER XIII. SUCCESSION IN TIME 198 CONTENTS. PART III. ENERGY. CHAPTER XIV. STANDARDS OF ENERGY XV PAGE 209 CHAPTER XV. ENERGY OF VOLUNTARY ACTION ............ 215 CHAPTER XVI. FATIGUE IN VOLUNTARY ACTION ............ 228 CHAPTER XVII. PASSIVE AND ACTIVE MOVEMENT ...... ... 248 CHAPTER XVIII. RESISTANCE AND HEAVINESS ,..261 CHAPTER XIX. LIFTING WEIGHTS ...... ... 267 CHAPTER XX. PRESSURE CHAPTER XXI. PAIN 283 3 2 CHAPTER XXII. FEELINGS ... 35 CHAPTER XXIII. SOUND 3 T 3 CHAPTER XXIV. XVI CONTENTS. PART IV. SPACE. CHAPTER XXV. PAGE STANDARDS OF SPACE 354 CHAPTER XXVI. BODILY SPACE 362 CHAPTER XXVII. TACTUAL SPACE 371 CHAPTER XXVIII. MONOCULAR SPACE 383 CHAPTER XXIX. MONOCULAR SPACE AND BODILY SPACE ... 412 CHAPTER XXX. BINOCULAR SPACE 420 PART V. PAST AND PRESENT. CHAPTER XXXI. AN INEVITABLE EVENT 436 CHAPTER XXXII. SOURCES OF THE NEW SCIENCE 442 CHAPTER XXXIII. FECHNER, HELMHOLTZ, WUNDT 454 CHAPTER XXXIV. THE PRESENT SITUATION 463 CONTENTS. XV11 APPENDICES. PAGE APPENDIX I. VALUES OF THE PROBABILITY INTEGRAL ... 475 II. SCHEMES FOR BERNOULLI'S THEOREM ... 476 III. THE MEDIAN 479 IV. LAMP BATTERIES 483 V. ON THE MEASUREMENT OF IMAGINATION... 484 VI. COLOUR SIGHT-TESTER 485 ,, VII. FORMULAS FOR. ADJUSTING MEASUREMENTS 487 VIII. FECHNER'S METHOD FOR RIGHT AND WRONG CASES 489 INDEX 49 i LIST OF ILLUSTRATIONS. FIG. PAGE AN EXPERIMENT ON RHYTHMIC ACTION... Frontispiece 1. EXAMPLES OF THOUGHT-TRANSFERENCE (AFTER HAN- SEN AND LEHMANN) ... 65 2. A CASE OF THOUGHT-TRANSFERENCE (AFTER HANSEN AND LEHMANN) 67 3. DRAWINGS BY THOUGHT-TRANSFERENCE (AFTER HAN- SEN AND LEHMANN) 68 4. EXPERIMENT WITH THE DYNAMOMETER ... ... 74 5. PENDULUM CONTACT (ENLARGED) 84 6. ARRANGEMENT FOR DIVIDING A SECOND INTO HUN- DREDTHS 86 7. A SPARK RECORD 87 8. APPARATUS FOR MEASURING THE LATENT TIME OF SENSATION (CATTELL) - ... 90 9. ENTRANCE OF A SENSATION INTO CONSCIOUSNESS (AFTER EXNER) 92 10. ELECTRIC COLOUR WHEEL WITH SPEED INDICATOR... 94 11. MIXING SENSATIONS BY RAPID REPETITION 95 12. RECORDING THE FLUCTUATIONS OF A SENSATION ... 98 13. RECORD OF FLUCTUATION ... 99 14. INFLUENCE OF DISTINCTNESS ON FREQUENCY AND DURATION OF FLUCTUATIONS IOO 15. THE FLUCTUATING BLOCKS ... ... 1OI XX LIST OF ILLUSTRATIONS. FIG. PAGE 16. SHORTEST NOTICEABLE STIMULUS AS DEPENDENT ON INTENSITY (CATTELL) 102 17. THE STROBOSCOPE (FISCHER) ... Io8 18. CYLINDRICAL STROBOSCOPE (ANSCHUTZ 112 19. PIECE OF KINETOSCOPE RIBBON 113 20. INTERIOR OF THE KINETOSCOPE 115 21. DETAILS OF UPPER PART OF THE KINETOSCOPE ... II 7 22. MECHANISM OF THE VITASCOPE Il8 23. REACTION KEY 121 24. RECORDING FLUCTUATIONS OF A VOLITION 124 25. FLUCTUATIONS IN A VOLITION INTENDED TO BE CON- STANT 125 26. FLUCTUATIONS IN THE STRENGTH OF A REPEATED VOLITION 125 27. DOUBLE CONTACT TELEGRAPH-KEY 126 28. FLUCTUATIONS IN THE TAP-TIME (BLISS) 126 29. DEPENDENCE OF TAP-TIME ON ATTENTION (BLISS) ... 127 30. INFLUENCE OF FATIGUE ON TAP-TIME (MOORE) ... 129 31. RESULTS OF EXPERIMENTS ON NEW HAVEN SCHOOL CHILDREN (AFTER GILBERT) 131 32. RECORDS OF TRILLING ON THE PIANO (AFTER BINET) ... 133 33- TOUCH-KEY ... 135 34. MULTIPLE KEY 139 35. A SERIES OF REACTIONS 148 36. PISTOL KEY 149 37. THE RUNNER'S REACTION-TIME :.. 151 38. PENDULUM CHRONOSCOPE ... ... 157 39- PENDULUM CHRONOSCOPE, ARRANGED FOR DISTANT EXPERIMENTS 159 40. THOUGHT AND ACTION APPARATUS ... .:. ... 1 66 41. RECORD OF TIME ESTIMATES 171 42. SERIES OF CLIKS 174 43. RECORDS OF RHYTHMIC ACTION ... ... 182 44. INVESTIGATING THE ARM MEMORY 189 LIST OF ILLUSTRATIONS. XXI FIG. PAGE 45. CURVES FOR TONE MEMORY (AFTER WOLFE) IQ2 46. LAW OF REPETITION IN MEMORISING (AFTER EBBING- HAUS) 193 47. DEPENDENCE OF ENERGY ON COLOUR (AFTER FERE) 222 48. DECREASE OF EFFORT OWING TO INTELLECTUAL WORK 223 49. DYNAMOMETER FOR PULLING (FULLERTON AND CATTELL) 22$ 50. IRREGULARITY DEPENDENT ON EFFORT (FULLERTON AND CATTELL) 226 51. FATIGUE IN CONSTANT EFFORT 228 52. FATIGUE IN REPEATED EFFORTS 22Q 53. ERGOGRAPH RECORDS FOR VOLUNTARY, NERVOUS AND MUSCULAR FATIGUE (AFTER MOSSO) 231 54. RECORDS SHOWING INDEPENDENCE OF MUSCULAR AND VOLUNTARY FATIGUE (AFTER MOSSO) ... 23! 55. REPEATED CONTRACTIONS 232 56. EFFECT OF MENTAL WORK (AFTER MOSSO) 234 57. INCREASE OF THE INACCURACY AND THE UNCER- TAINTY IN A SUCCESSION OF EFFORTS 236 58. APPARATUS FOR JUDGMENTS OF DEPTH BY EYE . MOVEMENTS (MOORE) 237 59. CURVE OF FATIGUE FOR EYE MOVEMENTS (CONSTANT ERROR) (MOORE) 239 60. CURVE OF FATIGUE FOR EYE MOVEMENTS (MEAN VARIATION) (MOORE) ... 241 61. CURVE OF FATIGUE WITH ONE EYE CLOSED (MOORE) 242 62. INFLUENCE OF FATIGUE ON ACCOMMODATION-TIME (MOORE) 245 63. BRUNS'S METHOD FOR RIGHT AND WRONG CASES ... 270 64. FECHNER'S LAW OF THE RELATION BETWEEN STIMU- LUS AND SENSATION 271 65. BLOCKS FOR MEASURING THE SIZE-WEIGHT ILLUSION 274 66. CURVE OF THE SUGGESTION BY SIZE (SEASHORE) ... 277 67. PERSISTENCE OF SIZE SUGGESTION (SEASHORE) ... 278 68. SIZE SUGGESTION INFLUENCED BY DIRECTNESS OF VISION (SEASHORE) 279 XXll LIST OF ILLUSTRATIONS. FIG. PAGE 69. SIZE SUGGESTION FROM DIFFERENT SENSES (SEASHORE) 280 70. PROBABILITY CURVES FOR THE PRESSURE THRESHOLD 286 71. DEPENDENCE OF THE LEAST NOTICEABLE CHANGE ON THE RATE OF CHANGE 299 72. CURVE OF AGREEABLENESS FOR RECTANGLES (AFTER WITMER) 309 73. CURVE OF AGREEABLENESS FOR PAIRS OF COLOURS (AFTER COHN) 310 74. THE TONE-VARIATOR (AFTER STERN) 316 75. THE TONE-TESTER (GILBERT) 318 76. SENSITIVENESS OF SCHOOL CHILDREN TO TONE- DIFFERENCES (AFTER GILBERT) 319 77. DEPENDENCE OF THE UPPER LIMIT OF PITCH ON INTENSITY 321 78. TONE MEASURER 325 79. CURVES OF SLEEP (AFTER MICHELSOX) 328 80. COLOURS IN THE SPECTRUM 331 81. THE COLOUR SYSTEM ON THE SIMPLEST SUPPOSITION (AFTER KONIG) 332 82. PROPORTIONS OF THE ELEMENTARY 'COLOURS IN THE SPECTRUM, FOR MONOCHROMATS AND DICHROMATS (AFTER KONIG) '.. 334 83. PROPORTIONS OF THE ELEMENTARY COLOURS IN THE SPECTRUM, FOR TRICHROMATS (AFTER KONIG) ... 337 84. PROPORTIONS OF THE FUNDAMENTAL SENSATIONS IX THE SPECTRUM (AFTER KONIG) .. 339 85. THE PSYCHOPHYSICAL TRIANGLE (AFTER KONIG) ... 340 86. THE PSYCHOLOGICAL COLOUR TRIANGLE (AFTER HELMBOLTZ) ... 343 87. THE COLOUR PYRAMID (SIDE VIEW) 346 88. END VIEW OF THE COLOUR PYRAMID SHOWING THE COLOUR TRIANGLE AND SPECTRUM CURVE 347 89. THE TRICOLOUR LANTERN 349 90. SET OF SLIDES FOR THE TRICOLOUR LANTERN ... 351 91. THE TILTING BOARD 363 LIST OF ILLUSTRATIONS. xxiii FIG. PAGE 92. THE ROTATION FRAME (MACH) 365 93. APPARATUS FOR SIMULTANEOUS TOUCHES (KROHN) 376 94. LINE ALPHABET FOR TOUCH 380 95. BRAILLE ALPHABET 380 96. NEW YORK ALPHABET (WAIT) 380 97. FIELD OF VISION ... ... 388 98. COMPARING DISTANCES BY THE EYE 396 99. DIAGRAM TO ILLUSTRATE THE JUST IMPERCEPTIBLE' AND THE JUST PERCEPTIBLE DIFFERENCES ... 397 100. PARTS OF THE LINE ILLUSION BOARD (HEYMANS) ... 400 101. ILLUSION FIGURES WITH ANGLE LINES LACKING (HEYMANS) 402 T02. ILLUSION FIGURE WITH INCREASED AREAS (HEYMANS) 404 103. ILLUSION FIGURES WITH AREA LINES (HEYMANS) ... 405 104. ILLUSION FIGURES WITH FILLED AREAS (HEYMANS) 405 105. ILLUSION FIGURES WITH NO ACUTE ANGLES (HEY- MANS) 406 106. ACCOMMODATION BOARD 410 107. MONOCULAR FIELD WITH POINT OF SHARPEST VISION AT O 413 108. RESULT OF CHANGING POINT OF SHARPEST VISION TO I BY EYE MOVEMENT 413 109. RESULT OF CHANGING POINT OF SHARPEST VISION TO I BY HEAD MOVEMENT 413 1 10. APPARENT CHANGE IN THE SYSTEM OF ORIENTATION AS THE EYE IS MOVED - 414 111. ROTATION BOARD 418 112. TWO MONOCULAR VIEWS FOR THE LEFT AND RIGHT EYES RESPECTIVELY 422 113. THE LANTERN STEREOSCOPE 424 114. MIXTURE OF THE TWO MONOCULAR VIEWS OF FIG. 112 425 115. EYEGLASS FOR THE LANTERN STEREOSCOPE ... 426 116. BINOCULAR FIGURES TO ILLUSTRATE CROSSED AND UNCROSSED DISPARITY 427 117. THE STEREOSTROBOSCOPE (MUNSTERBERG) 432 xxiv LIST OF ILLUSTRATIONS. FIG. PAGE Il8. GUSTAV THEODOR FECHNER 455 IIQ. HERMANN VON HELMHOLTZ 458 120. WILHELM WUNDT 460 121. RELATIONS OF MOST PROBABLE VALUE, MEDIAN AND AVERAGE, WITH AN UNSYMMETRICAL CURVE OF PROBABILITY 483 122. PRINCIPLE OF THE LAMP BATTERY 483 123. COLOUR SIGHT TESTER (FRONT) 486 124. COLOUR SIGHT TESTER (BACK) 486 THE NEW PSYCHOLOGY. PART I. METHODS. CHAPTER I. OBSERVATION. THE development of a science consists in the cle- velopment of its means of extending and improving its method of observation. The great step that has lately been taken in psychology lies in the introduction of systematised observation, by means of experimental and clinical methods. This change is one which the physical sciences have long since undergone, but which occurred in psychology only a few decades ago. Probably nothing could make clearer the point from which the new psychology takes its departure than Bacon's picture, if applied to psychology up to a short time ago : " The sciences to which we are accustomed have certain general positions which are specious and flattering, but as soon as they come to particulars, . . . when they should produce fruit and works, then arise contentions and barking disputations, which are the end of the matter, and all the issue they can yield. Observe 2 ' 2 THE NEW PSYCHOLOGY. also, that if sciences of this kind had any life in them, that could never have come to pass which has been the case now for many ages that they stand almost at a stay, without receiving any augmentations worthy of the human race ; insomuch that many times not only what was asserted once is asserted still, but what was a question once is a question still, and instead of being resolved by discussion is only fixed and fed ; and all the tradition and succession of schools is still a succession of masters and scholars, not inventors and those who bring to further perfection the things invented." x Strange as it may seem, the novelty of the new psychology results largely from the practical adapta- tion of a principle for whose application Bacon was so earnest. This principle can be summed up as a deep distrust of man's mind when left to itself, but a firm belief in its reliability when working in true comrade- ship with carefully determined facts. 2 We have now before us the point at issue between the old method and the new, namely : is simple observation of our minds adequate to the establishment of facts concerning mind ? The first criticism on unaided observation is that it gives us only general outlines of facts. Let a dozen persons pay a visit to Berlin ; each one is to write a book on the subject. On some main facts all will agree, e.g., the existence of Friedrichs-Strasse, the plentif ulness of the soldiers, and the cleanness of the streets. In many respects they will disagree, although all may have seen exactly the same things, e.g., the good temper of the inhabitants, the sensibleness of the house-numbering, and the efficiency of the police. The next criticism is that unaided observation falsi- fies to a greater or less extent what it states as facts, 1 Bacon, " Instauratio Magna," Preface. 2 Ibid., " Novum Organon," bk. i. OBSERVATION. 3 and that it is therefore unsatisfactory as a method of attaining accurate and trustworthy knowledge. If we consider the vagaries of the human mind even under the most careful control, we see at once why this falsification must occur. Every observation must in a certain sense be true, for the observing and recording of an event is in, itself an event. But before we proceed to deal with the supposed meaning of the record, and draw inferences, we must take care to ascertain that the character and feelings of the observer are not to a great extent the phenomena recorded. 1 The chief sources of untrustworthiness of observa- tion can be stated as (i) the error of prejudice, and (2) the error of unconscious alteration. The error of prejudice is a most dangerous one. The mind of man is like an uneven mirror, says Bacon, and does not reflect the events of nature without distor- tion. " It is difficult to find persons who can with perfect fairness register facts for and against their own peculiar views. Among uncultivated observers the tendency to remark favourable and forget unfavourable events is so great, that no reliance can be placed upon their sup- posed observations. Thus arises the enduring fallacy that the changes of the weather coincide in some way with the changes of the moon, although exact and impartial registers give no countenance to the fact. The whole race of prophets and quacks lives on the overwhelming effects of one success, compared with hundreds of failures which ate unmentioned and for- gotten." " Men mark when they hit, and never mark when they miss." 2 We should do well to bear in mind Jevons, " Principles of Science," p. 402, London, 1887. Ibid. 4 THE NEW PSYCHOLOGY. the ancient story of one who was shown a temple with pictures of all the persons who had been saved from shipwreck after paying their vows. When asked whether he did not now acknowledge the power of the gods, " Aye," he answered, " but where are they painted that were drowned after their vows ? " "The human understanding," says Bacon, "is no dry light, but receives an infusion from the will and affections, whence proceed sciences which may be called ' sciences as one would.' For what a man had rather were true he more readily believes. Therefore he rejects diffi- cult things from impatience of research ; sober things, because they narrow hope ; the deeper things of nature, from superstition ; the light of experience from arrogance and pride, lest his mind should seem to be occupied with things mean and transitory ; things not commonly believed, out of deference to the opinion of the vulgar. Numberless, in short, are the ways, and sometimes imperceptible, in which the affections colour and infect the understanding." 1 Our passions, our prejudices, and the dominant opinion of the day are abundant sources of dangerous illusion, by exaggerating the probabilities in their own favour and in depreciating the contrary probabilities. The vivid impression which we receive from present events, and which causes us scarcely to remark the contrary facts observed by others, is one of the prin- cipal causes of error against which we cannot be too much on our guard. 2 Habit and sympathy determine to a great extent our beliefs, and, we may add, our statements concerning our observations. It might be said that this all refers to common 1 Bacon, " Novum Organon," bk. i., Aphorism xlix. 2 Laplace, " Theorie Analytique des Probabilites," Preface, p. cii, Paris, 1820. OBSERVATION. 5 observers but it is, alas, true of scientific people also, even men in the laboratory. An observer is in general disposed to ignore a result as being erroneous that is in contradiction with an expected result or with other apparently good results. " It is my firm opinion that no man can examine him- self in the most common things having any reference to him personally or to any person, thought, or matter related to him, without being made aware of the temp- tation to disbelieve contrary facts and the difficulty of opposing it. I could give you many illustrations personal to myself about atmospheric magnetism, lines of force, attraction, repulsion, &c." x It is a fact of my own experience that the most difficult thing to learn and to teach does not lie in the manipulation of apparatus or the execution of experiments, but in the art of truthfully recording results and stating conclu- sions. Turning to the source of error spoken of as " uncon- scious alteration," we are tempted to say that the source of all error is prejudice, and the result is un- conscious alteration. This would, however, extend the word prejudice beyond its usual meaning of ten- dency to liking or disliking. By the error of uncon- scious alteration we wish to indicate those cases where no prejudice, in the usual sense, is to be assumed. I say, says Mill, that I saw my brother this morning. The actual observation consisted of a combination of patches of colour. From these I conclude that I saw my brother, i.e. } I conclude that they were like those patches which I had previously seen and which I was accustomed to call my brother. I might have seen some combination 1 Faraday, " On Mental Education," London, 1853 ; also in Faraday, "Experimental Researches in Chemistry and Physics," p. 463, London, 1859. 6 THE NEW PSYCHOLOGY. so similar that I was mistaken. I might have been asleep and dreamed the sensations, and yet have con- fused the dream with actual experiences. 1 In all these cases there were real observations, e.g., the patches of colour sensations. What was wrong was the adding of others and calling the whole an observation. It fre- quently occurs to me that I dream of some experience, and then a day or so afterwards am uncertain whether I actually had the experience or not. It often occurs on receipt of a letter that I think out the answer while going along the street. Then when I have time to write the answer I forget whether I actually wrote it or only thought about writing it. This has occurred so often that I have had to adopt a definite criterion : if I find the letter in a certain pigeonhole it has not been answered, otherwise it has. " If in the simplest observation, or in what passes for such, there is a large part which is not observation, but something else ; so in the description of an observation there is, and always must be, much more asserted than is contained in the perception itself. We cannot describe a fact without implying more than the fact." 2 Another kind of unconscious alteration is uncon- scious omission. Our travellers in Berlin undoubtedly did see a great deal, but there was much valuable information that escaped them. They noticed and recorded only a small portion of what their eyes saw, and while taking notes on the shop windows in the Kaisergallerie, they were blissfully unconscious of the watchful policeman around the corner. Yet this policeman's eye is more characteristic of Berlin than all the shops put together. With such dangerous sources of error ever present 1 Mill, " Logic," bk. iv., ch. i. 2. - 2 Ibid., ch. i. 3. OBSERVATION. 7 in our observations, it seems justifiable to conclude that mere observation is not adequate to completely establish the facts of mind Unaided observation can be trusted only for rather vague, cursory, and one-sided views of phenomena. Having thus been driven to the conclusion that unaided observation is an inadequate method, we must find a new method. Observation in general consists in paying attention to events. How can it be improved and rendered more accurate ? Improvement in the method of observation may be made by use of statistics, experiment, or measure- ment, or by combinations of the three. By taking statistics on numbers of persons we might determine if all persons had a green-blue after-image for a red colour. By taking statistics on the same person for different times of day, for different conditions of health, &c., we could settle the question of permanency of the relation of the after-image to the original colour. By using various hues of red, orange, &c., we might gain experimental basis for the statement that the colours can be arranged in a closed curve in such a manner that the colour of the after-image shall be found at the opposite end of the diameter drawn from the original colour. By combining statistics with experiment we might prove that the form of this curve is not the same for all persons. If now we introduce measure- ments with the colour-wheel or the spectrophotometer, we can determine the exact form of this curve with relation to all possible colours. By statistical measure- ments we can gather precise information on mankind down to the minutest detail that our apparatus and opportunities will allow us to seize. 1 1 It is true that to large and important portions of mental science we cannot yet apply the improved methods, and must still rely on 8 THE NEW PSYCHOLOGY. These methods of improving observation, however, presuppose the possibility of observing mental pheno- mena. This is an assumption that has been made throughout the chapter. The assumption has been seriously, earnestly, and violently questioned, and has been vigorously, emphatically, .and pugnaciously sup- ported. In fact, the question concerning the possibility of observing mental phenomena has been the source of one of the queerest quarrels in the history of science. This is the great feud concerning the validity of " intro- spection." What is "introspection " ? It can be briefly defined as "looking into one's own mind." Stated in other terms, observation is the directing of attention to phenomena of any kind, and introspection is observa- tion of a class of these phenomena. Now let us first consider some of the famous objec- tions urged against "introspection," or observation of our mental life. " Introspection mutilates the facts of consciousness even in contemplating them, tears them from their necessary connections, and hands them over to a tumultuous abstraction." z " The first difficulty in psychological observation arises from this, that the conscious mind is at once the observing subject and the subject observed. What are the consequences of this ? In the first place, the mental energy, instead of being concentrated, is divided, and divided in two divergent directions. The state of mind observed, and the act of mind observing, are what has been aptly termed " descriptive psychology." Neverthe- less, the last few years have seen the application of experimental methods to such apparently inaccessible problems as hallucinations, emotions, the thoughts of the insane, &c. 1 Herbart, " Lehrbuch zur Psychologic," 3. OBSERVATION. 9 mutually in an inverse ratio ; each tends to annihilate the other. Is the state to be observed intense, all reflex observation is rendered impossible, the mind cannot view as a spectator ; it is wholly occupied as an agent or patient. On the other hand, exactly in proportion as the mind concentrates ,its force in the act of reflective observation, in the same proportion must the direct phenomenon lose in vivacity, and, consequently, in the precision and individuality of its character. " In order to observe, your intellect must pause from activity ; yet it is this very activity that you want to observe. If you cannot effect the pause, you cannot observe j if you do effect it, there is nothing to observe." x The attempt is sometimes made to save the validity of introspection by saying that we observe the facts by means of memory, not at the instant in which we per- ceive, but the moment after, and that this is, in reality, the mode by which we acquire the best of our know- ledge of intellectual actions. Unfortunately memory, even immediate memory, is untrustworthy for more than crude outlines. Unaided observation was crude enough ; so-called " reflection," or introspection by memory, is still cruder. All the distortions of any method of observation, even " intro- spection," are added to the errors of memory. This claim for " reflection " was apparently the last argument for introspection. It has been said to be so manifestly valueless that people have sought to throw overboard not only " reflection " and " introspection," but all observation of ourselves. This is the standpoint of the older physiological psychologists. Comte, for example, claims for physiologists alone 1 Comte, " Positive Philosophy," ch. i. 10 THE NEW PSYCHOLOGY. the scientific knowledge of intellectual and moral phe- nomena. He totally rejects psychological observation properly so called, i.e., observation of the internal con- sciousness. Again, we hear : " Every study of psychology, whose object is the exact description of facts and research into their laws, must henceforth set out with a physio- logical exposition, that of the nervous system. This is the obligatory point of departure, not resulting from a passing fashion, but from nature itself, because the existence of a nervous system being the condition of psychological life, we must return to the source, and show how the phenomena of mental activity graft them- selves upon the more general manifestations of physical life." ' The final state of the quarrel leaves two parties : the observationalists asserting the validity of introspection, and the psycho-physiologists demanding its replacement by the alone trustworthy method of psycho-physiology. Is there any hope of adjusting such a difference ? In the first place, can agreement be found concerning the validity of introspection ? Let us consider what takes place in any observation. In observing objects we introduce a changed condi- tion of affairs. Whatever we pay attention to becomes a more prominent object than the rest of our ex- perience. After we have observed a particular flower the fields are not the same to us as before ; even when observing it w r e entirely overlooked many things we would otherwise have noticed. Or, while observing meteors in one region we overlook what is happening in another region. Again, after-images play a very small part in the lives of those who have never attended 1 Ribot, " English Psychology," p. 198. OBSERVATION. 1 1 to them ; but while observing these images the owners neglect everything else. In general, we may say that the act of observing introduces a change in the sum total of experience ; the more intentionally and syste- matically we observe, or the more carefully we experi- ment and measure, the greater the distortion and change produced. The act of observation, then, apparently introduces an error ; the error, however, is not in the observation, but in the conclusion drawn. Observation gives us information regarding the fact observed without regard to its relations to simultaneous or successive facts. The flower, the meteors, and the after-images were observed for themselves alone ; for our particular purposes the flower was the only thing growing in the fields, the meteors were the only things in the heavens, the after- images the only things we saw. But if a conclusion as to the general constitution of the fields, of the heavens, or of our vision, be drawn from the particulars men- tioned, the conclusion is necessarily wrong. We were not observing fields but flowers, not the sky but the meteors, not the whole visual space but the after- images ; to observe the larger units we would have to direct our attention differently. Turning to introspection, we find the case exactly similar ; introspection does distort things and lead to erroneous conclusions, but so does all observation. The objections to introspection apply just as completely to physical or botanical observations as to psychological ones. I observe the sparks from an electrical machine, or the flower in the field, and utterly overlook the machine itself, or the other plants in the field. In fact, I cannot help distorting and mutilating what I observe. If I wish to carefully observe the construction of the machine, I must neglect the spark ; if I wish to study 12 THE NEW PSYCHOLOGY. the tree, I neglect the flower. Likewise, if I observe a memory, I overlook an emotion ; if I study my despon- dent condition in one way, I neglect it in another. These difficulties are inevitable in any science ; they are necessary consequences of the method of observa- tion. The blunder of the critics of " introspection " lies in assuming that the results gained in a particular case by a particular procedure for a particular purpose could be supposed to represent the whole state of affairs. It is as if they said, " Any observation of the flower in that field must be worthless, because by so observing it you utterly distort and falsify the actual conditions pre- vailing in the field." Of course the reply is : "If you wish the whole field observed we will take proper steps to observe it. Indeed, even if you wish the whole field observed with the same carefulness as that flower the problem is not impossible, although with the time and means at present disposal it may not be profitable or practicable." Thus on the question of the validity of introspection we have granted to both parties the main contention namely, that it is a valid method, and that it is in a degree erroneous. The other contention was the improvement of methods. The psycho-physiologists claimed that an entirely new method, with experiments and measurements like those of the natural sciences, must be found ; the observationalists declared that any attempt to reduce mental life to brain processes was utterly absurd. Can we find an adjustment here ? At the present clay I think we can yield to the obser- vationalists the claim that mind and brain are not exactly the same thing. Perhaps mental phenomena can be present only when certain changes occur in the nervous system, but an idea is not explained if we know that at the time of its occurrence a certain change occurred in OBSERVATIo a certain part of the brain. Suppose I hav'e" a feeling of pain. It may be that before, at the time, or afterwards, some change has occurred in my brain ; it may be that such a feeling is always accompanied by a definite nervous change ; but is there any intelligible meaning to the statement that observation of the nervous change is the same as observation of the pain ? It is the same with all states of mind : under the closest investigation they always remain states of mind ; I can never resolve them into motions of particles of matter. The two sets of phenomena may be inseparably connected and parallel that is still a problem to be solved but it is evident that mental phenomena exist as mental pheno- mena ; and that, therefore, there ought to be a science of mental phenomena as distinguished from the science of bodily phenomena. Approaching the question from the other side, we must arrive at the same result. It may be that at some future time an anatomist can so accurately examine the brain with a microscope that he will be able to say with surety, " This person had such and such sensations, such and such memories," &c., but he can attach meaning to these statements only by calling up the phenomena to which they correspond in his own mind. A deaf investigator could never imagine what sensations of sound are, even if he could see and record all physical and physiological phenomena that accompany them. He who had such a perfect know- ledge of the finest and most complicated movements in the brain that at each moment he could tell the position of every molecule, would, in spite of this, not find there pleasure or pain, memories or volitions. Functions of the brain may correspond to or may hold some other relation to mind, yet mind and brain are not the same ; and observation of brains is not observation of sights, sounds, pains, volitions, &c. 14 THE NEW PSYCHOLOGY. Thus the great bone of contention has been yielded to the observationalists without going beyond what, I think, any psycho-physiologist of to-day must at once agree to. How about the claim on the other side, that the old method must be replaced by a new one ? This can be granted to the psycho-physiologist. A new method, a natural-science method, has been found ; it is the method of psychological experiment. It might long ago have been foreseen that some blunder must be the cause of the strife between the introspec- tionists and the psycho-physiologists. The cause of the strife can be removed by yielding to both parties just what each was really striving for. The introspectionist would maintain a true science of mind apart from phy- siology ; and rightly so. No physiological experiments or methods can ever reveal a mental act. The psycho- physiologists were animated with the desire for truly scientific \vork to replace the inaccuracy of the introspectionists ; and rightly so. The new psycho- logy gives both what they wish : a purely mental science founded on careful experiment and exact measurement. CHAPTER II. STATISTICS. ROUGH, general observation being insufficient for our science, it becomes necessary to devise methods of aiding observation. One method of doing this is to make the observations in large numbers and to count the proportion of agreements to disagreements. If a thousand persons observe the same thing, or if one person makes observations and obtains the same result a thousand times with not a single contradiction, the observation can be considered to be better established than if the number of contradictions is equal to the number of positive assertions. We count the number of times we perceive an object out of the total number of opportunities for perceiving it ; or we count the number of persons who can perceive the object ; or we count both the number of times for each person and also the number of persons. The method of counting agreements and comparing the results constitutes the method of statistics. It has long been observed that some regularity appears in the actions of men. Would it not be ^ possible to gain some valuable knowledge from a study of the relation of the number of times an act was committed to the number . of times it was not ? This thought has led to considerable activity in col- is 1 6 THE NEW PSYCHOLOGY. lecting statistics concerning the mental characteristics of man. But statistics do not consist simply in the collection of figures. Scientific counting is something more than setting off one number against another. The statement that 50 % of a group of persons are subject to halluci- nations may be a useful and important fact, but it is not sufficient for scientific deductions. Qualitative statistics involves in addition to the actual counting a considera- tion of the purposefulness and practicability of the plan of observation, the manner of carrying it through, the reliability and availability of the results, the combination of the judgments, and the critical justification of the conclusions. Statistics, says Meitzen, is the method of gaining judgments and conclusions concerning the re- lations of a mass of changing phenomena too numerous for a single general view, by counting characteristic qualities among them ; or, it is the method of judging appearances in mass by means of results in figures. When statistical methods are to be used for strictly scientific purposes the procedure must be systematically correct. This system can be illustrated by some of its rules. The first rule of a statistical investigation is : the phenomenon to be counted must be a countable fact that can serve as a unit. The fact must be clearly and definitely separable from all other facts. In many cases it is a very simple matter to say what things are countable ; in others it is very difficult. At first sight it would seem easy to count the number of houses in a town. But how large must a building be in order to be a house ? Is every place inhabited by human beings a house ? In a recent census of houses in India the very greatest difficulty was found in deciding where to draw the line. STATISTICS. 17 A non-countable object can often be transformed into a countable one by introducing some qualification. We cannot count the number of hot days in a year, because there is no definite limit between hot days and the days that are not hot. We should be continually puzzled as to whether a certain day is warm enough to be counted with the hot days or not, or whether a day that was warm in the morning but cool in the afternoon should be considered a hot clay or not. The phenomenon to be counted is not defined in such a way that counting is possible. We cannot count the number of quick children in the schoolroom, because we have no distinct limit between quickness and slowness. By introducing sufficient limitations the phenomena can often be rendered countable. We can readily count the number of days in the year in which the heat has exceeded 70 F. or the number of children who react to a signal in less than 0.200 s. Yet in a case where such a possibility of measurement exists we are really throwing away an accurate method of observa- tion for a poorer one. If we are to record the tempera- ture of each day, it is evident that some better method of discussing the results could be found than that of choosing some arbitrary figure for a classification of the results. Consider how little we have gained by counting the number of days above 70. Many of these days might have been terribly hot, or the whole lot might have been moderate. The days below 70 cannot be all cold days ; they might have been very cold days, or they might all have been moderately warm. Again, the choice of the limiting temperature may or may not entirely alter the result. If the limit had been put at 75 the number of days above that degree might be greatly changed or it might be almost the same. It is the custom for some health resorts to advertise so many 1 8 THE NEW PSYCHOLOGY. sunshiny days in the year. How many hours of sunshine are necessary for a sunshiny day ? How much cloudi- ness is necessary to ruin it ? It is very plain that with- out some definite agreement and measurement the accounts of various observers will differ greatly. In order to decide whether a day is colder or warmer than a certain temperature, or that a child reacts faster or slower than a certain figure, it is neces- sary to make a record for each case. But when such 'records are at hand it requires very little more labour to treat them according to the methods of measurement. By a merely qualitative statement we actually throw away a large portion of the results of our records. The second rule of a statistical investigation is that all things which are to be counted shall correspond com- pletely and exactly to the stated definition of the counted object and that nothing that does so corre- spond shall be omitted. This requires that all the properties of the thing counted shall be accurately de- termined before, the count begins and that they shall not be changed during the counting. For example, if we judge the culture of communities by the number of universities in relation to the popula- tion, we find that the single state of Ohio, U.S.A., is about twenty-five times as cultured as Germany, a state- ment that even a native of Ohio would hardly assert to be true. The trouble lies in the failure to properly define the term university. Again, statistics of children under the headings " bright, average, dull ; bright in general, bright in some particular," &c., convey little meaning owing to the indefiniteness of the terms used. The statement that the errors introduced will compensate themselves when large numbers are taken is not only mis- leading but also false, as these terms are subject to STATISTICS. 19 definite systematic influences from the particular con- ditions under which the judgments as to brightness are made. A study of St. Louis children led Porter I to the conclusion that tall children are brighter than short children. His measurements of height were according to a well-defined standard, but the judgment of " bright " or " dull " was made on the basis of examination marks. It is hardly needful to remark that the children who receive the best marks are often those of steady character but only moderate ability. It is, moreover, the experience of every teacher that the brightest boys generally receive only moderately good marks. It is also a fact that many of the apparently dull boys, when removed to a congenial atmosphere, turn into successful men. What is true of the more prominent cases will be true of the mass of pupils who are always along the dividing line. Judged by a different standard the bright and the dull would frequently change places. The inaccuracy in defining "bright" and "dull" chil- dren is to a slight extent avoided by taking the teacher's personal judgment instead of school marks. Gilbert 2 tested this definition and found, for the children of New Haven, Conn., apparently a relation between brightness and rapidity of response to a signal, but no relation between "brightness" and other mental qualities. There was no relation whatever between height and "brightness." The attempt to define " bright children " and " dull children " according to school rank or according to the teacher's impression violates every item of the rule. Some will be counted into one class who ought not to 1 Porter, The Growth of St. Louis Children, "Trans. Acad. Sci., St. Louis," 1894, vi. 335. 2 Gilbert, Mental and Physical Development of School Children, " Stud. Yale Psych. Lab.," 1894, ii. 71. 20 THE NEW PSYCHOLOGY. be in it, and some will be omitted who ought to be in. This is due to a failure in the fundamental requirements of an accurate definition of the terms employed. After the statistics have been gathered with the requisite care, and have been subjected to the most careful scrutiny, it becomes necessary to attach to the results degrees of validity based solely upon the results themselves. Let me explain briefly by means of a non- psychological example, what is meant by the " degree of validity." If a cubical die with one black face and five white ones be thrown a great many times, it will be found that one face appears upward about as often as any other, or about % of the time, and consequently that a white face appears about 5 times as often as the black one. If we suppose the die to be perfectly homo- geneous and all the faces and edges to be just alike, we can well believe that, as the number of throws is in- creased, the number of appearances of the black face will approach more and more closely to the fraction of the total number of throws. This fraction we call the probability of the appearance of the black face. The total number of faces of which any one may appear is n = 6 ; the number of black faces is r=i, and of white faces is s = $. The probability at any given throw for the appearance of the black face is p= - =J, and against its appearance is q = ^=%. This does not mean that the black face appears exactly once in 6 times. There may be a run of blacks so that for a certain set of 6 throws the black may appear every time. Nevertheless, in the long run the black will appear about -J of the time, and the longer the run the more closely the fraction will approach . The expression, " about $ of the time " has been STATISTICS. 21 accurately defined as depending on the number of throws. That is done in the following way : Suppose that we establish a scale of certainty ex- tending from i.ooo... for positive results down to o.ooo... for negative results. If a black face is to be expected with a certainty of i.ooo... we know absolutely that it will appear ; such would be the case if all the faces were black. If it is -to be expected with a certainty of o.ooo..., then no black face would appear; such would be the case if all the faces were white. Let us see what certainty we are to attach to the fraction J when we say that at any given throw with our original die the odds are i to 5 for the black. The solution has been found by Bernoulli. If n throws are to be made with our die, we can expect with a certainty of that the actual result differs from the ideal probability ^>=i by an amount which lies between k= The expression $ (r) is the well-known probability- function. A table of its values will be found as Appendix I. The quantity e is the basis of the natural system of logarithms, or = 2.7 1828. For example, supposing we are to make 3000 throws with the die, with how much certainty may we expect that the black face will appear not more than 505 times or less than 495 times ; or, in other words, that it will not differ from the ideal J- by more than 3~oVo = ew ? Here we have 11 = 3000, /> = J, q=%, and y /^= ^. 22 THE NEW PSYCHOLOGY. Performing the operations indicated, 1 we find that the degree of mathematical certainty is 0.21 that the assigned limits will not be exceeded. If, instead of a range of variation of +5 from the ideal 500, we assign successively 6, +7, +8, &c., we get greater degrees of certainty ; if we assign successively +4, +3, + 2, and i i, we get lower degrees. For example, for +10, we find P = o.38 ; or the chances are not quite 4 out of 10 that the limits will not be exceeded. By similar methods we can tell just what limits of variation to assign for any desired degree of certainty. In statistical work we generally demand a degree of certainty of P = 0.9999778, which is so near the unit mark as to be reasonably reliable. For this value 2 7=3. In the case just treated the allowable limits of variation from 500 for practical certainty can be stated as 86. Let us now take a psychological example. An in- vestigator publishes a series of conclusions in regard to the overestimation of an interval of time when filled with one kind of visual impression as compared with an interval filled with another kind. A slowly rotating cylinder presents colours before a square opening in a screen. The opening appears of each given colour for a definite length of time, and the observer states whether the two intervals of time appear equal or not. In one set of experiments a time interval filled with a constant colour is compared with another filled by a many-coloured band. In a total of 600 experiments 1 The scheme for solving such problems is given, e.g., in Meyer, " Vorlesungen iiber Wahrscheinlichkeitsrechnung," 107, Leipzig,i878, and is reproduced with slight changes in Appendix II. 2 For practical work it is sufficient to use the formula k = 3 */ The result is a trifle too large, but the error is on the safe side. STATISTICS. 23 made on six persons the constant colour appeared of longer duration than the changing one in 58.7 % of the cases. The conclusion is drawn that the constant colour actually seemed of longer duration. What degree of validity is to be given to this state- ment ? When it is required to say that one of two things is longer than the other, mere guess-work with- out any knowledge would make one of them longer in 50 % of the cases. Here we have 58.7 % for one of the things. Making the supposition that absolutely no errors were made in setting up the problem and carry- ing out the experiments, we find that according to the theorem of Bernoulli P = o.24, or that the degree of validity is about J on the scale of certainty which we have assumed. Of course, for a less stringent scale the degree would be greater. Up to this point we have treated of mathematical probabilities ; we have assumed an ideally perfect die, or we have supposed the statistics to be absolutely free from error. To such cases we can apply the laws of chance as given in mathematical works on probability. In actual investigations, however, it must first be proven that the results follow the laws of probability. Suppose we have as the result of a statistical investi- gation the fraction ,, where ri is the total number of cases and m' the number that have a certain character ; can we assume that the co-efficient of frequency p' = ^ can be treated as a mathematical probability p ? For example, in the case of time-estimate just considered n'\$- 600, w' = 352 and ^' = 0.587; we have treated p' as a mathematical probability, arid we must ask if this treat- ment was justifiable. If p' is a mathematical probability, a repetition of 24 THE NEW PSYCHOLOGY. the statistical count will give a value p" which does not differ from p' by more than m' , n'-m' ... -in" n"-m" , where p> = -,, q = , p a =-., q" = ^r and y is the quantity already used in considering Bernoulli's theorem. The amount of difference depends on the degree of validity we desire. For the usual statistical validity we take P = $ (y) = 0.9999778, whereby 7 = 3. If, in a statistical investigation where ' and n" are large, p'-p" exceeds + /, it is safe to assume that the two cases follow different laws of frequency. If. p'-p" exceeds + /, they may follow the same law of frequency, although there is no proof that they actually do so. In the time-experiments just mentioned the experi- menter took the average of the percentages for six observers ; he assumes thereby that the results of each observer follow the same mathematical laws of pro- bability. Let us take the first two observers each with 100 experiments: B, 59.5% and H, 63.8%, with a difference of 4.3 %. Does this difference exceed the limits allowable for considering them as following the same laws of probability? Here ^' = 0.595, q' = 0.405, ;/ = ioo, ^"=0.638, q" = 0.362, n"=ioo, 7 = 3. We can in a case of this kind consider 100 as a large number. We find that the allowable difference is 0.282, or 28.2 %, and consequently we can assert that the laws of frequency in the two cases may possibly be the same. Even when a series of counts does show an agree- ment sufficient to forbid our concluding from the above formula that the laws of frequency are different, we have not yet proven that they are the same. To prove this, it is necessary to show that, as the number of STATISTICS. 25 experiments or counts increases, the general value p 1 converges toward a limit p in the fashion required by the laws of probability. Suppose that n counts of z items each, n being large, give successively the co-efficients of frequency, Pu Pv 'i Pn- ^ these are mathematical probabilities, the most probable value for p is a=f l+ ^ + n " ' + ^ n - Moreover the variations of p 1} p 2 , . . ., p n from a should be grouped on either side of a according to certain laws. Even with only a fair number of series we can expect that the numerical values (regardless of sign) of p will be about half of them greater and half less than 04769 V2 a (ia) T , , t the probable error, r = - . If the counts and series could be infinite in number we would get a " true " value W for the result ; in a limited series we are confined to the most probable value a. The trust- worthiness or "precision" of a in representing W is indicated by the value of r ; that is, if two independent series are carried out under like conditions, we can trust them inversely as the relative values of r. Each value of p lt p 2 , . . ., p n has likewise its precision, namely, h---=- If we take the single A/2 a (ia) variations x l =p l a, x,=p 2 a, . . ., x n =p n a and put y = h x, we have, with y in its usual meaning, an ex- pression that indicates the probable frequency with which the errors are to be found lying within #. The variations should follow a certain law of frequency, as indicated by the successive values of d> (y) in the Table for y. For practical work it is generally sufficient (P = $ (y) = o.5o) to assume that about half the errors lie within and half without d=- ^ 769 . If they do we 26 THE NEW PSYCHOLOGY. conclude that the statistical results may be treated as mathematical probabilities ; and if they do not, that they may not be so treated. If more than half fall within +d, the separate experiments or counts were probably not independent of each other but causally connected ; e.g., each successive experiment might by practice make the observer more skilful, and the results would therefore hold good neither for the unpractised nor for the practised observer. If more than half fall without rf, we must conclude that uncertain influences are at work, e.g., fatigue, distraction, &c. z Let us see how these values of probability are to be applied to the results of a study of memory. We now take a published report of an admirably executed investigation, and proceed to apply the rules with no knowledge of what the result may be, and with no anticipation excepting a favourable impression from a cursory glance at the figures. For visual memory the apparatus consisted of several series of ten small squares of paper of different colours, and of several series of black numbers each mounted on a square white card of the same size as the coloured squares ; they were exposed on a black background. For auditory memory the names of the colours or the numbers were spoken by the conductor of the work. Several corresponding series of coloured squares and mounted numbers were supplied to the persons experi- mented upon. After having seen the original series, the subject arranged these latter colours and numbers in the order of the original series as well as he could remember. The subject saw or heard the original 1 For the brief view of statistics which I have presented I am much indebted to Lexis, " Einleitung in die Theorie der Bevol- kerungsstatistik," Strassburg, 1875 ; " Zur Theorie der Massener- scheinungen in dermenschlichen Gesellschaft," Freiburg, i. B., 1877 STATISTICS. 27 series only once ; the recollecting was done immediately at the conclusion of each series. Thirty-two different series with a total of 2,140 colours and numbers were used. Proceeding to the results, we will assume that the experiments are entirely free from sources of error, and that the results can be accepted just as they are stated. The result for the first person experimented upon for visual memory is 420 errors out of 2,140 colours and numbers, or 18.7%. The result is a single fact in itself, but before we can use it we must prove that it is a true probability. The author should have done this by com- paring the results of the separate series that go to make up the 2,140 results, but, as this was not done, the only light we can get on the subject is by comparing together the results for the five subjects. These results are 18.7%, 19.3%, 17.1 %, 22.4%, 25.1%. If the results are governed by the laws of probability, these numbers should not exceed certain limits. Let us take the ex- treme cases 17.1 % and 25.1% ; if these do not exceed the allowable limits, the others, of course, do not. Putting, as previously explained, ^'=0.171, p"=o.2$i, and 7 = 3, we find that the allowable difference is 1 = 0.053, whereas the actual difference is 0.080. We are apparently justified in assuming with practical certainty that the two cases follow different laws, and that we cannot apply the deductions of probability. But what difference does it make, however, whether they follow the laws of probability or not ? Simply this ; no special laws were established for these results, therefore we try to apply at least the law of chance. If they do not follow even the law of chance, our work stops completely ; the figures may be of interest as personal facts, but if these facts are utterly capricious, we cannot use them for scientific deductions. 28 THE NEW PSYCHOLOGY. Let us remember, however, that these were the extreme cases, and that the disagreement between the calculated and the actual difference is not so very great. We can, without very great wrong, give up our deduc- tion of disagreement and leave the question open for a positive answer. Let us assume, then, that the results have stood the first test and proceed to the next test. The most probable value for a series of results is assumed to be the average. The average for the five subjects is 20.5 % ; are the variations grouped as demanded by the laws of chance ? We find that the number of counts (unfortunately not large) is = 5 and that the number of items in each count is 2=2140. The most probable value for the five percentages is ^_o.i87+o.i93+o.i7i+o.227+o.25i_ Q The differences betw r een a and the individual results are successively 0.018, 0.012, 0.034, - OI 9> 0.046. Two or three of them should be greater and two or three less than r= 0.006. As they are all greater, there is no proof that they follow the same laws of probability. We cannot apply the calculations to the separate values for the single observers, as no data are furnished by the authors. Since there is no evidence whatever that the laws of probability govern the case in hand, we cannot use the average for the five subjects. For, if the average is assumed as the most probable value the laws of proba- bility should follow the deduction, whereas they do not ; on the other hand, if the average is assumed as a capri- cious value, it has no scientific worth. We can, there- fore, consider only the results of single subjects. All data fail that can enable us to judge whether the laws of probability or any other laws hold good or not. If not, our work stops completely ; as, however, the STATISTICS. 29 authors proceed to draw deductions, we will assume, in order to keep the illustration, that the laws of probability are valid for the particular cases, and will proceed to test the conclusions. We will use the results for the first subject mentioned. The number of errors for visual memory was 18.7 % ; for audible memory, 34.6 % ; for visual and auditory working together, 44.4 %. The conclusion is drawn : when the two senses act together in recollection, they hinder each other. This result is so unexpected that we must ask whether this difference is great enough to warrant the conclusion that pure chance may not have produced it. Proceeding as before, we find that we can say that, with practical certainty, the difference 0.444 0.341 = 0.103 exceeds the limit 0.053 allowable for considering them as following the same law and arising from chance. In other words, the difference is a real one. The same holds good for each of the other particular cases, and, admitting the assumptions we have made, we can decide that the general conclusion is valid for all the cases. 1 1 To serve as a subject for dissection is a thankless task. In looking over a number of statistical investigations for this purpose, I finally decided to use the best piece of work I found. The par- ticular investigation selected thus pays the penalty of its goodness. CHAPTER III. MEASUREMENT. WHENEVER we are treating of an event that either happens or does not happen, we are working with qualitative facts ; but whenever one thing may be greater or less than another, the phenomenon observed has a quantitative character, and can, if proper instru- ments are provided, be made the subject of measure- ment. Phenomena upon which we can pass judg- ments of greater, equal or less in relation to one another, we call quantities. If a quantity be expressed by a concrete number, i.e., by an expression composed of a number and the name of the unit-phenomenon, we call the result the value of the quantity ; the process whereby the value is obtained, we call measurement. We are all familiar with commercial and physical measurements : we have all measured butter or cloth, temperature or electric potential. But are there such things as " mental" measurements? Can we measure our sensitiveness, our judgment, our will power, our memory, our feelings, our beliefs ? Many of these can be measured without difficulty, others only roughly, still others not at all. For none of them, however, is measurement impossible ; the same fundamental method is applicable in all cases, and if it has not been applied 30 MEASUREMENT. 31 to all mental phenomena, the fault lies in the lack of men of ability to devise the means of applying it. The first step in establishing any fact as a quantity consists in determining that it is equal or unequal to, greater or less than, another fact. What are meant by " equal," " unequal," " greater," and "less"? Psychologically, that is, from direct experience, we all know without more aclo. If in each hand we lift a glass of water, we can say whether we can distinguish a difference in heaviness or not. If we can distinguish a difference, we say that they are unequally heavy ; generally we can also say that one of them is more or less heavy than the other. If we distinguish no differ- ence, we say that they are equally heavy. But are they " really" equal ? Is there not a physical method of determining their " real " equality as con- trasted with "apparent " psychological equality ? Let us make the two glasses of water appear equal in heaviness, so that no difference is distinguished between the glass in the left hand and the glass in the right hand. There is a possibility that these two glasses, judged to be equal when glass A was lifted by the left hand and glass B was lifted by the right hand, may not retain their apparent equality if the circum- stances are reversed. Let us try them with glass B in the left hand and glass A in the right hand. They appear, let us say, no longer equal ; B is heavier than A. To make them alike we must add water to A. If we do make them alike in this way, A will be heavier than B when we return to the original arrange- ment. Evidently, in order to make them equal, we ought to add to A just half as much water as the difference between the two, and to take away a like amount from B. 32 THE NEW PSYCHOLOGY. Suppose we make A on the right hand equal to B on the left hand by adding a quantity of water to A ; then, by pouring a like quantity off, let us get the difference separately. This difference D we divide in two by pouring it into two glasses and adjusting the two portions till they appear equally heavy, one of them, A, being on the left hand, and the other, B, on the right hand. We want to get ; we actually do get D a + b. On changing the glasses to opposite hands we again find a difference. It is evident that a division of the first difference into the two parts, a and b, was not into halves ; we did not get = a b. To correct a and b so that the two parts shall be equal, we evidently need to add half the difference d = a b to the lighter half. We must proceed to divide this new difference in two as before, but again we fail to get exact division. By continuing in this way we finally come to a quantity so small, that we can detect no difference between its two halves. We can then add all these halved difference to A, and can say that A is equal to B, at least, as nearly as we can judge by lifting with two hands, thus, Psychologically they are equal; are they "really" equal ? Let us go further by a finer method. If we adopt the method of lifting the two glasses in succession at an interval of about two seconds, by the same hand, we find that we can still detect a difference by this method. In judging by the one-hand method we lift one glass after the other. This difference in time may, and in MEASUREMENT. 33 fact does, have an influence. If A is lifted first, and B is adjusted to equality with A y then a reversal of the order by lifting B first will make A appear too heavy. We must therefore proceed in the same way as before to adjust the successive differences, till a last difference is divided in two parts without our being able to distinguish between the parts. When the two glasses are adjusted by this method till no difference is distinguished, we feel a trifle more satisfied with the equality. The two glasses may not feel equal on any one occasion, yet we recognise that each particular method of judgment differs from every other one, and that no single one gives a perfectly satisfactory equality. As the final equality, we take the result obtained by eliminating the differences due to particular methods. Is the result yet a " real " equality ? When an equality, established in a certain department of mental life, does not give satisfactorily accurate results, we transfer the establishment of the equality to another department. The equality which we have established in our glasses would not be satisfactory for judging gold or diamonds. Let us transfer the judg- ment to the department of sight. This transference is obtained by means of apparatus. The usual method in which judgments of heaviness can be changed to judgments by sight is by use of the balance. When two objects are laid in the pans of a balance the beam tips down. If, when the objects are reversed in the balance, the same one again goes down, it is heavier than the other. We proceed to increase the lighter weight till the beam ceases to tip. The weights are now judged indirectly by sight to be equal. By reversing the position of the weights we see that the beam tips, and consequently that the balance is a little 4 34 THE NEW PSYCHOLOGY. one-sided. Our judgment of the tipping is made by sensations of sight, and is a mental one. We might proceed to get nearer a sight-equality by halving the differences, as we did originally with the two glasses of water. But we have already learned that the quickest way is to improve our apparatus ; so we scrape a little off one of the scale pans, or add a little weight to the other one till equality appears. Is this the "real" equality ? No ; for by transferring the judgment to a still finer balance a difference is still detected. Thus continuing to use the sense of sight the methods can be made ever finer by means of improved apparatus, but there never comes a time when we can say that we have found a perfectly true equality with absolutely no difference. Our last judgment always ends in a comparison of two sensations, with the knowledge that the judgment can be improved by the use of finer methods, Our ultimate criterion in any case is therefore a psychological judgment of equality. What, then, is the " real " equality ? Practically, it is the psychological equality at the last stage to which we have carried it ; theoretically, it is the equality at which we would arrive by forever improving our methods of judgment. We have not left the region of psychology for a moment ; we improve our arm-apparatus by judging in sequence instead of simultaneously, we use the balance for transferring the judgment to the sense of sight, and we improve the balance for making the sight- judgments finer. The balance did not take us any more or any less out of the region of psychology than did the arm ; the measurement was as much psychological and as much physical in one case as the other, and the "real " equality is likewise just as mental as our original judgments. Just what is meant by the common term "physical MEASUREMENT. 35 equality " as opposed to " psychological equality," can be stated as follows. In the physical sciences and in psychology phenomena can be considered as equal when the differences that exist, between them are proven to be so small as to be entirely negligible for the purpose in view. The equality is obtained in any way and by any kind of judgment that may be con- venient or possible. This equality is often called " physical equality " to distinguish it from the equality obtained by any particular sense. The real difference in the ordinary use of the terms appears to be this : two things are said to be " psychologically " equal when they are judged directly by the same sense to which the equality refers ; and they are said to be " physically " equal when they are judged equal for one sense by means of ap- paratus involving a different sense, or the same sense under different conditions. When equality is judged by means of apparatus instead of direct sensations of the property involved, it might be better to speak of instru- mental rather than physical equality. This instrumental equality may be established between the most different departments. With the scale and the balance we judge weights by sight. With the micro- meter caliper we measure lengths that might be judged directly by sight or by touch on the skin or by muscular sensations. This instrument is so arranged that by a peculiar sensation of pressure we can judge differences far finer than otherwise, and the actual judgment of equality is made by this sensation, while the reading of the scale is done by sight. Similar cases are found in all apparatus. The final reading of the instrument is in all cases necessarily a direct, psychological comparison ; this comparison is nearly always by sight. If we read a 36 THE NEW PSYCHOLOGY. thermometer, we compare by sight the top of the mercury column with some mark on the scale. Clock and galvanometer readings and nearly all judgments of length are of the same kind. All measurements, physical as well as psychological, thus consist ulti- mately in the comparison between two phenomena of consciousness, generally two sensations of sight. All physical measures have been developed out of these psychological estimates. 1 We measure temperature by noting the agreement of the length of the column of mercury with a certain portion of the scale ; we measure the strength of an electric current by noting the angle through which the mirror is deflected or through which the needle passes, and this very angle in turn is measured by some length of arc, chord, or tangent ; we measure time by the agreement of the angle over which the hand has passed with a mark denoting the end of another angle taken as a standard. We have thus completed the first step in establishing quantitive relations between phenomena ; we have obtained what we consider to be trustworthy judg- ments of equality. The next requisite in measurement is the establishment of a graded scale of quantities with any one of which the given quantity can be compared in respect to its equality. In just the same manner as that in which we estab- lished an equality of two weights on the basis of a judgment of "equal" and "unequal," we might proceed to establish a whole series of weights, of half, quarter, double, triple, &c. the weight of some standard from which we start. We proceed on the assumption that i + i =2, and that the equality is to be established by methods 1 Wundt, Die Mcssiing psychiscJtcr VorgHnge, " Essays," 158, Leipzig, 1885. MEASUREMENT. 37 sufficiently fine for the practical purpose in hand. We make two weights equal (physically or psychologically, as you may please to call it) to each -other; this gives us i and i. Then we make another equal to both together ; this gives us 2. And so on, with 2 + i = 3, 3 + 1 = 4, &c., till the whole scale is established. In similar fashion we obtain scales of length, time, &c. This does not imply that, when we take our scale back to the original kind of judgment from which we started, we shall find it to be confirmed. We did not even find the equality confirmed. It was a peculiarity of the judgment by simultaneous lifting that one hand overestimated the weight as compared with the other hand. It may just as well be that the scale of apparent multiples may be quite different from the one just established. If out of a series of weights exactly alike in appearance, we pick out, by lifting, the set that apparently bear the relations of i, 2, 3, 4, &c., we find that we have chosen those that do not agree with the judgments of 1 + 1=2, 1+2=3, &c. We are mentally so constituted or mentally so trained that apparent judgments of a succession of i, 2, 3 may not agree with the scale. These differences represent pecu- liarities in the construction of the individual at the time. Some confusion has been caused by the statement that psychologically we are able to judge only equality and inequality, with implication that in physics we are able to do something more, namely, to measure one object as a fraction or a multiple of another. Even if in physics we could directly do this, it would mean nothing more than that we could do so in psychology also, because when we compare two physical lengths we are only performing a psychological process. When we say that one line is apparently three times as long as another, we simply mean that the two mental pictures 38 THE NEW PSYCHOLOGY. bear that relation, or that the series of muscular sensa- tions produced by running the eye over the lines bear that relation. The fact is, however, that in the absence of graduated scales we express one quantity as a multiple of another only by estimates from our sensations. The graduated scales, by means of which we always work wherever possible, and by means of which we obtain the accuracy of modern science, are really only records of direct judgments of likeness or difference. The zero point on the thermometer means that the mercury column occupied that place under certain definite condi- tions, namely, immersion in the water of melting ice ; the 100 mark means that the column was just so long when the thermometer was surrounded by steam at 760 mm. barometric pressure. We usually divide the intermediate space into 100 parts, but these divisions of themselves mean nothing. It is only by placing the thermometer in liquids of the intervening temperatures and directly recording the height of the column at each temperature, that we get a definite graduation. As this latter method is too cumbersome, the marks are made at intervals by the dividing machine and then the actual value of each mark is determined by sending the mercury up to it, and noting the temperature required to do so. Thus each mark on the thermometer means that at some previous occasion of a certain character the mercury column reached to that point ; when we now make a measurement of temperature we simply compare the length of the column at present with the record of its length for some previous time. The same is true of the galvanometer, the clock, and all apparatus in which the graduation is in units of length ; exactly similar processes are used to arrive at other scales. 1 1 Scripture, Psychological Measurements, " Philos. Rev.," 1893, ii. 678. MEASUREMENT. 39 Having established such scales of weight, length, time, &c., what do we measure with them ? In the first place we measure our sensations. In using the word " sensation " I am not introducing any of the technical terms usually employed in psycho- logy. We here have nothing to do with the usual distinction between "sensations" as elements of mind, " percepts " as compounds, &c. In practice this dis- tinction is not carried out. The subject of colour is treated under the heading of sensation, whereas much of the colour work deals with highly compound mental facts. Again, under the heading " perception " you will find, for example, the whole treatment of space, whereas the elements of space are as simple as anything in mental life. With terms such as sensation, perception, intellec- tion, emotion, conation, &c., w r e have nothing to do ; we shall find all the facts of mental life in their proper places, and I venture to hope in connections more natural and intelligible than when arranged grouped to suit a particular scheme of classification. Therefore, when I use a word like sensation, feeling, emotion, &c., I do so only in the meanings implied in common speech. Everybody knows what a sensation of warmth or a feeling of hunger is, but there is no need of an attempt to prove that the sensation of warmth is an elemen- tary process, and that hunger is not an emotion. We might possibly speak of measuring sights, hearings, touches, &c., but such expressions are contrary to the genius of our language, and we are accustomed to employ such terms as " sensations of sight " for sights, " sensations of sound " for hearings, &c. We measure, then, our sensations of sight, hearing, touch, warmth, &c. The millimetre measure that lies before me is one of my sensations of sight ; I know it to be a scale established in a way similar to that in 40 THE NEW PSYCHOLOGY. which the scale of weight was established. Here is a line drawn on a piece of paper. This line is also one of my sensations. Applying the scale to the line, I find an equality between my line and a certain mark on the scale, and the value thereby deduced is the measure of the length of my line. I have measured the length of one of my sensations of sight. It does not make a particle of difference whether there is an extra-mental world with an extra-mental scale and an extra-mental line ; both the scale and the line are facts of my conscious experience, and I measure one by the other. It would be the same if the line were what is called a " hallucination " ; I use the scale and I measure it regardless of whether I have reason to believe it to be a " real " or an " unreal " line. In an exactly similar manner we apply measurement to the other regions of mental life. Again, we measure the accuracy of judgment. In all the methods of lifting weights we find " sources of error." The difference due to using two hands can be called the error of the two-hand method ; its size can be roughly determined after the equality-adjustment by the same method, or it can be more accurately deter- mined after the equality-adjustment by the balance. The difference due to using one hand can be called the error of sequence, the second weight appearing the heavier. We might correct the error of the two-hand method by placing an extra weight on one hand, the size of this weight being found by the two-hand method itself. In a similar manner we might correct the error of the one-hand method by always using an extra weight for the first one to be lifted. We correct a balance in the same way by adjusting the scale pans till the beam remains steady when the weights are reversed. With MEASUREMENT. 41 cheaper balances we scrape the heavier horn pan or we put bits of paper on the lighter pan. We thus measure the errors for the particular methods. I have spoken of " sources of error" in these different methods of measuring. They are "errors" only from the point of view of trying to reach absolute equality ; otherwise they are phenomena for investigation. The error of the balance, like all other errors of apparatus, is a property of the apparatus. This latter, however, very properly bears the name of "error of the ap- paratus " because the balance was built for the par- ticular purpose of establishing equality, and all devia- tions are opposed to its purpose. Nevertheless this very error is in certain cases made the subject of investigation. The " error " of the two-hand method is a property of the person lifting the weights, and, unless we are trying to compensate or eliminate it, we would no more call it an "error" than we would call anger or an association of ideas an error. It is itself a mental quantity and should also be measured. When trying to eliminate it, we may call it the " error of judgment," otherwise it is better to name it the " inaccuracy of judgment." Here, again, I use a term in the meaning given to it by everybody. Speculate as much as you please about the processes of logical thought involved ; but when I lift two weights and say " unequal," I know nothing of such processes. I have a very definite feeling that I express by saying " un- equal," and it is this feeling that I term judgment. The expression for this feeling is found, for this particu- lar case, in a certain difference between weights. Inac- curacy of judgment is the term applied to this difference. We not only measure sensations and the inaccuracy of judgment, we also measure sensitiveness, or fineness of judgment. 42 THE NEW PSYCHOLOGY. Let us use a set of fine weights on a rough platform scale. We find that the scale fails to notice a difference of less than 60 g. on a weight of 120 g. On using a very ordinary grocer's balance we find that the balance notices a difference of, say, 6 g. on 120 g. The sensi- tiveness of balances or scales is said to be inversely proportional to the just noticeable differences in a given weight, or directly proportional to the recipocals of these differences. Thus, for the weight of 120 g., the relation of the sensitiveness A of the platform scale to that B of the grocer's balance is given by A : B = 6 : 60 = ^ : . Or, the balance is ten times as sensitive as the platform scale. By lifting the weights with one hand or two hands we can evidently measure our own sensitiveness in exactly the same way as we measured the sensitiveness of the balance. We get for one person with the two-hand method a just noticeable difference of .p I} and with the one-hand method p 2 ; for another person q t) g 2 , &c. The sensitiveness in each case is said to be in the ,. , I I I I Q ratios of j-, jri -j-> fT> &c ' This sensitiveness is generally called the " sensitive- ness to differences." What is this " sensitiveness " ? This term is used to- day throughout experimental psychology, much as the word " force " was lately used in physics to indicate a vague, mysterious agency governing phenomena. Scientific thought demands precision of the concept. In the first place, to speak of " sensitiveness " as de- termining the just noticeable difference seems wrong. All we know about it is the just noticeable differ- ence ; sensitiveness is a term by which we compare objects in inverse order to the just noticeable differ- ences. MEASUREMENT. 43 With the various scales of units thus established, it might seem that nothing more is necessary than merely to apply them. This is not the case. The application of scales to quantities to be measured is not a simple process to be performed by everybody ; there is a refined and difficult art of doing so and a well-developed science of treating the results. 1 The fundamental principles of the science of measure- ment are somewhat as follows : In general it is not sufficient to measure a thing only once ; we repeat the measurement a number of times. If the measurements agree, we are justified in con- cluding that our apparatus is not fine enough to detect the differences due to the infinite number of sources of error always present. By using finer apparatus the accuracy of the result can always be pushed one or two decimal places beyond agreement. For example, in measuring the sensitiveness of a balance, if we always obtain the same result, we may feel sure that the weights we have used for the measurement were not finely enough graded. We know that from changes in the position of the knife-edges, from friction, from tempera- ture, from air currents, &c., the results of our measure- ments will vary, provided our weights be fine enough. The like holds true for all measurements, psychological as well as physical. Suppose I attempt to measure the diameter of a coin. I report that in ten measurements the result was of an inch every time. I now take a fine steel mechanic's ruler, graduated in 64ths of an inch, and again measure the coin ten times. I report the diameter to be f^- of an inch on nine occasions, but ff on one occasion. From previous experience you know that my eyes are sharp enough to 1 Scripture, Accurate Work in Psychology, " American Journal of Psychology," 1894, vi. 427. 44 THE NEW PSYCHOLOGY. use the ruler correctly, and you suspect that the source of disagreement lies in the coin. You therefore limit me to one particular diameter between two finely marked points on the circumference. In placing these points you may not have got them on a line exactly through the centre ; but we will overlook this error and consider the linear distance between these two points to be the true diameter of the coin. To free myself from all responsibility for your assumption that this distance is the diameter of the coin, I state my problem anew as the determination of the linear distance between two marks on the edge of the coin. Using the mechanic's ruler, I always obtain -JJ as a result. Your previous experience tells you that agree- ment means comparatively coarse measurements ; you advise a scale graduated in looths of an inch and the use of a magnifying glass. I obtain 0.89 of an inch without disagreement. This work is very trying to the eyes, and if I keep on making measurements they begin to disagree owing to fatigue. I find that I cannot get the divisions of the ruler exactly over the marks. The subdivision of the ruler might be pushed further, but nothing would be gained, as the inaccuracy of the eye would produce disagreement. You therefore suggest the transference of the measurement to the sense of touch. Therefore I now apply a micrometer caliper to the coin. I screw up the head till the rod just touches the coin. What do I mean by " just touches" ? I mean a slight but certain sensation of resistance. I can make the sensation weaker or stronger, whereby the rod presses against the coin less or more ; the instrument yields, and I must settle on the degree of yielding to be chosen. Long practice has made me use a certain degree which I keep in memory. MEASUREMENT. 45 When the ruler was used, we assumed that it was correctly graduated ; likewise we will assume that the graduations on the rod and the barrel of the caliper are correct. I report to you that the measurements no longer agree. You reply that my hand must be out of practice. I practice for a while measuring a piece of steel till I get no disagreement when measuring. I try the coin and still find some disagreement. My method is fine enough to be blameless and you suggest that, owing to the wideness of the marks on the edge, I do not always get exactly the same line. I now fix the coin and one end of the caliper immovably together. Agreement results, and I report the diameter as 0.887 of an inch. . Agreement always means that the method should be made finer. On the back of the caliper I find a gradua- tion enabling me to read to the io,oooth of an inch. First proving to your satisfaction that my hand is delicate enough for adjustment to the io,oooth of an inch, I report that there is now disagreement and that the average gives 0.8869 ^ an i ncn And so we might go on. If the measurements agree, the conclusion is that the method of measurement is not fine enough to detect the differences due to indefiniteness in stating exactly what is to be measured, or due to changes in the quantity measured owing to neglect of conditions that should be kept constant. If the measurements disagree, the con- clusion is one or both or all of three things : (i) The method of measurement is inaccurate to a certain amount ; (2) the irregularity is due to inclefiniteness of the problem ; or (3) changes occur in the quantity measured. In the case of agreement we can go no further without finding new methods and apparatus. In the 46 THE NEW PSYCHOLOGY. case of disagreement we can, by making the method more accurate, by more carefully defining the problem, or by more accurately controlling the quantity measured, study any one of these three facts. Illustrations of how this is done will be found in Part II. How shall we treat our results where they disagree ? Suppose that we have made a set of measurements to such a degree of fineness that the last few decimal places disagree. In stating the result of our work we cannot give every individual measurement ; some one value must be chosen or deduced which best represents the lot. The most frequent representative is either the average or the median. Such a representative result is generally called a mean. The average is found by adding together all the results and dividing by the number of results. Suppose we had a series of nine measurements of the time it takes to walk from our front door to our office, say 3041, 3047, 3039, 3042, 3046, 3049, 3045, 3094, 3047 seconds. To find the average time we add them all up and divide by nine. To make matters perfectly general, let us denote the number of seconds in the first result by a,, in the second result by a 2 , &c., up to a n . Then we have for the average a= * 2 ^" . It is evident that this formula will serve for bushels of wheat, dollars, years, or anything else that can be expressed in multiples of a concrete unit. The median is determined by counting off the results in the order of size and taking the middle one. This can generally be clone by simple inspection ; for the sake of clearness let us in our examples actually arrange the results in this order. Beginning with the smallest, we have 3039, 3041, 3042, 3045, 3046, 3047, 3047, 3049, 3094. The middle one or median is 3046. MEASUREMENT. 47 I cannot here go into a discussion of the relative advantages of the average or the median. 1 I will only point out that an extreme result, like 3094, exercises a far greater influence on the average than any one of the others does, whereas it does not have any more effect than any other result in determining the median. The average is the best representative value for some pur- poses ; it is the customary one for all. In psychological work I have found that the average frequently mis- represents the group of results, whereas the median does not. In those cases where the average gives a good result, it turns out to be practically the same as the median. In this book I shall use the average almost exclusively in order not to introduce what might seem a strange term. It is not sufficient to know the mean result (average or median) ; we must know something of its uncertainty. This is most readily determined by calculating the mean variation. Let us write the original results in a column, add them up, and find the average. Then we find the difference between each result and the average (never mind the Those especially interested will find the subject treated in " Studies from the Yale Psychological Laboratory," vol. ii., New Haven, 1894. 48 THE NEW PSYCHOLOGY. sign), and write it in the column v. Now we average all the figures in this column. The result is called the mean error or mean variation. Here we have a measure of uncertainty. 1 The mean error for the median is found in exactly the same way. The small numbers here indicate a con- 111 v 3 '" thousandth of a ittirnJ ill loo 'fo aJ ifo joe jft> ^ a j Fig. 30. INFLUENCE OF FATIGUE ON TAP-TIME. joints of the arm. The general sequence in order of rapidity is elbow, wrist, shoulder, finger. A joint on the right side is generally more rapid than the corres- ponding one of the left side. The superiority of the boy's right side over the girl's right side is slightly greater than the superiority of the boy's left side over the girl's left side. 2 The rapidity of tapping varies with age. Bryan has determined the progressive development for the various 1 Bryan, On the Development of Voluntary Motor Ability, "Am. Jour. Psych.," 1892, v. 123. 2 Ibid. 10 130 ' THE NEW PSYCHOLOGY. joints during the different years of school life. In his experiments the highest rate out of 46 children was attained by a girl of 12 years, whose record exceeded that of the average of the age by 30 % to 40 %. She looked the type of robust health. When asked if she played the piano, she said : " Only by ear, but I play base ball, though ; " adding, a moment later, " I can strike two over the octave on the piano." Another girl, 13 years, who had taken lessons on the violin for two years, gave records almost as much above the average as the girl just mentioned, except for the left elbow, and especially for the left shoulder. The high rates of the joints most, involved in playing the violin and the low rate of the left shoulder illustrate the effect of practice. The results of measurements of tapping-time on one hundred New Haven school children of each age from six to seventeen are shown in Fig. 31. The figures at the left give the number of taps in five seconds, those at the bottom the ages. The little children are very slow ; the boys at each age tap much faster than the girls. 1 In these experiments the children continued tapping after the five seconds recorded. After tapping thirty-five seconds longer a record was again taken. The difference between the two sets of records tells how much the child lost owing to fatigue. At six years of age, the boys lost 23 % of the original number of taps. The amount of fatigue was greatest at eight years, and decreased with advancing age. It is very remarkable that, without exception of a single age, the girls were less fatigued than the boys. A comparison of the results suggests a conclusion as to the impetuosity of the boyish character. 1 Gilbert, Researches on the Mental and Physical Development of Schoolchildren, "Stud. Yale Psych. Lab.," 1894, " 63. TIME OF VOLITION. Such work on fatigue suggests the possibility of an experimental study of the pathological cases of fatigue 35 3V 33 32 31 JO 29 29 27 26 ZS M 23 22 2.1 20 TAPPING BOYS A ND GIRLS SOYS GIRLS 6 7 o 9 10 U /z 13 /t If 16 /7 Fig. 31. RESULTS OF EXPERIMENTS ON NEW HAVEN SCHOOL CHILDREN. in tapping that appear among telegraphers, violinists, piano players, &c. Might it not also be possible by 132 THE NEW PSYCHOLOGY. preliminary experiments on fatigue to detect and warn would-be students of telegraphy or type -writing, who are in danger of being suddenly incapacitated in their chosen trade ? The seriousness of losing a means of livelihood attained after costly training would justify an attempt to detect the weakness beforehand. According to Dresslar the rapidity of tapping varies with the time of day. The average of six weeks of work gave the following results : at 8 a.m. the time required for making 300 taps was 37.8" ; at 10 a.m., 35. 5 s ; at 12 a.m., 34.6 s ; at 2 p.m., 35.5 s ; at 4 p.m., 33.5 s ; at 6 p.m., 35. I s . It is noticeable that these results corre- sponded to the habits of the previous two years of the person experimented upon ; these years were spent in public school work with a daily programme, beginning at 8 a.m. and closing at 4 p.m., with an hour and a half intermission at noon. The rapidity of alternating volitions has been studied in several particular forms. It has been thought worth while to devise an apparatus for studying the rapidity of a boxer's blows. It consists of a small stiff cushion, against which the fist is struck : an electric contact is made at each blow. The rapidity with which such blows can be struck is a matter of some interest. One curious fact has been noticed : the number of blows per second, for both hands striking in alternation, is only about 30 % greater, instead of twice as great as the number for one hand singly. It seems to be in some way a question of the difficulty of willing two things rapidly in succession. A special form of this problem has been investigated in the case of producing trills, i.e., alternations of two movements on the piano. 1 1 Binet and Courtier, in "Rev. Scientifique"; reported in "Nature" 1895, 1. 11597, from which I quote the account. The account also appears in " L'Annee psychologique," 1895, ii. 201. TIME OF VOLITION. 133 The apparatus consists chiefly of an incliarubber tube, placed under the key-board, united at its extremities to a registering capsule. When the notes of the piano are played, the pressure on the tube causes waves of air to be sent through it into the capsule, whereby a record may be made on the drum as in Fig. 24. The board on which the tube rests is regulated by means of wedges adjusted by a screw, the board being either lowered or raised. When raised it almost reaches the keys of the piano, and in this case registering action takes place ; but if it is lowered, the whole apparatus is disconnected from the key-board. Fig. 32 illustrates trills, and shows Fig. 32. RECORDS OF TRILLING ON THE PIANO : A. BY AN AMATEUR J B. BY A PROFESSIONAL. clearly the equality or inequality of touch ; the records show, too, the amount of irregularity. It has perhaps seemed strange to consider tapping as a mental affair. When we will to press the button once and do so, the single tap was evidently an act of will. We likewise will and execute the second tap, the third, &c. We can repeat the tap faster or slower, regularly or irregularly, strongly or weakly, just as we will to do. There are certain limits that we cannot pass ; we cannot in particular go beyond a certain rapidity, or attain more than a certain regularity. The actual rate is influenced by the amount of work done (space traversed or resistance overcome) ; more than a certain amount of work we cannot do, unless 134 THE NEW PSYCHOLOGY. the conditions are changed, e.g., by excitement. An effort of will represents an expenditure of just so much energy, which in a careful investigation might be calcu- lated. When it is said that with the key in Fig. 23 or Fig. 27 just so many taps were made, it is meant that just so many efforts were put forth to move a weight of so many grammes through a distance of so many milli- metres and back. It seems quite justifiable to assume that the rapidity of tapping represents the rapidity with which the impulses to do the required amount of work are re- peated. I think it unquestionable that the results of distraction, excitement, &c., are due to changes in the process of willing. Possibly, also, the fatigue is to a large extent mental, if not mainly so. Following out the same line of thought, we are driven to the conclusion that successful men of muscle must be men of mind also. Walking, running, rowing, &c., require the rapid repetition of certain muscular acts. The rapidity and regularity attainable depend upon the will. The maximum rate attainable is a fairly constant figure. The constancy of the maximum rate of motion is indicated by the small limits within which the racing records of a given individual vary. Notwithstanding the large number of motions made by a horse in running one mile, a dozen successive race records are not ex- pected to have a gross variation of more than two or three seconds, if the horse, the track, the weather, &c., are each time in about the same conditions. The same holds true of bicycle riders, oarsmen, &C. 1 1 Bryan, as before. CHAPTER VIII. TIME OF REACTION. BY reaction we mean conscious action in response to a signal. Experimental arrangements are made for pro- ducing a signal and recording it simultaneously on the drum, and for recording a movement in response. This can be done readily and accurately by use of a touch-key and the telegraph-key. The touch-key, Fig. 33, is so arranged that at the moment the rubber button at its end touches the skin Fig. 33. TOUCH-KEY. it breaks an electric circuit ; it closes the circuit again instantly, so that the current is ready for interruption by the telegraph-key. This telegraph-key is shown in Fig. 27. The finger is placed on the knob ; the current is sent through back contact. Both keys are placed in the primary circuit of the spark coil just as the pendulum contact was for the 100 fork (Fig. 6). Any movement of either key breaks the circuit and makes a spark ; conse- quently there is one spark on the time-line for the touch and one for the responding movement. The number of thousandths of a second is easily read off. 135 136 THE NEW PSYCHOLOGY. The instructions to the subject are : close your eyes and get ready to press the key instantly at the moment you are touched. The subject knows the movement that is to be made and prepares himself so that the act of will follows without any consideration of what is to be done. It follows at the moment the sensation is strong enough to be noticed. The time marked off between the two sparks thus includes the time required for the sensation to arise, and the time of the voluntary act. With practice and strict attention to the desired conditions, the total time can be reduced to about loof. For accurate work, however, the subject must be absolutely free from disturbance or distraction. This requires that he shall be alone in a perfectly quiet room, and this requirement brings the necessary consequence that the methods of experimenting shall be so modified as to permit such isolation. My experience with the unavoidable noisiness of the quietest rooms at other universities led me to attempt the construction of an isolated room at Yale. I selected a small room in the middle of the building, where, with the exception of a door, the surroundings consisted of solid walls and floors. In this room an interior room of light wood was built. This interior room was supported by four pieces of rubber. The space between the walls of the two rooms, which everywhere exceeded six inches, was filled with sawdust. Around the doorway and the ventilator the sawdust was kept back by canvas. There was thus no solid connection between the exterior and the interior room except through the rubber. Both the outer and the inner room possessed thick doors. The quietness of the isolated room is remarkable. Very loud sounds in the adjacent rooms or overhead can still be heard through the ventilators. Heavy waggons on the street shake the whole building, TIME OF REACTION. 137 and can be felt through the feet but not heard. The main difficulty lies in the method of ventilation. A rotary fan blower in a distant part of the building forces a large volume of air through the three sound- killers. The sound-killer consists of a large box lined with felt, and containing felt diaphragms whereby the air is forced to take a zig-zag path. The sound from the blower cannot well pass through such a tortuous path, where the soft walls prevent reflection. The first sound-killer is close to the blower. From this the air is carried about fifty feet to another sound-killer just above the isolated room. As the air enters into the room it passes down to the floor through the third sound-killer. For high grade work such an isolated room is as necessary in the psychological laboratory as the room of constant temperature in the physical laboratory or the non-shakeable base for the astronomical observatory. As the result of my own experience, I would suggest numerous important changes in any such room that may be constructed in the future. I will not go into details of the reasons, but will sketch briefly the isolated room as it should be. The ideal isolated room should be in the centre of a special small building with nearly unbroken walls. If the building is far back from the street no special isolation by rubber is necessary ; the room will be simply a part of the building. The room should be surrounded in every direction by experiment rooms, and should be separated from them by brick walls covered with tiles. These brick walls should be made practically air-tight. Various openings in these walls would allow experiments and observations from the outside. The blower should be in another building, and should have a large air-shaft and several sound- 138 THE NEW PSYCHOLOGY. killers. The most important improvement is to be made in furnishing the room. Persons entering our room through the heavy double doors for the first time are sometimes very nervous. Of course, as we seldom experiment on any but trained observers who are perfectly at home, this does not usually matter. Yet future work will doubtless cover cases where people enter a laboratory for the first time ; more- over, it is a good principle to make every one at home. Therefore, the room should be furnished and lighted exactly like a comfortable room in the evening. All wires and apparatus should be concealed. The person entering it should suppose it to be only a reception room. He is to believe that he is merely on a visit ; in a quite casual way he can be induced to pick up the key from a table and react to a concealed telephone or to a Geissler ornament. For the study of movements or of expressions a kinetoscopic camera can be con- cealed in some unsuspected place. Chairs, sofas, and rugs can be made to record movements. Proper control of the speed of the blower, or of an exhauster, and of the air supply, will render it possible to produce an atmosphere of any desired density, humidity, and temperature. Among the modifications of apparatus made neces- sary by the complete separation of the subject from the experimental room, we must first notice the means of sending signals to the isolated room and at the same moment producing a spark-record on the drum. This is accomplished by means of the multiple key. The multiple key contains two levers revolving accurately around the same centre. When the key is at rest the lower lever at its rear end keeps two electric circuits closed. As the upper lever is made to descend by pressing the button, its two contacts in front strike the TIME OF REACTION. 139 corresponding two front contacts of the lower lever ; this closes two electric circuits simultaneously. But at the moment this occurs the lower lever is forced to move, whereby the two rear circuits are broken. Thus two circuits are closed and two are broken at exactly the same moment. These combinations are necessary in various experiments. In the following illustration of reaction to a tone we shall need only one of the front, or make, and one of rear, or break, contacts. The other contacts on the key are for breaking or closing circuits Fig. 34. MULTIPLE KEY. just before or after the simultaneous contacts ; we shall need only one of them. To produce a tone in the isolated room a current is sent from a battery through a vibrating fork of the desired pitch, say 500 complete vibrations, then through a make-contact of the multiple key, and from here by wire to a telephone in the isolated room, and back again to the battery. 1 Nothing is heard till the key is pressed down. 1 At Yale the connection is by a switchboard, similar to a telephone switchboard, which receives seven wires from each of eight of the rooms of the laboratory. The arrangement is shown in Fig. 208 of Scripture, " Thinking, Feeling, Doing," 140 THE NEW PSYCHOLOGY. To register the moment of the production of the tone and of the response a current is sent through the spark coil, through one of the closed contacts of the multiple key, then to a reaction-key with closed contact (Figs. 23 or 27), and back to the battery. At the moment the front contact strikes, whereby the tone is produced, the rear contact breaks and makes a spark record. At an instant later the point on the front of the lower lever plunges into a mercury-cup, whereby the spark circuit is closed again, ready for the break of the key in the isolated room. At the moment the subject responds by pressing the reaction-key, a second spark record is made. The distance between the two sparks gives the time in thousandths of a second. A typical experiment would be carried out in the following way : After shutting the doors, the observer takes his place in the easy-chair in the isolated room. Generally he will leave the electric light turned on, as it has been proven that a steady light is at least as favourable to mental action as darkness. 1 The reason probably is that in darkness we notice waves of light (so-called retinal light) rolling over space in front of us. Telephone connection enables the subject to communicate directly with the experimenter in the recording room. The subject takes the reaction-key in his hand, and is ready to respond to the tone from the telephone which lies on the table. The click of a sounder warns him to pay attention. Shortly afterwards he hears the tone. As soon as he hears it, he moves his finger. This is all that concerns him directly. If he knows that for some reason he was inattentive, or if anything 1 Bliss, Investigations in Reaction-Time and Attention, " Stud. Yale Psych. Lab.," 1892-93, i. 18. TIME OF REACTION. 14! else happened to disturb him, he telephones to the experimenter to cross off the record. Meantime, what is happening in the experimental room ? The experimenter starts the fork and drum going. He touches a key that produces the click of the sounder, the " warning," as it is called. About two seconds after this he presses the multiple key, whereby he sends the tone, and at exactly the same moment registers a spark on the drum. Shortly afterward a second spark is registered, coming from the reaction- key. The experiments are repeated at intervals of about fifteen seconds. After the set of experiments is finished the paper is removed from the drum, run through varnish, and dried. The number of whole waves between each pair of sparks is counted and the fractional tenths are estimated. The results give the reaction - times, or " simple " reaction - times, as they are often called, in thousandths of a second. The numbers are placed on a record blank, and the average and the mean variation (p. 47) are calculated. The following is a characteristic record : 0.7* 147 3-3 153 2.7 141 9-3 142 8.3 155 47 158 7-7 155 47 151 0.7 150 0.3 I50-3 4-24 What do these figures, A 150.3"" and mean ? 142 THE NEW PSYCHOLOGY. In the first place, we know the apparatus to be exact to 10- ; therefore both the average and the mean varia- tion are psychological quantities. In the next place, the mean variation of 4.24*7 means that in another set of experiments, under exactly the same circumstances, we can expect the subject to vary around his average of 150.3*7 in a way indicated by his mean variation. This mean variation from ten records is of a size that indicates the writing of the results as 1500- and 40- instead of 150.30" and 4.240; Finally, the question arises : Is the average to be stated to be 1500- when, for the sake of brevity, the mean variation is omitted ? When we say that a line is 150 mm. long, we mean that its length is between 149.5 mm. and 150.5 mm. Likewise to say that the reaction-time is 150* means that it lies between 149.50- and 150.50-. The mean variation shows that this is not true. Therefore, when we omit all mention of the mean variation, we cannot state the time to be 1500-. The time is really uncertain to about 50-, but we are justified in stating it to be 15 s, where ? IQO- = o.oi s . To state the result as 150* without adding the mean variation is to produce an appearance of great accuracy which is really not present. When pro- fessedly scientific laboratory work is published with results reading to the thousandth of a second, while all indication of the mean variation is systematically suppressed, the procedure can hardly be said to be exactly correct. The most important fact concerning the mean vari- ation is its character as a psychological quantity. As we know the apparatus to be practically correct, the quantity MV must be attributed to the subject ; and in just the same way as the reaction-time was treated as a psychological process, so we can consider this mean TIME OF REACTION. 143 variation to be a psychological affair. What is indicated by this mean variation, or index of irregularity, in regard to the mental processes of the subject ? In physics we would say that such a mean variation indicated the average value of various sources of error, that as whole neutralised themselves when the average was taken. In psychology we say that it indicates the average value of various mental influences modifying our individual reaction-times to make them different from the average. These mental influences are, from one point of View, errors ; from another they are residual phenomena await- ing investigation. In explaining to visitors what the reaction-time is, I am generally met with the objection : " But different people differ." There is, in the first place, the vague notion that individual minds are unique and do not conform to any law ; this is readily cleared up by a reference to a statistical investigation. Individuals do differ, but these differences occur according to definite laws, and the mean variation of the separate averages from the final average gives an index of this irregularity. In the second place, such a visitor does not comprehend that the purpose of the psychological laboratory is not ordinarily to collect statistics, but to determine funda- mental laws. No two pieces of wire or anything else were ever exactly alike, but the physical laboratory is able to establish a law of relation between resistance, electro-motive force and intensity of current. No two cases of fever ever ran exactly the same course, yet the general laws governing various fever-diseases are quite capable of determination. No two minds were ever exactly alike, yet all follow the same general laws. Proceeding with the investigation of the laws of reaction-time, we first ask : does the reaction-time differ for the different intensities of the sensation ? Let us try 144 THE NEW PSYCHOLOGY. tones. The intensity of the tone is regulated by the intensity of the current sent through the telephone ; the amount of the current is governed by a resistance-box. The tone can be made of any loudness between unbear- able intensity and silence. As no practicable method is at hand for measuring the intensity we must be content with such degrees as " very loud," " loud," " medium,'.' &c. Experiments with tones of different intensities show no noticeable change in the average reaction- time. 1 Does the time depend on the pitch of the tone ? Experiments made with tones of 500, 250, and 100 complete vibrations gave for one observer 16^ 18^ and 242 respectively. 2 The pitch does change the reaction- time. Experiments by a somewhat different method give the following results for tones and a sharp clicks : Tone = 33 c' = 264 c ii! = 1,056 C iv = 2,II2 Noise. ist Observer 172 I5S 142 132 112 2nd 16 14 13 12 12 3rd 15 14 12 II II The reaction-time decreases as the pitch rises. The supposition that this decrease is due to a constant sensation-time of ten vibrations is contradicted by Martius's results, and the supposition that it is due to a constant sensation-time of three vibrations is contradicted by Slattery's. Tones of high pitch are more energetic, physically, than those of low pitch ; for the same ampli- tude of vibration the amount of work performed by a 1 Marti us, Ucber den Einfluss dcr Intensitiit der Rcizc aitf die Rc- actionszeit der Ktiinge, "Phil. Stud.," 1891, vii. 469. 2 Slattery, On the Relation of the Reaction-Time to Variations in Intensity and Pitch of the Stimulus, " Stud. Yale Psych. Lab.," 1893, i.7i. 3 Martins, as before. TIME OF REACTION. 145 vibrating particle increases as the square of the number of vibrations. It might be supposed that the decrease in time for the high tones corresponded to an increase in the energy of the tone. This supposition is contra- dicted by the fact that, with a tone of constant pitch, the reaction-time does not decrease as the energy increases. The dependence of reaction-time on pitch thus stands as an unexplained fact. Let us now turn to sight. When the stimulus is to be light, a Geissler tube is placed in the isolated room and is connected with the secondary poles of a spark- coil whose primary circuit is the same as that of the telephone used for the tone. When the key is depressed the tube is illuminated. The colour of the light can be varied by using tubes with different gases. The intensity can be changed by placing pieces of grey glass before the tube, or by allowing the tube to illuminate a white surface placed at various angles. In a series of experi- ments 3 in which the intensity of the light (though not from Geissler tubes) was widely varied, the results were as follows : Intensity . i 7 23 123 315 1,000 * ** Time in 2 34 27 34 23 22 22 21 20 The intensity i was just visible ; the intensities above 1,000 were not numerically determined. The time is longer for weak lights than for strong ones. For electrical stimulation an induction coil with a pair of electrodes can be substituted for the telephone used in reaction to tone. With electrical stimulation the reaction- time decreases steadily with increase of the intensity of 1 Berger, Ucber den Einfluss der Reizstiiike auf die Daitcr chi- fachcr psycliiscJicr Vorgfliigc, " Philos. Stud.," 1886, iii. 63. II 146 THE NEW PSYCHOLOGY. the stimulus. 1 The relation to the frequency of the shock has not been determined. For the sense of touch the touch-key (Fig 33) is used. It requires a person in the room with the observer ; the multiple key is not used. The point of hard rubber is touched to the observer's skin. This breaks the electric circuit for an instant and makes -a spark on the drum. To experiment with warmth and coolness, a metal ball is screwed on in place of the rubber tip and is heated or cooled as desired. Reaction to touch is quickest, coolness the next, and warmth the last. Fairly specimen figures would be : touch ii^, coolness 12*2, warmth 132. Increase in the intensity of the temperature decreases the reaction-time. With a very hot or cold stimulus the reaction becomes very irregular owing to the sensa- tion of pain which follows that of temperature. In the foregoing experiments the stimulus has been varied and the results noted. Let us now vary the act used in responding. The first point to consider is the particular act per- formed. With a stimulus applied to the arm the reaction time for the foot is 42 to 52 longer than that for the hand. 2 When it applied to the thigh, there is a similar but a much smaller difference of i^. Still another variation is found in producing an extra muscular tension in the finger by having a weight pull against it. Pulleys were so arranged that a weight of i kilo, pulled upward on the reacting finger when the hand was put in position for reacting. The following is a characteristic record for a set of ten experiments on myself : 1 Berger, as before ; Slattery, as before. 2 Dolley and Cattell, Reaction-Times and the Velocity of the Nervous Impulse, " Psychol. Rev.," 1894, i. 159 ; also "Mem. Nat. Acad. Sci., U.S.," 1896, vii. 393- TIME OF REACTION. 147 A. MV. Reaction to sound, without weight 1720- 300- with 136 16 light, without ,, 152 26 with 128 II Corresponding results were obtained from two other subjects. 1 There is a decided shortening of the time in each case, and a great increase in regularity. These changes were due (as was very evident to the subject himself) to the increased attention which the subject was forced, by the strain on the finger, to pay to the experiment. As the reaction-key was directly beneath the stimulus for sight, the increased attention made the sight reactions unusually short. The length of the reaction-time depends upon the interval between the warning and the stimulus. 2 With intervals of ij s , 3 s , and 6 s the reaction with sensory attention, i.e., paid chiefly to the stimulus, steadily increases in length in a manner illustrated by the figures 262, 28^ and 30^ respectively. For muscular attention, i.e., paid chiefly to the reacting finger, similar but smaller differences exist, e.g., 132, 132^ and 152. When no warning at all is used the sensory reaction is slightly lengthened, e.g., to 302, whereas the muscular reaction is greatly lengthened, e,g., to i&s. When the subject is taken quite unprepared for reaction, the time runs up to, say, 382. When reactions are repeated rapidly in succession the problem becomes somewhat different from that of single reactions. In the latter the effort is made to keep the person's " attention " at the same level by means of a preliminary signal shortly before the experiment, 1 Details will appear in " Stud. Yale Psych. Lab.," 1896, iv. 2 Dwelshauvers, UntcrsiicJnnigcn zur Mcchanik dcr activcn Anf- nici'ksaiukcit, " Phil. Stud.," 1891, vi. 217. 148 THE NEW PSYCHOLOGY. and by ten seconds of rest between experiments. When, however, the reaction-stimulus occurs regularly at an interval of 2 s , each experiment serves as a pre- liminary signal for the following one. The subject, who knows about when the stimulus is coming, is to react to Fig. 35- A SERIES OF REACTIONS. it as quickly as possible after he has received it. This involves an effort to shorten the time of sensation, and the time of action. To perform the experiment a drum of the kind shown in Fig. 12, rotating regularly once in 2 s , is arranged to break an electric circuit at every revolution in such a TIME OF REACTION. 149 manner that a sound (or light, or electric shock) is produced at every revolution. The subject reacts with a break telegraph-key and produces a dot on the drum. In Fig. 35 the first dot on each line indicates the moment of the stimulus ; the other indicates the reaction. At first the reactions are quite irregular in length ; then they become quicker and more regular, showing practice ; finally, they become longer and very irregular, showing fatigue. Experiments made after this manner 1 show charac- teristic differences among people ; for example, a physician and a student gave records similar to that of Fig. 36. PISTOL KEY. Fig. 35, while a child of seven years gave a record with great irregularities, but with very little general lengthening of time clue to fatigue. Education in rapidity of reaction is obtained from various sports and games requiring quickness. Sprint racing is one of the most efficacious methods. 2 For investigating the changes in reaction-time due to 1 Patrizi, La graphique psychotnetrique de V attention, "Archives italiennes de biologic," 1894, xxii. 187. 2 Scripture, Reaction-Time and Time-Memory in Gymnastic Work, "Ninth Ann. Meeting Am. Assoc. Phys. Ed.," 1894, 44. 150 THE NEW PSYCHOLOGY. practice in starting to run, I have devised a special pistol contact (Fig. 36). I The blast from the pistol- barrel a moves the fan / so that contact is broken at d for an instant, the lever being drawn back by a spring. Only a few experiments have been made with the apparatus. These, however, have brought to notice these two facts : i. The reaction-time is about one-third shorter for short- distance runners, who are trained to start quickly, than for long-distance runners. 2. The reaction-time for movements of the whole body is longer than for movements of a single member. A remarkable illustration of the presence of reaction- time at a runner's start is to be seen in an instantaneous photograph reproduced in Fig. 37. The picture was evidently caught after the report of the pistol and before the start of the runners. Let us, in conclusion, consider what a reaction- time means from a psychological and* from a physiological standpoint. Suppose we are sitting in the isolated room, waiting to react to the flash of a Geissler tube ; the flash appears, and we execute a movement of the finger. We feel that time was occupied by the appearance of the flash and by the action. We can divide the whole interval of time into two parts, the time for sensation and the time for action ; the relative proportions and the amount of time as recorded on the drum are unknown to us. Our apparatus states that the interval between the stimulus and the movement of the finger consisted of so many hundredths or thousandths of a second. But how much of the reaction-time is psychological, how much physiological ? To the observer, as we have 1 Scripture, as before ; also Sonic New Apparatus, "Stud. Yale Psych. Lab.," 1895, iii. 107. TIME OF REACTION. i5i ^ ^ P If i II 152 THE NEW PSYCHOLOGY. seen, the whole experiment consists in the appearance of the light and the will to act with the lingers. The various processes of recognition, choice, &c., have been practically eliminated by practice and warning signals. On the drum in the distant room he afterward sees a wavy line with two dots on it. By careful tests it can be proved that the Geissler tube flashed almost at the same instant as the spark made the dot. We can, therefore, assume that the production of the hrst dot and the production of the flash are two practically simultaneous occurrences in our visual field. The same holds good for the movement of the finger and the second dot. The number of waves between the two thus gives the time between the occurrence of the flash and the execution of the movement. Now, I do not say that we "see" the flash the moment the dot is made. For an object to be seen it must have a certain strength and clearness ; we must be more or less fully conscious of it. This takes time. We do not really see the flash till it has been some time (of course, a very minute interval) in our visual field ready to be seen. This is the latent time of vision ; it does not exceed io, L< , R >, L ^>. The difference was then found between each line for the left hand, and the preceding one for the right hand. With opposite movements the line with the left hand was made on the average 8 mm. too short, while with identical move- ments it was made 12 mm. too short. This was on a line averaging 50 mm. The average uncertainty was the same in both cases, namely, 5 mm. These results were obtained for a single interval, and for a single person, namely, myself ; it is desirable to know if these peculiarities would be found with other intervals and persons. Wolfe x has made a series of experiments on memory for tones according to the statistical method. A tone was produced on a reed instrument that maintained it for one second ; after an interval of / seconds either the same tone or one differing from it by a definite amount was likewise produced for one second. The observer was required to say whether the second tone was the same as the first or not. The number of times that he answered correctly depended on the length of the interval t. For example when t = I s an observer would answer correctly 93 times out of 100 ; when t = 2 s , 92 times ; when / = 3 S , 89 times, &c. The influence of the elapsed time thus shows itself in a decreased percentage of correct answers. By mere chance the answer would be correct in fifty per cent, of the experiments ; any increase above this amount is due to some effect from the former tone lasting over the interval of time. This we ordinarily say is the effect of the person's memory of the tone ; 1 Wolfe, Untersuchnngcn fiber das Tongcdtichtniss, "Phil. Stud.," 1886, iii. 534. 192 THE NEW PSYCHOLOGY. more properly we should say this is the memory of the tone. Experiments on nine subjects with intervals from I s to 6o s give results as shown in Fig. 45. SOO 700 600 900 800 700 13*710 if 20 zr 30 no fc 60 Fig. 45. CURVES FOR TONE MEMORY. The law of memory for tones under these circum- stances has been stated by Wolfe to be -. = j t + c TIME INFLUENCE. 193 where r indicates the number of correct answers, / the number of wrong answers, t the interval of time elapsed and k and c two constants depending upon the particular individual and the circumstances of the experiment. For example, if for the subject L we put k 12, c = 5.2, and if for W we put k = 4.43, c = o we get series of values that correspond well to the actual results so 40 30 20 10 20 30 Fig. 46. LAW OF REPETITION IN MEMORISING. obtained. These series, of values are indicated by the dotted lines in Fig. 45 ; the agreement with the actual results is fairly satisfactory. We can thus accept the above formula as the law for tone memory. Experiments with nonsense syllables, as already men- tioned in Chap. II., have been made by Ebbinghaus. 1 A number of syllables, about 2,300, w^ere formed with a Ebbinghaus, " Ueber d. Gediichtniss," Leipzig, 1885 194 THE NEW PSYCHOLOGY. vowel between two consonants, e.g., dob, fik, &c. These were mixed together, and were picked up just as they happened to come. A certain number of these syllables formed a series which w r as learned by repeating them ; the series was considered to be learned when it could be given without mistake or hesitation from beginning to end at a regular rate. The first problem settled was the dependence of the number of repetitions on the length of the series. The results are shown in Fig. 46. For series up to seven syllables only one repetition is necessary ; after that the amount of work increases with great rapidity for each additional syllable. The next problem was concerned with the depend- ence of the amount remembered on the number of repetitions of the original series. Each series consisted of sixteen syllables, and was repeated 8, 16, ..., 64 times. After 24 hours the series was repeated until learned again. The rate at which the syllables were repeated was 150 to the minute. The results are shown in the following table : After x repetitions the series was earned 24 hours later in y seconds. Amount saved in seconds. Saving per syllable for each repetition. X = y = o 1270 8 1167 103 12.9 16 1078 192 12.0 24 975 295 12.3 32 863 407 12.7 42 697 573 13-6 53 585 685 12.9 64 454 816 12.8 Thus when such a series had not been seen before it. took i,27o s to learn them. When they had been repeated 8 times it took 1,167' * relearn them, &c. A TIME INFLUENCE. 195 repetition of 8 times in the first place saved 103" in relearning them, or I2.cf per syllable. That is, under these particular conditions the memory effect increased proportionally to the number of repetitions. The third problem related to the dependence of the memory effect on the length of the elapsed interval. A series of thirteen syllables was repeated until it could be given without mistake. It was then laid aside for a definite time /, at the end of which it was again learned. Any memory effect would show itself in a decrease of the necessary number of repetitions in the second case as compared with the first one. The results for various intervals were as follows : After x hours so much was still retained that in relearning there was a saving of y per cent, of the original labour. The amount forgotten was equivalent to v per cent, of the original labour. X = y= Y = 0-33 58.2 41.8 I. 44.2 55-8 8.8 35-8 64.2 24. 33-7 66.3 48. 27.8 72.2 6 x 24 254 74.6 31 x 24 21. 1 78-9 It is evident that the rate at which we forget things is at first very rapid until we finally come down to a small residuum that persists with great constancy. Ebbinghaus's results agree well with the formula ^ = (TogfTc wnere ^ denotes the amount retained and v the amount lost, while k and c are two constants depend- ing upon peculiarities of the observer and the condi- tions of the experiments. In both Ebbinghaus's and Wolfe's experiments we find a peculiar logarithmic form for the law of memory. 196 THE NEW PSYCHOLOGY. A final problem is that of the repeated learning of the syllables. At intervals of just one day after the first learning the series was repeated until on each occasion it was relearned. For example, a series of twelve syllables required 16.5 repetitions for the first learning ; 24 hours afterwards it required 1 1 repetitions to relearn it ; 24 hours after this relearning it required only 7.5 repetitions, &c. The results of Ebbinghaus's experi- ments were as follows : Number of syllables in a series. Number of repetitions necessary for relearning the series in successive days . I. II. III. IV. V. VI. 12 16.5 ii 7-5 5 3 2-5 24 44 22.5 12.5 7-5 4-5 3-5 36 55 23 ii 7-5 4-5 3-5 I stanza of " Don Juan." 7-75 3-75 1-75 0-5 o o Miiller and Schumann, 1 with more elaborate methods, extended the investigation of memory to cover various problems, such as the influence of rhythm, the available quantity of attention-energy, the influence of practice, &c. For example, with three subjects (Germans) a series of syllables was learned more quickly if repeated in trochee ^ than if repeated in iambus ^ . This may arise from the general cha- racter of the German language, which is trochaic. Again, the second syllable of a trochaic or iambic measure has a tendency to recall the first syllable of the 1 Miiller and Schumann, Experimentelle Bcitriige z, Untersnchitng dcs Gedachtnisses, "Zt. f. Pysch. u. Phys. d. Sinn.," 1893, vi. 18, 257. TIME INFLUENCE. 197 same measure rather than that of the following measure. Series learned in trochee require more work if relearned in iambic, and likewise the reverse. I must here close the consideration of time-influence. Concerning one of its laws, U = F (t), we can conclude that it has a logarithmic form. Concerning the other law, C=f (t), and concerning the various modifications of both laws under different circumstances, we are still practically in ignorance. CHAPTER XIII. SUCCESSION IN TIME. THE investigations on time-influence, or memory, lead us to the problem of what causes an idea to be reproduced. Suppose, for example, at a certain moment t 1 see a tulip and at a later moment U a memory of this tulip occurs to me ; what produced it in the second case ? There are three factors to be considered (i) the original idea ; (2) the state of mind immediately preceding the moment ti ; (3) the past history of the individual. The first factor has remained almost entirely unin- vestigated experimentally. The only question that has been formulated concerns the relative superiority of visual, auditory, or motor memories, or their combi- nations. The experiments have been carried out by methods that hardly satisfy the demands of the pro- blem, and with different observers have led to con- flicting and irregular results. The effort has been made to investigate the effects of vividness, repetition, &c., of the original idea. 1 The results confirm our general experience that memory is aided by vividness, repeti- tion, recentness, &c. The various other questions concerning the qualities of the original idea can be answered only in terms of ordinary experience, and 1 Calkins, Association, "Psych. Rev.," 1896; Monograph Supple- ment, No. 2. 198 SUCCESSION IN TIME. 199 remain uninvestigated scientifically, although a con- siderable amount of practical knowledge has been accumulated for educational purposes. 1 The second factor namely, the state of mind imme- diately preceding the revival of the idea has received considerable attention under the name of association of ideas. In the first place, how are ideas associated ; or, in other words, what is the relation between an idea and the one that is brought forward in connection with it ? The answer cannot at present go beyond the qualitative stage. A convenient method of presenting visual ideas is to have them placed as objects, pictures, or words in front of a photographic lens, with a shutter having a pneumatic release. The subject is placed so that he has before him a plate of ground glass like the focusing plate of a camera. When the shutter is released, he sees in front of him the object on the ground glass. Auditory ideas are most conveniently presented by leaving the subject in darkness and simply speaking the word or producing the sound. Objects can be touched, tasted, &c., in a similar fashion. An investigation 2 was carried out by these methods with the purpose of determining, without prejudice from or relation to the Aristotelian "laws of associa- tion," just what really took place in an association of ideas. In the first place, it was noticed that the primary, or inducing, idea generally underwent some transformation before an association took place. One change con- 1 A brief consideration of some methods of improving memory will be found in Scripture, "Thinking, Feeling, Doing," 247, Meadville, 1895. 2 Scripture, Uebcr den associativen Verlanf der Vorstcllnngcn, Diss., Leipzig, 1891 ; also in "Phil. Stud.," 1891, vii. 50. 200 THE NEW PSYCHOLOGY. sisted in the loss of some part. For example, the word FLUCH was followed by, or perhaps \ve should say was changed to, the word FLUSH. This change can be indicated by the scheme : a, a, a 3 a 2 a 3 a 3 a, b In another case the inducing idea was a feeling of roughness derived by touching the lingers to some blotting paper. This was followed by the touch-idea, rough paper, and this in turn by the visual-idea, brown paper. This would be represented by the following scheme a (rough) a b b (paper) ' c (brown) In other cases the inducing idea apparently underwent no change, and the induced idea consisted in something added to it. For example, BIG becomes BIGGER, or a sound became the sound of a certain bell. In still other cases the inducing idea entirely disappeared. For example, the word STAND was followed by a visual memory of the theatre, because, as the subject ex- plained, he generally stands at the theatre. Examples were found of all intermediate stages. The next fact noticed in the investigation was a differ- ence between two methods in which the induced idea was connected with the inducing idea. The two may be connected directly or indirectly by means of a third idea. For example, a taste of lemon-juice is followed by the word "lemon " ; this would be a direct connec- tion. A case where the colour, red, is followed by a SUCCESSION IN TIME. 2OI somewhat indefinite memory of strontium light, and this in turn by a scene from an opera, is a series of direct connections where the middle idea is not fully clear. From this it is but a succession of steps through continually more indefinite and unnoticed ideas to those that are completely unconscious. This is what is meant by indirect connection, or mediate association. Sir Wm. Hamilton x first called attention to such associations : "Suppose, for instance, that A, B, C, are three thoughts that A and C cannot immediately suggest each other, but that each is associated with B, so that A will naturally suggest B, and B naturally suggest C. Now it may happen that we are conscious of A, and immediately thereafter of C. How is the anomaly to be explained ? It can only be explained on the principle of latent modifications. A suggests C, not immediately, but through B ; but as B ... does not rise into con- sciousness, we are apt to consider it as non-existent . . . Thinking of Ben Lomond, this thought was immediately followed by the thought of the Prussian system of education. Now, conceivable connection between these two ideas there was none. A little reflection, how- ever, explained the anomaly. On my last visit to the mountain, I had met upon its summit a German gentle- man, and though I had no consciousness of the inter- mediate and unawakened links between Ben Lomond and the Prussian schools, they were undoubtedly there the German Germany Prussia and, these media being admitted, the connection between the extremes was manifest." The question of the possibility of mediate association arose during my experiments on the course of ideas, 1 Hamilton, "Lectures on Metaphysics," lect. xviii., vol. i. 352, Lond. and Edin., 1859. 202 THE NEW PSYCHOLOGY. and, not knowing of Hamilton's observation, I made an attempt to answer it. In order to investigate the subject experimentally, the following method was devised. 1 On one card there was a German word and some Japanese characters. On another card there was a strange word (Japanese, in Roman letters), with the same characters. A series of cards, comprising half of each kind, was shown in irregular order. For example, in one experiment the following series (the Japanese characters being re- presented here by Greek letters) was shown in the order here given : (i) HANA a /3, (2) HITO y g, (3) IUKU C , (4) KURU rj0, (5) MENSCH T g, (6) GEHEN C , (7) KOMMEN ?/ 0, (8) BLUME /3. The subject \vas asked to state if he had noticed any associations between the first four words and the second four ; he had not. Thereupon the words alone without the characters were shown him, with the request to state the first thing that entered his mind after each. The results were as follows : (i) HITO MENSCH, (2) KURU KOMMEN, (3) HANA ? (4) IUKU GEGEN, (5) KOMMEN- IUKU, (6) GEHEN -? (7) MENSCH HITO, (8) BLUME- HANA. At the end the subject declared that all the associa- tions were involuntary, that he could give no reason for the associations, and that the Japanese characters had not occurred to him at all. Several of these associations were, nevertheless, correct ; it seems probable that they were brought about by the influence of the Japanese characters which, nevertheless, had not entered into consciousness. This probability is increased by other experiments in which the word-association was cor- 1 Scripture, Ucbcr d. assoc. Verl. d. Vorst., "Phil. Stud.," 1891, vii. 81. SUCCESSION IN TIME. 203 rectly made and was followed by the occurrence of the characters. In still other cases the association was correctly formed without thought of the characters, whereas the subject could reproduce them when asked. Finally, the characters themselves were found to be in all stages of indefiniteness and forgetfulness, even in correct associations. It is to be remembered that all experiments were rejected in which any associations were made between the two parts of the series while they were being shown. 1 As this was the first attempt to investigate mediate association by means of experiment, the method was necessarily very crude ; more striking results are to be looked for whenever a better form of experiment can be devised. The problem has been made the subject of further investigation by Aschaffenburg. 2 In his experiments on the association of ideas, a number of cases occurred in which the connection between the two ideas was intelligible only on the supposition of an intermediate idea. In the greatest number of cases this intermediate idea appears to have been a sound-association with the inducing idea, while the relation of the induced idea to the intermediate one was of any kind. The following cases are some of many that occurred where there was absolutely no relation between the two associations ; the supposed intermediate idea, which makes the association 1 Several other investigators have failed to find cases of mediate association : Munsterberg, " Beitrage z. exper. Psychol.," iv. i ; Howe, "Am. Jour. Psych.," 1894, vi. 239; Smith, "Zur Frage von der mittelbaren Assoc.," Diss., Leipzig, 1894. 2 Aschaffenburg, " Experimented Studien iiber Associationen," I. Theil, Leipzig, 1895. See also Thomas, Ein wcitcres Beispiel von Assoziation dnrch cine Geruchempfindiing, "Zt. f. Psych, u. Phys. d. Sinn.," 1895, xii. 60. 204 THE NEW PSYCHOLOGY. clear is placed below (Aschaffenburg's examples are, of course, in the German language). Allmacht mater alma Leibarzt Prophet Professor Fuchs Hund Jagd hunt Flachs weich Wachs Nelke Microskop Nelkenol Hochmuth ArcheNoah wegen Hochmuth Siindfluth Similar examples in English would be : pride Niagara pride goeth before a fall Caffir breakfast coffee flax candle \ / wax The intermediate idea in most cases did not remain completely unconscious, but appeared as a following SUCCESSION IN TIME. 205 association. To illustrate by a personal experience : On one occasion, to the word "shoe" I associated the phrase "baby's shoes," and immediately there- after I realised a dim idea which I had felt to be the cause of the association, namely, a kindergarten scene in which the phrase of a song " baby's shoes " stood out most prominently. There are some further investigations that have bearings on the fact of mediate association. It has been experimentally proved x that an idea can be brought forward by an association with something of which the subject is not conscious. Cards were prepared which contained a picture in the middle, and a small letter or character in one corner. A series of four or five such cards was flashed in succession on the ground glass of the apparatus described above. The time of exposure was made so short that, at the most, the subject was able to recognise only the picture without the small letter. Thereafter the small characters were exhibited alone, and the subject had to state which of the pictures first occurred to him. The following is a specimen series, the pictures being indicated by words. Negro. C. The results on one occasion were I cat, : : flag, A shield, C negro, F ?. Upon being questioned, the observer stated that he had not recognised any of the characters in the original series j he consequently had no reason to 1 Scripture, Ueber d. assoc. Verl. d. Voi'st., "Phil. Stud.," 1891, vii. 136 ; see also p. 391. 206 THE NEW PSYCHOLOGY. give for his associations. In some cases the sub- ject would feel that a certain picture belonged to a certain letter, although he had not seen the letter before, as far as his knowledge went. From a number of experiments of this kind, I feel justified in drawing the conclusion that an idea which has not entered into the subject's full consciousness can be associated to an idea in consciousness, and can serve to reproduce it on a future occasion. The completion of the experiment not yet attempted would lie in exposing the character alone for too brief a time to be seen, and noting whether it then would be able to reproduce the picture to which it was associated. A case of such association through unnoticed ideas is reported by Jerusalem. 1 A forgotten scene of three years past was suddenly remembered, apparently without the slightest cause. After persistent search the connection was found in the presence of an unnoticed odour from a flower, with which the subject had first made acquaintance on the occasion of the scene. Wundt 2 points out that the inducing idea must have been in consciousness, although not noticed or perceived. Both Aschaffenburg and I have found these inter- mediate ideas in all degrees of consciousness, from full consciousness, in which the succession appears as a series of three ideas, down to complete unconsciousness, where the idea is completely forgotten, or is not even recognised when shown. Of interest in this connection are some experiments that show the influence of forgotten associations. 1 Jerusalem, Ein Bdspicl von Association dnrch iiubcwitsste Mittelglieder, "Phil. Stud.," 1894, x. 323. 2 Wundt, Sind die Mittelglieder einer mittclbarcn Association bewnsst oder nnbcwusstf "Phil. Stud.," 1894, x. 326. SUCCESSION IN TIME. 2O/ Kraepelin l used on seventeen successive clays the same series of inducing ideas, and measured the association- time. This time decreased during the first few clays, and then remained at a constant level of about one half the original time. After an interval of one and three-quarter years the same ideas were used among others in measurements of association-time ; for these ideas the association-time was much shorter than for the others, although the earlier associations had been forgotten. In conclusion, we can say that the fact of the existence of mediate association can be considered as proven, although these associations do not occur oftener than according to Aschaffenburg about four times out of a hundred. Aschaffenburg has also found that the average association-time for these cases is longer than for ordinary associations. Turning to the third factor of association, namely, the past experience of the individual, we find the experi- mental data to be extremely limited. Galton 2 counted the number of associations derived originally from child- hood and early youth, from manhood, and from the immediate past. In his particular case most of them were derived from the period of manhood, and least of them from the immediate past. On several occasions groups of students have been asked to write down a number of words as rapidly as possible. Various results have been obtained. On one occasion the women were found to use proportionately more words referring to wearing apparel, furnishings, foods, &c., whereas the 1 Kraepelin, Ueber den Einflnss dcr Uebitug anf die Dauer von Associations, "St. Petersburg, med. Wochenschrift," 1889, No. I (cited from Aschaffenburg). 2 Galton, Psychometric Experiments, "Nineteenth Century," 1879; " Brain," 1879, ii. 149 ; and " Inquiries into Human Faculty," 185. 208 THE NEW PSYCHOLOGY. men most frequently wrote words referring to the animal kingdom, verbs, implements, &c. On another occasion it was found that the women most frequently used abstract terms, adjectives, words referring to the animal kingdom, to educational matters, &c. x It cannot be said that definite conclusions have been reached by these tests. Beyond this, our knowledge ends with commonplaces, such as : persons will most frequently associate ideas from their particular circles of interest, familiar ideas will occur more frequently than unfamiliar ones, &c. In conclusion, we may say that the problem of the association of ideas has not been solved. The old " laws of association " by similarity, contrast, contiguity in space, and succession in time, are mere schemes for classifying associations. The real law of association which shall express the probability for the recall of a certain idea as dependent on its original intensity, on the past life of the individual, and on the present cir- cumstances, has never been found. 1 Nevers, Dr. Jastrow on Community of Ideas of Men and Women, " Psycho]. Rev.," 1895, ii. 363. PART III. ENERGY. CHAPTER XIV. STANDARDS OF ENERGY, SUPPOSE we are about to grind the coffee for breakfast. In the first place, we test the empty mill by a few turns of the crank ; the effort was hardly worth noticing. Putting some coffee in the mill we proceed to the grinding. Considerable effort is required ; if kept up long we become fatigued. The result of the effort is that a number of ounces of coffee have been changed from beans to particles ; we have done some work. If we turn the mill rapidly we feel that we are making more exertion ; but we are rewarded by the extra amount of coffee ground per minute. Both the effort, or work required, and the result, or the work accom- plished, are greater. If we turn the mill slowly the effort is less, and the result is smaller. If we adjust the mill to grind coarsely, an ounce of coffee goes through the mill with less effort than if we had adjusted the mill to grind finely. It takes less work to grind one ounce coarsely than to grind one ounce finely. To regrind the coarse coffee into finer coffee we must perform just about enough additional 15 209 210 THE NEW PSYCHOLOGY. work to make the total of the two grinclings from bean to coarse and coarse to fine equal to one grinding from bean to fine. Fine coffee evidently represented more work than coarse coffee. To obtain ground coffee from the bean we must work for it. The ability to do this work is called energy. Suppose that we grind coffee during the time of one minute. If we can put forth a very strong effort we can grind a great deal more than if we can make only a weak effort. The amount of work done depends on the intensity of our ability to do the work. One of the factors of energy is its intensity. Take the case of a store where the coffee is ground by machine power. We will suppose that the machine can grind s kilos, of coffee per minute to a certain grade of fineness. The amount of coffee-grinding energy in our store is s kilos, per minute. If a second machine is placed in the store the amount of available energy is 2s kilos, per minute. If the store can accommodate r machines, the amount is r.s kilos, per minute. The number of kilos, s for each machine has remained the same ; the intensity-factor of the units of coffee-grinding energy has remained constant ; but the amount of energy depended also on the capacity of the store to hold these units of intensity. Energy thus has two factors, its intensity and its capacity. 1 In general E ci where E is the amount of energy, c the capacity for energy in a given case, and i the intensity of the energy per unit of capacity. While we are grinding coffee we are producing work, but as time passes we feel fatigued, till finally we can work no longer. We have performed a certain amount of work. Our ability to perform this amount of work 1 Gibbs, On the Equilibrium of Hetcreogeneous Substances, "Trans. Conn. Acad.," 1875, iii. 108, 343. STANDARDS OF ENERGY. 211 was, before starting, the amount of energy we possessed. As we performed more and more of the work, the ability for work, or the amount of energy, left became less. In the following chapters we shall especially consider the intensity-factor, this being what is meant by the usual expressions : intensity of effort, intensity of sensa- tion, &c. The capacity-factor has been subjected to little investigation. Energy is known to us under various forms, of which the most prominent are energy of movement, energy of space, energy of warmth, energy of light, &c. Energy passes from one form to another. Suppose a ball to be thrown against a wall. There was- originally mental energy in the form of effort, then energy of movement in the arm, then energy of movement in the flying ball, and finally energy of warmth in the surface struck by the ball. The amount of energy in any case is measured by the quantity of work that can be per- formed. The work done may lie in changing the position of an object, in producing heat, in electricity, in chemical combination, &c. The end of the process in any case is a capacity for more work. If an object is raised upward by work, its position,is really an ability for more work to be done by falling. If heat is pro- duced, this very heat can do work in its turn. Energy in a closed system can, according to modern theories, never be lost. If it performs work, the result is the production of an equal quantity of energy of the same or of a different kind. Among the different kinds of energy the form to which we try to reduce all others is mechanical energy. We therefore need a standard of mechanical energy. With the maximum energy we are capable of, let us start various balls in succession rolling along the bowling- alley. Some balls will go slowlv>^fi^^hw If the 212 THE NEW PSYCHOLOGY. balls are all of the same material, the big ones will go slowly and the little ones swiftly. If they are of different materials, the leaden ones will go more slowly than the wooden ones. Since the same quantity of energy was put into each, there must be a relation between the swiftness of movement and the kind of ball. The swiftness of the movement can be regarded as the intensity of the energy present in the moving ball. If with the same total energy there is a difference between the different balls, the balls must have different capacities for energy. This capacity of an object for energy is termed its mass. Leaden balls consume more energy than wooden balls of the same size, and their mass is said to be greater. As the standard of mass the kilogramme des Archives is assumed, and a scale is formed from its multiples or sub-multiples. The unit of mass for scientific work is the thousandth part of a kilo., or a gramme. It is, perhaps, hardly needful to call attention to the fact that by " mass " we mean no reference to matter. As Ostwald puts it : " Since the factors of energy, which are proportional to one another, such as mass, weight, volume, capacity for heat, and capacity for chemical energy, always appear bound together at some point in space, we have adopted the habit of considering them all as contained in a bearer or vessel of energy to which we give the name ' matter.' In reality we experience nothing of this so-called matter but the energy-factors mentioned. When we note that these always appeal- without separation in space, we have given the total result which the hypothesis presents to us of a bearer of energy different from the energy itself. It seems superfluous to set up a special hypothesis for so simple a fact ; it is also not to be denied that it has worked as a great hindrance to the formation of clear concepts concerning the character of energy. ' Matter ' is thus STANDARDS OF ENERGY. 213 nothing but a sum of energy-factors not separated in space. Those factors of energy that are proportional to one another and to mass, we are accustomed to name the fundamental properties of matter, whereby we give preference to the mechanical ones (mass, weight, ' im- penetrability,' or volume), although others, e.g. t the susceptibility to chemical changes, are no less properties of all matter than the others. The other factors of energy that are not necessarily proportional to the former, such as velocity, temperature, electric potential, &c., we are accustomed to name temporary attributes or conditions of matter." x We can therefore dismiss at once all notions of bodies except as aggregates of energy. Is the standard of energy a physical or a psychological one ? Just as in the case of time, the establishment of standards of energy is made on the basis of our mental experience. By an effort, by the exertion of force, we push and pull objects about ; we thus derive our notions of bodies as exerting forces on one another. In lifting a weight we feel the force of gravity ; in stopping a flying ball we feel the work of resistance. Modern mechanics defines force in terms of mass and acceleration, i.e., the movement of a given mass through a given distance in a given time. In this way we regard it only as an unknown factor related to motion ; but this abstraction does not mean anything to us mentally till we imagine some muscular force behind it. The standard of energy is thus both a physical and a psychological one. It is physical because it is ultimately established by instrumental means ; it is psychological because no step of the process goes outside of our experience. 1 Ostwald, Studien zur Energetik, "Zeitschr. f. phys. Chemie," 1892, x. 375. 214 THE NEW PSYCHOLOGY. The force of gravity is the factor that manifests itself in the acceleration of a falling body. When holding a ball in the hand, we counteract the force of gravity by a muscular exertion. If we let the ball fall, it falls at an accelerated speed. The acceleration of the ball is taken as the measure of the force of gravity ; it can also be used, with proper regard to the weight of the arm, &c., as the measure of the muscular exertion. Proceeding just as in the case of time, we improve our methods of testing and comparing falling bodies by introducing other senses, apparatus, &c., till by careful elimination of sources of variation we come to a result that gives the maximum of agreement for the measure- ment of force. The generally adopted unit is the force which, acting upon a gramme for one second, produces a velocity of one centimetre per second. In mechanics the unit of mass and the units of time and space are used as the fundamental units ; the unit of energy is treated as a derived unit. The unit of mechanical energy is the erg, or the amount of work done by a unit force acting through a centimetre ; or, it is the amount of energy contained in a body of i g. moving through a distance of icm. in I s . It is the amount of work which would be required to generate the motion of the body, or is the amount of work which the body would perform if stopped. Practically, the difference between using time, space, and mass, and using time, space, and energy as funda- mental units is of minor importance ; theoretically, however, any intelligible treatment of mental life must start from energy as a prime factor, CHAPTER XV. ENERGY OF VOLUNTARY ACTION. WHEN we press the thumb and index finger on the dyna- mometer (Fig. 4), we are more or less distinctly conscious of the intensity with which it is done. We can at any rate be fully conscious of the energy with which we intended it to be done ; we can intend to make two suc- cessive pressures alike or different ; we can intend to make one of them twice or three times as energetic as the other. The first problem in dynamo metry is to investigate our scale of voluntary action. We will suppose for the present that the marks on the scale of the dynamo- meter are in millimetres or any other arbitrary units. You have the dynamometer between your thumb and finger (eyes closed), and I tell you to produce a momentary light pressure of any strength you desire. You do so, and I privately record the result. Now I tell you to produce a pressure twice as strong. You do so to the best of your ability. I again record the result. Likewise we obtain pressures three, four, &c., times as strong as the first. Here we have, in the first place, a definite intention in each case to produce a pressure and a definite resulting pressure recorded in arbitrary units. The definite intention we can call by the usual name, volition, For psychological purposes we do not need to inquire into the physical and anatomical processes underlying 215 2l6 THE NEW PSYCHOLOGY. the execution of the volition. We may be totally ignorant of the laws of elasticity for the dynamometer- rods, but we know by experiment that the application of standard weights to the rubber button of the dyna- mometer produces certain deflections, and thus we get a scale of weights. We may be quite in doubt as to the parts played by muscular sensitiveness, the skin, and the joints in arousing the peripheral nerves ; we are abso- lutely in ignorance concerning the further processes in the nervous system ; and even if we did know all about them, it is very doubtful if the knowledge would in the least affect our volitions and their results. Consequently, in the present investigation, we are concerned only with the .deflections of the dynamometer in response to volitions of different intensity and with the deflections in response to weights placed upon it. By means of these latter deflections we establish a standard scale for voluntary energy. In order to establish a standard scale of voluntary energy we must proceed, in the manner previously ex- plained, to apply the rule of i + i = 2. A volition of any desired energy is produced and the result is recorded on any convenient form of scale, let us say an angle- scale of a dynamometer. Then, as we know metal weights to be more constant than our volitional efforts, we obtain a weight that produces the same angular deflec- tion. Then we take two such weights and apply them to the dynamometer, then three, &c., with the result that the angle-scale can be changed to a weight-scale. This weight-scale is then adopted as the standard. With this standard we then compare our particular scale of volition-energy, The graduation of the dynamometer in grammes is a purely arbitrary affair. We might have used angular deflections, or millimetres of movement of the point ENERGY OF VOLUNTARY ACTION. 2I/ We used grammes because in supporting objects, e.g., by the outstretched finger, much (but not quite) the same volitions come into play, and because the gramme is the unit of energy for that particular case. The arbitrari- ness of the gramme-scale can be seen from the fact that of the actual energy expended by the muscles about three- quarters go to produce heat and one-quarter to produce the pressure. We might with just as much right, and perhaps with just as much success, use the rise in the temperature of the muscle as the preliminary scale. Again, the work done by the muscles need not neces- sarily be proportional to that arriving along the peripheral nerves, or starting from the brain. The point to be borne in mind is that, following the volition, there is a whole series of processes ending in the movement of the pointer over a scale-plate, and that not one of these processes bears the remotest resemblance to the original volition. The graduation in grammes has advantages over any other for the dynamometer, and it is used for con- venience. A man whose hand has been amputated can perform and apparently (for him) execute the same volitions. For him some other apparatus and prelimi- nary scale would be necessary, possibly a pair of elec- trodes on the arm- stump with a determination of the change of electric potential. If the experiment could be successfully carried out, this scale would be just as appropriate as the gramme-scale of the dynamometer. In any case, the scale we are seeking is the volition- scale for the particular mental phenomenon of pressure. This pressure has no resemblance whatever to the work done by a weight mechanically deflecting the dynamo- meter. There is really no " pressure " of the weight on the dynamometer ; there is only a change in the distribu- tion of energy. The application of the term " pressure " to this case arises from the fact that in most cases of THE NEW PSYCHOLOGY. pressure, as the execution of a volition, we find results happening similar to those in cases where weights are applied. If a person should grow up with reading telescopes (for a galvanometer) fixed to his eyes and various electrodes to the surface of his body, ''pressure" would mean to him introspectively the same thing as for all of us ; but, referring to his visual experience, it would mean degrees of mirror deflection and not grammes. We might mark the scale-plate of the dynamometer in volition-units, starting with the first light pressure as the unit. This would be preferable if all the experi- ments of the investigation were to be made on a single occasion, and if the investigation were not to be com- municated to others. But if the experiments are carried out on different occasions or on different persons, they can be compared only by reference to some common scale. If the scale of the first person is used, it is just as arbitrary for the others as the gramme- scale. Finally, for communicating results reference must be had to some generally accepted scale and not to an arbitrary one. This scale of volitions is not a standard scale, but is the actual scale present in us at the particular moment. It undoubtedly changes from time to time, and under various circumstances; its particular form is probably due to past experiences. Experiments that I have made on establishing scales of volition in the thumb-and-finger grip, give the following results for three subjects : Volition Scale : i 2 3 4 Subject I. 0.6 Z.I 2,1 3-3 kilos. II. 0.4 1,2 2.1 4-3 HI- 0.6 I.I I.Q 3-9 i Relative values I. i 1.8 3-5 5-5 II. I 3 5-3 13-8 HI. I 1.8 3-2 6-5 ENERGY OF VOLUNTARY ACTION. 219 With a scale of volitions thus obtained, we naturally turn next to the various mental influences modifying our volitions. Researches on dynamometry have been very numerous. The results I shall give here are not derived from any one investigation, and were not obtained with any one apparatus. The most common apparatus is a dynamometer for the whole grip of the hand, which is unfortunately not an accurate instru- ment. It is needless to go into apparatus details, how- ever, as the experiments can all be repeated under even better conditions with the apparatus I have described. In one important respect we find ourselves dis- appointed. The results of previous investigations are generally only qualitative, and not quantitative. Never- theless, numerous interesting and valuable facts have been discovered. I will give some of the results briefly. At the outset we notice that the investigations have been almost entirely confined to the study of the amount of the maximum effort that can be exerted ; the problem almost always refers to the greatest possible grip of the hand. The object in most of these cases is to compare the maximum energy of different persons, e.g., of the two sexes, of different races, &C. 1 Such measurements, though valuable for anthropological purposes, are seldom carried out in a way to throw any light on mental processes. " The greatest possible effort depends on the general mental condition. It is greater on the average among the intelligent Europeans than among the Africans or Malays. It is greater for intelligent mechanics than for common labourers who work exclusively, but un- 1 A summary of these results is to be found in Ellis, Man and Woman, 150, London, 1894, 220 THE NEW PSYCHOLOGY, intelligently, with the hands. Intellectual excitement increases the power. A lecturer actually becomes a stronger man as he steps on the platform. A schoolboy hits harder when his rival is on the same playground. A bear's fear for the safety of her cubs might well be considered proportional to the number of pounds difference in the force of her blow." The amount of the greatest possible effort can be in- creased by practice. Curiously enough, this increase of force is not con- fined to the particular act. In a set of experiments made to test this point, 1 the greatest possible effort in gripping was made on the first day with the left hand singly and then with the right hand, ten times each. The records were : for the left 15 Ibs., for the right 15 Ibs. Thereafter, the right hand alone was practised nearly every day for eleven days, while the left hand was not used. The right hand gained steadily day by day ; on the twelfth day it recorded a grip of 25 Ibs. The left hand recorded on the same day a grip of 21 Ibs. Thus the left hand had gained 6 Ibs., or more than one third, by practice of the other hand. A great deal has been said of the relation of physical exercise to will power. I think that what I have said sufficiently explains how we can use the force of act as an index to will power. It is unquestionable that gym- nastic exercise increases the force of act. The con- clusion seems clear : the force of will for those par- ticular acts must also be increased. It has often been noticed that an act will grow steadily stronger although not the slightest change can be found in the muscle. Of course, I do not say that the developed muscle does not give a greater result for the same impulse than 1 Scripture, Smith, and Brown, On the Education of Muscular Control and Power, "Stud. Yale Psych. Lab.," 1895, ii. 118, ENERGY OF VOLUNTARY ACTION. 221 the undeveloped one ; but I do claim that much of the increase or decrease of strength is due to a change in will power. If we consider the matter on the physio- logical side, this would be equivalent to the assertion that the change in the force of the act is due partly to a change in the amount of energy liberated by those higher nervous centres which are most immediately involved in the volition. The force of will varies according to what we hear, feel, or see. With the thumb-and-finger grip the greatest pressure I can exert during silence is 4 kilos. When some one plays the giants' motive from the ! ^ J ^ I - -9- _ <^ -j- 0- -9 / = p Rheingold my grip shows 4! kilos. The slumber motive from the Walkiirie reduces the power to 3^ kilos. 1 The effect of martial music on soldiers is well known. The Marseillaise helped to achieve the French Revolution. Just how much of the effect is due to the rhythm, the time, the melody, and the harmony, has not been determined. A very great deal depends on the pitch. Plato emphasises the influence of the proper music on the formation of character, and proceeds 1 Scripture, "Thinking, Feeling, Doing," p. 85, Meadville, 1895. 222 THE NEW PSYCHOLOGY. further to specify the general scales in which music should be written. The high Lydian is plaintive, the Ionian and Lydian are soft and convivial, the Dorian is the music of courage, and the Phrygian of temperance. Aristotle agrees in general but considers the Phrygian Fig. 47. DEPENDENCE OF ENERGY ON COLOUR music as exciting and orgiastic. It has long been sup- posed that the difference among the scales was one of arrangement of the intervals within the octave, corres- ponding to the major and the minor, but a more recent opinion is that the difference is one of pitch. The Lydian is a tone to a tone and a half higher than ENERGY OF VOLUNTARY ACTION. 223 the Phrygian, and the Dorian is a tone below the Phrygian. The Dorian is neither too high nor too low, and expresses a manly character. It might be suggested that the special melodies asso- ciated with each scale may have had much to do with the case. Nevertheless it has been proven that the pitch itself has an effect on the greatest strength of grip ; tones of a moderate pitch increase the power of the grip whereas very high or very low tones weaken it. 1 The sight of colours has been found by Fere to change the power of the grip, particularly in hysterical persons Fig. 48. DECREASE OF EFFORT OWING TO INTELLECTUAL WORK. (Fig. 47). I have not been able to detect such differences in regard to colours in my experiments on college students ; the experiments should be repeated with careful attention to the purity, brightness, and extent of the colours, the absence of sources of disturbance and distraction, &c. Mental work requiring attention decreases the energy of any particular voluntary act. The following experi- ments 2 with a hand dynamometer show this effect ; the 1 Fere, " Sensation et mouvement," 35, Paris, 1887. 2 Loeb, Mnskdthcltigkcit als Maass psychischer Thfltigkeit, " Archiv f. d. ges. Physiologic" (Pfliiger), 1886, xxxix. 592. 224 THE NEW PSYCHOLOGY. records of the dynamometer were made in a purely arbitrary scale of degrees. I give a few specimen results ; the figure denotes the maximum pressure under the particular circumstances. Experiment i. No distraction, 77 ; reading and understanding, 15 ; reading mechanically with no attention to the meaning, 67. Experiment 2. No distraction, 76 ; reckoning 6x7 = 42 (very little distraction), 74. Experiment 3. No distraction, 104 ; reckoning 13 x ^18 = 234, 25. These figures, being purely arbitrary, give only a vague impression of the amount. With my dynamograph I have obtained tracings readable in kilos. Fig. 48 shows such a tracing ; the scale of kilos, is at the left. The maximum of the thumb and finger grip is about 7 kilos. ; the loss due to reading is about 3 kilos. Turning from the experiments with the maximum energy to the study of other degrees of energy, \ve find only one extended research. 1 The instrument used (Fig. 49 2 ) consisted of a heavy spiral spring enclosed in the brass cylinder (R P), to which the handle (H) is attached by a bar. The bar runs on double wheels almost without friction. When the handle is pulled out the amount of force applied is shown on the scale (P), as in an ordinary spring balance. The pointer, however, not being attached to the bar, is only pushed forward, and stays at the point of the maximum pull. The experimenter can thus take the exact reading before replacing the pointer. By means of the bar, pivot, and screw (at N) the spring can be set 1 Fullerton and Cattell, "On the Perception of Small Differences," 65, Philadelphia, 1892. 2 Figs. 49 and 50 were kindly furnished by Professors Fullerton and Cattell. ENERGY OF VOLUNTARY ACTION. 225 at any point up to 15 kg. In such a case, the observer must pull the set amount before the handle moves, while the force of his pull beyond this amount is registered on the scale. The initial force of movement may be kept the same, while the extent and rate are altered, and the total extent of the movement may be made as small as desired. The movement used was a free pull with the arm. The observer was told to give a pull of (say) 2 kg. As might have been expected, his error in estimating a standard magnitude was usually very great. He was Fig. 49. DYNAMOMETER FOR PULLING. then told the direction and approximate amount of his error and allowed to try again. This was repeated until he had made five trials, by which time he could usually give the standard without great variation. A series of ten judgments was then made, the observer giving in each trial first the standard pull from memory, and then a pull as nearly as possible equal to it. The results show, in the first place, certain constant errors varying with the magnitude of the standard and with the particular observer. What we are particularly interested in, however, is the mean variation around the observer's own average. With standards of 2, 4, 8, 16 226 THE NEW PSYCHOLOGY. and 1 6 kilos, the mean variations for five observers were 0.19, 0.30, 0.43, and 0.46 kilos. We have seen that when two sensations are compared the mean variation expresses the subject's irregularity of judgment, and that when movements are made it expresses his irregularity of execution. Cattell has shown the way to analyse the irregularity of actual execution into irregularity of movement and irregularity of sensation or perception. I will illustrate this by the case of one observer F. After each pair of intentionally equal pulls had been made, the observer was required to decide which of the two had actually been the 5.0 * Fcvce cf tyov 2,00 <,'CO fco TbOC Fig. 50. IRREGULARITY DEPENDENT ON EFFORT. greater. For a pull of 2 kilos. F felt correctly 71 % of the time when the second pull was really less, and 69 % of the time when it was really greater. He could thus himself often correctly distinguish a difference, even a difference between two pulls that he had intended to be equal. Similar results were found for all observers. The conclusion drawn by the authors is as follows : The error (irregularity) of execution is complex, being partly due to an error of perception and partly to an error of movement. If the entire error, in the attempt to make the two pulls alike, were due to an error of perception, the pulls would seem, when completed, exactly alike, and the observer's judgment would have been a mere guess, as likely to be wrong as right. If, ENERGY OF VOLUNTARY ACTION. 22/ on the other hand, the observer did not make the two movements apparently alike, he should perceive his error of movement as a difference, and this difference would give a percentage of right cases corresponding to its size. Further, the average irregularity of per- ception, when used as the amount of difference in the method of right and wrong cases, gives 78.7 % of right cases. If the error of movement gave this percentage, we should conclude that the error of movement and the error of perception were equal. The per- centage is regularly less than this amount ; by the difference that corresponds to this percentage we determine the size of the error of perception as com- pared with the error of movement. For example, F gave 71 % of correct answers for the judgment of second pull for 2 kilos. If he had given 78.7 %, the ratio of his error of movement to that of perception would have been i to i ; for 71 %, however, it is as T 7 g- to i. x The total error (mean variation) was 0.18 kilos. ; how much of this belongs to perception, how much to movement ? According to the law by which errors combine, the total error is the square root of the sum of the squares of the separate errors. Thus the errors bear the relation of 0.7 to i.o ; their squares are as 0.49 : i.oo. The total error will stand in the relation of \/o.49 + i.oo, or 1.2, to the others. Thus the error of movement is -fa of the total error, or o.n kilos. ; and the error of perception is yf of 0.18 kilos., or 0.15 kilos. The general course of these errors for standard pulls of 2.00, 4.00, 8.00, and 16.00 kilos, is shown in Fig. 50. * The values are found by the table in Appendix VIII. CHAPTER XVI. FATIGUE IN VOLUNTARY ACTION. IN pressing the dynamometer we are performing work. As work is performed, our capacity for work decreases ; this decrease is generally known by the term " fatigue." Fatigue, like memory, introduces a change in the phenomenon itself and a change in its regularity. Fig. 51 shows a portion from a curve with the dynamograph Fig. 51. FATIGUE IN CONSTANT EFFORT. where the maximum grip was being exerted ; it is the rear end of the same record as Fig. 48, a large portion from the middle of the record being omitted. The maximum grip exhibits large fluctuations, going from very low to even higher than the maximum at the start (Fig. 48). It is also to be noticed that the grip becomes very uncertain and tremulous. Are these effects of fatigue clue to bodily changes of FATIGUE IN VOLUNTARY ACTION. 229 which we have no knowledge ? or are they due to a change in will power ? Let us first change the method of experimenting. Instead of maintaining a constant pressure the subject is told to press on the dynamometer repeatedly as hard as he can and to continue to repeat these grips till told to stop. A record of such a series of grips, taken on myself, is shown in Fig. 52. It will be noticed that the grips steadily decrease in extent to a condition of complete paralysis ; then follows a partial recovery ; then a paralysis. In longer records this fluctuation repeats itself continually. It Fig. 52. FATIGUE IN REPEATED EFFORTS. will also be noticed that the fluctuation occurs not only in gripping, but also in letting go. When the paralysis occurs, the grip does not sink to zero, but remains at a medium point. During the whole experi- ment I conscientiously gripped as hard as possible. Concerning the minor changes I knew nothing. At the points of paralysis I could not even will the grip ; I felt a complete mental paralysis and did not suppose that I had gripped at all. On the other hand, I did not sup- pose that I had relaxed the grip. A kind of mental daze came over me at the points of paralysis ; I felt absolutely unable to do anything with the fingers involved. I did not feel that I was willing the grip 230 THE NEW PSYCHOLOGY. as strongly as ever, but I felt a weakness in the very effort itself. This change in will-power became very marked when I was able to increase it after the time of paralysis had passed. Returning now to the original method, that of main- taining a steady maximum grip (Fig. 51), I find analogous feelings of mental paralysis and daze, although the differences in the volitional effort are not so marked. In the light of such experiences I do not hesitate to regard a portion of the fatigue as a fatigue in volitional energy for the particular movement involved. This view is sustained by the experiments of Mosso and Lombard. To measure the work done in muscular movements Mosso x has invented the ergograph. It consists of a rest in which the arm is fixed so that the middle finger can be moved alone without involving any of the others. The fingers to each side of the middle finger are kept in position by being inserted into tubes. A cord is attached to a ring on the first joint of the finger. This cord runs over a pulley and supports a weight at the end. Just behind the pulley arrangement a smoked drum is placed. A light pointer is attached to the cord ; and each movement is thus recorded. In Mosso's experiments the w r eight was raised as high as possible and then lowered every two seconds until complete fatigue occurred. This produced on the drum a series of tracings beginning with a long one and declining to zero at the end. Each of these tracings represents the amount of work done in raising one kilo, through a certain distance, and this distance represents the maximum energy present at the particular moment. 1 Mosso, Ueber die Gesetze der Enm'idung, "Archiv f. Physiol." (Du Bois-Reymond), 1890, 89. FATIGUE IN VOLUNTARY ACTION. 231 The curve according to which this energy decreases with successive efforts is the curve of fatigue. The Fig. 53. ERGOGRAPH RECORDS FOR VOLUNTARY, NERVOUS AND MUSCULAR FATIGUE. general course of this curve is exhibited by a line supposed to be drawn along the tops of the tracings. The curve of fatigue differs according to the way in which the movement is originated. Fig. 53 shows : (i) a tracing when the movements were voluntary ; Fig. 54. RECORDS SHOWING INDEPENDENCE OF MUSCULAR AND VOLUNTARY FATIGUE. (2) a tracing when the movements were produced by electrical stimulation of the nerve ; and (3) a tracing 232 THE NEW PSYCHOLOGY. when they were produced by electrical stimulation of the muscle. The actual amount of work done and the course of the curve of fatigue thus depend on both muscular, peripheral and mental, or central, factors. The curious interrelation between voluntary movements and those due to electrical stimulation of the nerve is exemplified in Fig. 54, where E indicates the movements due to suc- cessive electrical stimuli and V those due to voluntary efforts. After complete fatigue had occurred for electrical stimulation the person was at first quite fresh for the voluntary effort ; he became, however, very Fig. 55. REF-EATED CONTRACTIONS. rapidly fatigued. Thereafter there was a very slight recovery for each kind of movement. The independence of voluntary and muscular fatigue has also been proven by Lombard r in the following way : He contracted the muscles alternately by a volition and by an electrical stimulus. The result is shown in Fig- 55- 2 The tops of the electrical contractions are 1 Lombard, Some of the Influences which affect the Power of Voluntary Muscular Contractions, "Journal of Physiology," 1892, xiii. i. 2 This is a copy of an original record kindly furnished me by Prof. Lombard. FATIGUE IN VOLUNTARY ACTION. 233 iii general lower than the voluntary ones ; they decrease very slowly in height. The others which are the results of the voluntary contractions are at first much higher ; they decrease steadily until they are almost the same as the electrical ones. Just beyond this point there is a recovery of voluntary power, which lasts for a short time only, to fall and rise and fall again in constant succession. It has thus been definitely proven by Lombard that the fluctuations in the voluntary efforts, such as are seen in Fig. 54, are not due to the muscles. 1 We can conclude, therefore, that a considerable portion of the total fatigue in voluntary muscular con- tractions is a fatigue of will-power, and also that the fluctuations represent fluctuations in the effort of will. Taming again to Fig. 51, we can say that, while the average strength may decrease from causes unaffected by our will-power, the fluctuations "of the curve represent fluctuations in effort of will. The fatigue for a particular voluntary movement does not mean necessarily a fatigue for other voluntary acts. It is quite a mistake to regard the will as one single thing ; there are as many wills as there are things to be willed. The fatigue of a particular kind of will does not involve a central will on which others depend. There are, however, cases in which we use the fatigue of a particular form of will-power to indicate the general changes in the total sum of will-power in the individual under particular circumstances, just as we use the changes in a particular kind of sensation to indicate the changes in his general sensitiveness. We do not imply a 1 Lombard, The Effect of Fatigue on Voluntary Muscular Contrac- tions, "Am. Jour. Psych.," 1890, iii. 24 ; also Effet de la fatigue sur la contraction nnisculairc voluntaire, " Archives italienne de biologic," 1890, iii. 380. 234 TIIE NEW PSYCHOLOGY. central will-power in the first case any more than we do a central sensation-power in the other. Among the subjects thus investigated we find the effect of general mental fatigue on the fatigue of move- ment. Of the curves shown in Fig. 56, the first shows the work done by the finger in Mosso's apparatus at nine o'clock in the morning by Dr. M. From 2 p.m. till 5.30 he was engaged in orally examining students under the most trying mental conditions. At 5.45 the second curve was taken ; it shows the first contraction as strong as ever, but the voluntary energy is quickly exhausted. Fig. 56. EFFECT OF MENTAL WORK. The third record was taken after supper at 7.30, and the fourth at nine o'clock. Of course, not all of the increased fatigue is central ; similar curves with electrical stimulation show changes ; they are, however, less marked. A part of the change is undoubtedly central, and is, according to our point of view, also psychical. Mosso's explanation of the central fatigue as due to changes in the constitution of the blood or any other physiological explanations do not have any bearings on the psychological side of the question. We feel, mentally, that our voluntary power falls off more rapidly vi the one case than in the other, and we assume that the FATIGUE IN VOLUNTARY ACTION. 235 rate at which it falls off bears some relation to the actual curves obtained. Lombard has investigated a number of the influences that affect volition-energy. In most of the cases we shall find that his results are confirmed by ordinary experience ; others, however, are not so usual. The day's work leaves us with less energy than we start with in the morning. In Lombard's table 1 for each day of nearly a month, we find the percentages of loss for the evening: 59, 34, 39, 3, n, 55, &c. Only on five days out of twenty-three is there a gain in the evening ; this accords with the experience that occa- sionally one feels unusually fresh in the evening. The same series of experiments shows the gains for every morning over the preceding evening ; in only two cases was there a loss. In general, Lombard found that the following influ- ences decreased the power to do voluntary muscular work in his experiments: general and local, fatigue, hunger, decreasing atmospheric pressure, high temper- ature, humidity, and tobacco. He found that the follow- ing increased it : exercise, rest, sleep, food, increasing atmospheric pressure, and alcohol. In the experiments of Mosso and Lombard fatigue was produced rapidly by giving the finger a large amount of work to do. When such hard work is not required the fatigue is, of course, much less rapid and the work can be continued for a longer time. Experiments of this kind with the dynamometer have been carried out under my direction. 2 A dynamometer was used of the kind shown in Fig. 4, adjusted for very light grips. The subject started with any moderate grip he chose. This grip was then repeated with the same effort for 1 Lombard, as before. a Full tables will appear in " Stud. Yale Psych. Lab.," 1896, iv. 236 THE NEW PSYCHOLOGY. sixty times. Ten sets of experiments were taken. The results, as given in Fig. 57, show in the curve F the average increase for each successive grip over the first grip, and in the curve M the mean variation of the Fig. 57. INCREASE OF THE INACCURACY F AND THE UNCERTAINTY M IN A SUCCESSION OF EFFORTS. successive grips. These quantities are analogous to the inaccuracy C and the uncertainty U that have already been discussed in Chap. XII. Experiments of a similar kind have been made by FATIGUE IN VOLUNTARY ACTION. 237 Moore. 1 The particular voluntary movements inves- tigated were those of the eye muscles. The apparatus is shown in Fig. 58. The cylindrical beads A and C were stationary at i m. apart ; B was adjustable. As a bead was raised by the appropriate mechanism, it was seen by the subject looking through a slit in E. The experiment began each time with the carriage of the second bead placed at the end of the slot nearest the observer. All beads were out of sight. By a push of the lever the first bead was raised, its position was noticed and it was allowed to fall. By the cord in the left hand the second bead was raised and drop- ped. Then by a pull of the lever the third was raised and dropped. The judg- ment was made as to whether or not the second bead was in the middle. If not, the middle bead was moved further away by turn- ing a wheel and the expe- riment was repeated. This was done until the bead was judged to be in tl e middle. 1 Moore, Studies of Fatigue, "Stud. Yale Psych. Lab.," i895,iii.68. 238 THE NEW PSYCHOLOGY. The distance of the first bead from the eyes was a half metre ;. this was not short enough to cause any strain. The thiid bead was a metre and a half away. The part of the scale from the middle toward the eyes was called negative and the other positive ; they were indicated by the signs and +. Each individual experiment resulted in a position of the middle bead somewhere near the middle point, or o. Its divergence from this point was recorded in milli- metres + or . The first question to be considered was the position of the estimated middle point for the first experiment on the successive days of work. The results were : during May, 27, 60, 33, 28, 74, 97, 83, 96 ; during June, 75, 48, 48, 81, 80, 80, 90, 74, 61, 76, 86 ; during July, 92, 97, 102, 92, 103, 121, 136, 126, 70, 104 millemetres, all being -f- or deviations beyond the true middle. In the normal position for the eyes at rest the visual axes are parallel and the point of convergence is infi- nitely distant. When the eyes are converged on a nearer object a voluntary effort is required, which is greater as the object is nearer. Any fatigue would therefore show itself in an over-estimation of the actual amount of effort put forth, and this would result in placing the object nearer to infinity or further away from the eyes in just the same way that when tired we would consider a quarter of a mile much greater than when fresh. In these particular experiments the near point and the far point were fixed ; the fatigue would show itself in the change for the middle point in relation to the other two. This change of the middle point can be attributed directly to fatigue. When the observer began in May he recorded that he was in excellent physical condi- FATIGUE IN VOLUNTARY ACTION. 239 tion ; outside work was, however, soon required, and the pressure was so great that he could go to the no 100 80 60 SO 40 2 M A A/ * /\ / v ,-\ \N I v v v / A A N / / i \ i V /\ A/ V /W / V / v /^ A / / s~-^ \ I v/J .A-'' V A A/ /' \ / ,' "X^stri* I number of txfiirt/ntn ( / y f/ro/- / v '' w \/N.y vv v ; JUNE. -. " \J MAY f /O If ZO 2? JO Jf 4-0 Fig. 60. CURVE OF FATIGUE FOR EYE MOVEMENTS (MEAN VARIATION). The next point investigated was the effect of fatigue when the experiments were made with a single eye, 242 THE NEW PSYCHOLOGY. The left eye was placed directly in the line of the beads ; the only work done by that eye was in accommo- dating the lens to different distances. The other eye, however, which did not see anything, was, as is well no - 10- 20- B I I I I I I . I I $ JO /S 20 2S- 30 JS 40 45 Fig. 6l. CURVE OF FATIGUE WITH ONE EYE CLOSED. known, converged and accommodated on each occasion for a point somewhat beyond the actual distance of the bead. There was thus a fatigue of accommodation in both eyes and of convergence in one ; we would FATIGUE IN VOLUNTARY ACTION. 243 naturally expect the effect to be similar but somewhat less than in the experiments with both eyes. The results for three different persons are shown in Fig. 61. To eliminate the accommodation and convergence of the closed eye while retaining nearly all the accommo- dation of the seeing eye, an observer (C) was found who had lost his right eye. The results shown in the figure conclusively prove that fatigue of accommodation altered the estimate of depth. B showed no fatigue. As fatigue enters into a voluntary act, does it increase the time necessary for executing that act ? This ques- tion has been answered by Moore x for the act of accom- modating the eye to different distances in an experiment similar to that just reported. The apparatus used was that invented by Seashore for the study of accommoda- tion-time. 2 This apparatus consisted of a pneumatic camera-shutter to which electrical connections were added. There were two arrangements of the slide and the electric connections : (i) to drop the slide and expose the nearer point ; (2) to raise the slide and expose further point. In the first arrangement one end of the electric wire was connected with the metallic body of the shutter. The other end was fastened to a binding post which was connected (i) with a wire spring which made contact with a projecting spring-arm on the slide at the moment the further point was cut off from view and the nearer point exposed, and (2) with a metal plate on which the projecting arm rested and made permanent contact when the slide came down. Both the contact-point and the metal plate were isolated from the metallic body of the shutter. In the second arrangement the slide was made to fly up and stop 1 Moore, as before. 2 Seashore, On Monocular Accommodation-time, " Stud. Yale Psych. Lab.," 1893, i. 56. 244 THE NEW PSYCHOLOGY. against a special catch. When the slide flew up, its projecting arm struck the special contact spring at the moment the nearer point was removed from view and the further point was exposed. The special catch against which the slide finally rested at the top, and with which it made permanent contact, was connected with the same binding post as the metal plate in the other arrangement. The current went through a closed- circuit reaction-key by means of which it could be interrupted. The current was made for an instant when the slide arm struck the special contact spring, permanently made by the slide arm resting on the metal plate or the special catch, and again interrupted by the reaction-key. The time required was that indi- cated between the first closing of the current and the breaking by the reaction-key. From the far object to the near object the distance was 825 cm., while from the near object to the eye it was 23 cm. The far object was a large capital E with a height of 25 mm., and the near object was a small capital E with a height of 7 mm., fastened on the slide of the camera-shutter. The far point remained stationary, while 'the nearer was pre- sented or removed by a sudden movement of the shutter. A brass tube extended from the eye to the shutter. When the slide was up, the eye could see nothing except the large letter on, the white back- ground. The slide was raised and the observer focused on the far object. The experimenter touched a key which was electrically connected with a sounder in the recording-room. The recorder pushed down a key which closed the primary circuit. The experimenter now snapped the slide j this made a clot on the smoked paper and then closed the circuit. As soon as the observer saw the small E clearly and distinctly, he broke the circuit by the reaction-key, thus making FATIGUE IN VOLUNTARY ACTION. 245 another clot on the smoked paper. When the recorder saw the two sparks, he raised the key and kept out all further sparks until the fifth repetition of the experi- ment in quick succession. A record was thus made of the time of every fifth experiment. The wave-lengths between the two dots could easily be counted and the time of accommodation obtained. This time included the subject's regular reaction-time. The results for three different sets of experiments, namely, Seashore, Moore 1893, and Moore 1894, are X, serial number of fxfxritntnt \r . . hurtdrtd-thi of a second i s> 71 10 lit if I lit lit lit IT/ J7 >ti J.U Jf' 3U Fig. 62. INFLUENCE OF FATIGUE ON ACCOMMODATION-TIME. shown in Fig. 62. It is conclusively proven that as fatigue enters in the time is persistently lengthened. In Chapter VII. it was mentioned briefly that fatigue caused a change in the maximum rate of repeating a movement of the finger. A special investigation has been made l with very careful methods. The subject was to begin when warned by a click from the sounder at his side and to continue to tap as rapidly as possible until his finger could move no more, or until told to stop. The finger was never completely Moore, Studies oj Fatigue, " Stud. Yale Psych. Lab.," 1895, iii. 92. 246 THE NEW PSYCHOLOGY. fatigued because sufficient records could not be obtained upon the drum. " I once made 480 taps, but am quite sure that I could not have made 100 taps more at the close of any record, for it was always with great diffi- culty that the last 50 or 75 were made." " The usual experience was as follows : Pain was first felt in the muscles of the forearm, then in the upper arm. Suddenly the blood rushed to the face and head, and the temples were rilled with sharp pains. The whole right side (the work was clone with the index finger of the right hand) seemed to partake of the trouble. After the experiment was completed, the arm seemed paralysed. I could not even handle the record- sheet with safety. The arm, especially the forearm, and often the shoulder would feel painful for a half hour afterward. Restoration was not complete in less than two hours and a half." A specimen record was given in Fig. 30. The fluctu- ating nature of the tapping is made evident ; quite note- worthy are the extremely long taps that occur with increasing frequency toward the end. In performing such experiments the subject when fatigued often feels for an instant a complete paralysis of the will. It is not a paralysis of the muscles with the intention to move still retained ; on the contrary, the person feels abso- lutely lost and unable to will or desire anything for an instant. In these experiments fatigue is generally shown by the time the 7oth or 8oth tap is made. A profes- sional cornet player, who had not played for a year, showed no fatigue before 150 taps had been made. A woman who played on the piano, showed no fatigue until 200 taps were made. She affirmed that she felt no fatigue at all, but the incipient fatigue had left its traces in the records beyond the 2Ooth tap. FATIGUE IN VOLUNTARY ACTION. 247 In conclusion, it is perhaps desirable to point out the views expressed in this chapter that differ from the usual ones. " Fatigue" is defined as the decrease in the capacity for work ; fatigue in this sense may or may not have definite relations to the peculiar sensation known as the " feeling of fatigue." Fatigue in voluntary action is at least partly fatigue of the will, as is made plainly evident not only by Lombard's experiments but also particularly by the inability to relax the muscles in the experiments described on p. 229. The major fluctuations, amounting to complete loss of power at what I have called " points of paralysis " but followed by immediate recovery, as first noticed by Lombard, I regard as specially characteristic of fatigue of the will. Finally, the chief ll fatigue -functions " (if the term may be permitted) find their numerical expressions in the constant, or progressive, error (change in intensity, extent or time of the exertion) and in the mean variation, or mean error (change in regularity). CHAPTER XVII. PASSIVE AND ACTIVE MOVEMENT. IN experiments on passive movements Goldscheider * used an apparatus, of which the fundamental principles can be illustrated by its arrangement in studying the movement of the first interphalangeal joint of the index finger. The first phalanx of the finger was fixed on a plaster cast, and a thick close rubber shell was pushed over the last two phalanges. This shell hung from a broad band passing over an aluminum roller, 10 cm. in diameter, so that the line of the finger was perpendi- cular to the plane of the roller. Another band, hanging down from the roller on the other side, carried a small cork pan. By means of small weights, which could be put on the cork pan or on the finger-shell, the two sides of the apparatus could be balanced. A plate of lead on the cork pan maintained the last two phalanges in position without muscular tension. Small additional weights were laid on this lead plate and then removed, whereby passive movements, upward or downward, of the finger were produced. A fine lever was arranged, to write on the smoked drum. These records on the drum were carefully scaled in degrees of movement around the joint moved. This apparatus could thus 1 Goldscheider, Untersnchnngeti ilbct den Mnskdsinn, " Archiv f. Physiol." (Du Bois-Reymond), 1889, 372. 248 PASSIVE AND ACTIVE MOVEMENT. 249 produce movements of different velocities and distances as desired. For movements with other joints, where the appa- ratus just described was not applicable, a hydrostatic method was employed. In a lower room a pressure pump forced water outward or inward, through a leaden pipe, connected to a second pump-cylinder in the ex- periment room, whereby the piston of the latter was moved upward or downward. The segment of the limb, e.g., the forearm that was to be moved, rested in a support on the end of the piston-rod of this second pump. In this manner, passive movements, i.e., movements without any intention on the part of the subject, were produced with various degrees of distance and velocity. With extremely small movements nothing whatever was perceived. With somewhat greater movements, a pe- culiar, indefinite sensation was felt ; this sensation was localised in the joint, but was not felt as a movement. With still greater movements, a sensation of movement appeared, in which, however, the direction of the move- ment was not apparent. Finally, when the movement had reached a certain size it was felt as a just percep- tible passive movement. The following table * gives the threshold of movement, i.e., the just perceptible movement, around the various joints, for the greatest velocity obtainable without jarring. The figures indicate degrees. 2nd interphalangeal (between nail segment and middle segment of the finger) ... 1.03 to 1.26 1st interphalangeal (between middle and basal segments) 0.72 1.05 1 Goldscheider in V Zeitschrif t f. Psych, u. Physiol. d. Sinn.," 1890. i. 146. 250 THE NEW PSYCHOLOGY. Metacarpo-phalangeal (between basal seg- m Wrist ment and hand) 0.3410043 st 0.26 0.42 )W ... 0.40 0.61 alder ... O.22 o ^o 0.42 O 70 e ... 0.50 vj./y O.7O t I.K I.^O Hip Knee Foot With other velocities the rule was found to hold that for those joints where the extent of the just noticeable movement was smallest, the necessary velocity was also the smallest. Finally, there appeared a special relation between the extent of the movement and its velocity, namely, that increased extent could make up for dimi- nished velocity. Special attention was paid to the question whether the threshold of movement for a given joint depended upon the position from which the movement was started ; a noticeable dependence could not be found. It was, moreover, conclusively proved that these sensa- tions of movement do not depend upon sensations of pressure from the skin. They are connected physiolo- gically with the membranes of the joints. The question arises concerning the possibility that what has been called a sensation of movement may be derived from sensations of position. x These sensations of position are made up of pressure sensations from the skin, resistance sensations from the joints, heaviness sensations from the sinews, and possibly other sen- sations from other parts of the body, e.g., muscles, periosteum, &c. These sensations enter into different combinations with each position of the part moved. It is unquestionable that in any movement executed, these 1 Miillerand Schumann, Ueber die psychologischcn Gnuidlagcn dcr Vcrgleichung gchobencr Gcwiclite, " Archiv f. d. ges. Physiologie " (Pfluger), 1889, xlv. 71. PASSIVE AND ACTIVE MOVEMENT. 251 sensations play more or less important parts. Gold- scheider has proved, however, that special sensations of movement exist in addition to them. By faradisation of the finger the knowledge of position could be com- pletely removed and yet" the sensitiveness to movement was still present and was not necessarily diminished. Again, the existence of a movement could be perceived when the movement was not great enough to give a knowledge of its direction. The existence of a special sensation of movement can be regarded as conclusively proven. The size of the just perceptible passive movement has been found to be subject to several remarkable influences. In the first place, children are much more sensitive than adults, whereby it is to be remembered that the move- ment is measured as an angle. Such a result seems quite opposed to the results of experiments on the blind. 1 Blind persons who are practised in feeling are much more sensitive than other persons. The cause of this increase in sensitiveness lies in sharpening of the attention, and in practice in the interpretation of sensa- tions whereby scarcely perceptible sensations can be made use of. Up to this point the movements have been passive ; in " active " movements other elements are added. There are present the intention to perform the move- ment and the volition which causes its performance. Goldscheider measured the just perceptible active movements with the same apparatus as for passive movements. The experiments showed that the least perceptible movement was practically the same for both active and passive movements. Faradisation of the joint reduced the ability to say whether the 1 Hocheisen, Ucbcr den Mnskclsinn bei Blindcn, " Zt. f. Psych. u. Phys. d. Sinn.," 1893, v. 239. 252 THE NEW PSYCHOLOGY. intended movement had actually been executed or not. For example, for the first interphalangeal joint the just perceptible passive movement was 0.72 to 1.05; for active movement it was 0.76 to 0.85 j 1 with a current through the joint it was, for passive movements 3.66, and for active movements 3.09, the reduction of sen- sitiveness being about the same in both cases. The knowledge of the presence of movement seems, there- fore, to depend practically entirely on the sensations of movement and not on the intention or the volition. This fact is brought out by Goldscheider's experi- ments 2 on imperceptible active movements. The end phalanx of the index finger was placed on a rubber capsule such that the slightest impression caused a recording pointer to make a mark on the smoked drum. Sensations of touch were deadened by a thick rubber cap on the finger. As long as the subject could say definitely that he had not moved his finger the pointer remained still. Although Goldscheider does not say so expressly, this is presumably quite independent of any mere memories of the movement. The person then willed a slight movement of the finger. The condition was found in which he believed that he had moved it, but was not sure whether the movement was real or only imaginary. At every such experiment, however, there was a slight excursion of the recording pointer. The execution of a movement, whether passive or active, is made known to us by means of sensations from the part moved. If they are present without any intention to move, the movements are considered passive. If they agree with the movements intended, 1 Goldscheider, Unters. u. d. Muskelsinn., "Arch. f. Physiol." (Du Bois-Reymond), 1889. Suppl. Bd., 207. - Goldscheider, as before, p. 211. PASSIVE AND ACTIVE we consider them to be active movements. If they are unclear, we are doubtful if our intention has been executed. Active movements vary between two extremes, volun- tary active movements, and involuntary active move- ments. The complete process that occurs during a voluntary active movement contains, in the first place, an idea of the movement to be performed. Then follows a process of willing to execute this idea. Finally, there result certain sensations which tell us that the movement has actually been executed. It is necessary that these latter sensations agree with the original idea of the movement, if the movement is to appear voluntary. If the two do not agree, as in the case of certain muscular disturbances whereby the movement occurs in a different direction from the intended one, then the person feels as if he were subjected to a passive movement whereby his own intention was overcome. In what is called an involuntary movement the pre- liminary idea of the movement to be performed is lacking ; the person acts without intending to do so. Even a fixed determination to remain inactive would hardly prevent the ordinary man from starting at an unexpected shrill sound. The unperceived involuntary movements are at the bottom of the phenomena of "table tipping," and "thought transference." Perhaps I ought not to mention such subjects without repeating Faraday's apology for his experimental investigation. 1 " I am a little ashamed of it, for I think in the present age, and in this part of the world, it ought not to be required." 1 Faraday, Experimental Investigation of Table-Moving, "Athen- aeum," 1853, July 2 ; also in " Experimental Researches in Chemistry and Physics," 390, London, 1859. 254 THE NEW PSYCHOLOGY. But there is a particular reason why the psychologist should have his attention called to them. Faraday wished merely to show that the phenomenon of table tipping was not a physical one, but a psychological one ; this, however, brings the matter home to the psycho- logist since it is part of his business to investigate un- perceived involuntary actions. Faraday's investigation was, as usual, a model of experimental methods and deductions. 1 "The effect produced by table-turners has been referred to electricity, to magnetism, to attraction, to some unknown or hitherto unrecognised physical power able to affect inanimate bodies to the revolution of the earth, and even to diabolical or supernatural agency. The natural philosopher can investigate all these supposed causes but the last ; that must, to him, be too much connected with credulity or superstition to require any attention on his part. " Believing that the first cause assigned namely, a quasi involun- tary muscular action (for the effect is with many subject to the wish or will) was the true cause ; the first point was to prevent the mind of the turner having an undue influence over the effects produced in relation to the nature of the substances employed. A bundle of plates, consisting of sand-paper, millboard, glue, glass, plastic clay, tinfoil, cardboard, gutta-percha, vulcanised caoutchouc, wood, and resinous cement, was therefore made up and tied together, and being placed on a table, under the hand of a turner, did .not prevent the transmission of the power ; the table turned or moved exactly as if the bundle had been away, to the full satisfaction of all present. The experiment was repeated with various substances and persons, arid at various times, with constant success ; and henceforth no objection could be taken to the use of these substances in the construction of apparatus. The next point was to determine the place and source of motion, i.e., whether the table moved the hand, or the hand moved the table ; and for this purpose indicators were constructed. One of these consisted of a light lever, having its fulcrum on the table, its short arm attached to a pin fixed on a cardboard, which could slip on the surface of the table, and its long 1 Faraday, On Table Turning, " Times," 1853, June 30 ; also in "Experimental Researches in Chemistry and Physics," 382, London, 1859. PASSIVE AND ACTIVE MOVEMENT. 2$ 5 arm projecting as an index of motion. It is evident that if the experimenter willed the table to move towards the left, and it did so move before the hands, placed at the time on the cardboard, then the index would move to the left also, the fulcrum going with the table. If the hands involuntarily moved towards the left without the table, the index would go towards the right ; and, if neither table nor hands moved, the index would itself remain immovable. The result was, that when the parties saw the index it remained very steady ; when it was hidden from them, or they looked away from it, it wavered about, though they believed that they always pressed directly downwards, and when the table did not move, there was still a resultant of hand force in the direction in which it was wished the table should move, which, however, was exercised quite unwittingly by the party operating. This resultant it is which, in the course of the waiting time, while the fingers and hands become stiff, numb, and insensible, by continued pressure, grows up to an amount sufficient to move the {able or the substances pressed upon. But the most valuable effect of this test-apparatus (which was afterwards made more perfect and independent of the table) is the corrective power it possesses over the mind of the table-turner. As soon as the index is placed before the most earnest and they perceive as in my presence they have always done that it tells truly whether they are pressing downwards only or obliquely, then all effects of table-turning cease, even though the parties persevere, earnestly desiring motion, till they become weary and worn out. No prompting or checking of the hands is needed the power is gone ; and this only because the parties are made conscious of what they are really doing mechanically, and so are unable unwittingly to deceive themselves." These involuntary active movements are clues that reveal a person's thoughts to the muscle reader. In most such cases, the movements are so faint that the subject does not know of their existence, whereas the muscle reader feels them. A characteristic case is Cumberland's first experiment. 1 " I took my host by the hand . . . and led him from the break- fast-room ; not quickly as I do now, but slowly and lingeringly. 1 Cumberland, A Thought Reader's Experiences, " Nineteenth Century," 1886, xx. 867. 256 THE NEW PSYCHOLOGY. We entered the study, and I immediately felt that I was in the correct locality. A moment more and I placed my hand upon an object, which, according to the impression I then received, I believed to be my subject's selection. I was quite right." A still more striking illustration of involuntary active movements is found in another case : " We then resumed connection with the hands, and in another moment I found myself flying across the room. In my experiments I always take the lead ; but in this case my ' subject ' took it." Cumberland afterwards tells the subject : " I felt you were so intent on ' willing' me to go to the spot, that in the very intensity of desire, you unconsciously dragged me the whole of the way ; I did nothing but remain quite passive, until I came to the table where the toy was, and common sense told me to lift up the tambourine and take it out." Cumberland's statement of the source from which he derives his knowledge, is as follows : " In my case, ' thought-reading ' is an exalted perception of touch. Given contact with an honest, thoughtful man, I can ascertain the locality he is thinking of, the object he has decided upon, the course he wishes to pursue, or the number he desires me to decipher almost as confidently as though I had received verbal communica- tion from him." The complex character of the involuntary twitchings is illustrated by the following case. In describing an experiment before the Khedive, Cumberland relates : "Paper and pencils were brought and a sheet of the former was gummed upon one of the gilded doors. The Khedive thereupon thought of a word, and, without any sort of hesitation, I wrote on the paper the word Abbas (the name of his son) in Arabic chatacters. I did not know at the time a single letter of the Arabic alphabet ; and . . . the experiment was entirely im- promptu." The important point in these matters lies in the suggestion for systematic quantitative study of the PASSIVE AND ACTIVE MOVEMENT. 257 manner in which the amount of energy expended in these unconscious movements depends on the various mental conditions. This can probably be done with dynamometers of various strengths (Figs. 4 and 24). Faraday's apparatus gives the suggestion for a com- plete apparatus that can be arranged in the laboratory. The subject's arm is supported on a plate hanging from a pulley overhead ; the amount of muscular tension desired is regulated by a weight at the other end. The force of the movement in any direction can be measured by arranging a dynamometer so that the plate pushes against it. To measure the complete exertion in all directions, three dynamometers are to be attached to the plate, so as to act in the three cardinal directions of space ; the records can be made on the drum by three piston-recorders. A study of unconscious movements of the arm has been made by Jastrow, 1 who found that a person tends in general to move toward an object to which atten- tion is being paid. Delabarre's suspended planchette apparently renders it possible to enter upon a further scientific exploration of unconscious movements. The subject's hand or arm is rested on a small board sus- pended by cords from a high ceiling. A recording point attached to the board leaves a record of every move- ment. Delabarre finds that looking or listening with close attention to an object induces in some subjects an immediate and decided movement of the arm toward the object ; in others, a similar movement after more or less considerable delay ; in others still, an apparent lack of effect, or even a movement in the opposite direction. Thinking of an object in some definite position is attended by similar movements. The result 1 Jastrow, A Study of Involuntary Movements, "Am. Jour. Psych.," 1892, iv. 398. 18 258 THE NEW PSYCHOLOGY. depends to a very great degree upon the success with which the subject can withdraw his attention from his arm and its movements, and concentrate it entirely upon the object. The suspended planchette has been used in experi- ments by Delabarre on cultivated automatic movements in normal persons, in imitation of Binet's experiments on double consciousness. The conclusion was reached that, provided the attention can be completely absorbed elsewhere, it is possible to cultivate in probably all persons automatic movements of greater or less com- plexity, which continue indefinitely, or start, stop, or change their character, in accordance with slight, un- consciously received suggestions communicated to the arm. Two subjects, both of them entirely normal in temperament and health, exhibited similar phenomena with the suspended planchette as a support for the arm experimented with. Attention was distracted by reading or by conversation, and the experimenter then com- municated to the subject's arm movements of various types. After continuing to impress these movements for some time, the experimenter endeavoured to dis- continue his own pushing movements without attracting the subject's attention, in order to see if the arm would continue its movements automatically. This did not occur at first, or occurred only slightly and at intervals. But after several sittings marked success was attained. The forms of movement tested were the straight-back and forward, the elliptical, the circular, and movement in form of the figure 8. Very slight touches were found sufficient to start, stop, or change the movement. The hand would also itself sometimes initiate movements, and continue them for several minutes, even when the experimenter was at some distance from the subject the latter having by this time gained sufficient skill PASSIVE AND ACTIVE MOVEMENT. 259 in withdrawing attention from his arm to make him unconscious of its movements, thus favouring its execu- tion of the automatisms it had learned. The degree of distraction of attention of course varied from time to time, and always with marked effect upon the automatic movements. For instance, whenever a page was turned in reading, the experimenter could from the first detect an increased resistance and hesitation in the arm. Animated conversation was found the most successful means of distraction, and during its progress the move- ments would proceed quickly or slowly in apparent variation with the interest and animation of the subject. These results add confirmation to Binet's conclusion, that it is possible to cultivate in normal persons motor automatisms, of a simple nature at least, analogous to the phenomena presented in cases of so-called " double- consciousness." x A most interesting case of these unconscious move- ments is found in involuntary whispering. In the experiments of Hansen and Lehmann referred to in Chap. IV., the subjects noticed a marked tendency to\vard action of the muscles of speech whenever a number was thought of for a while. This tendency was suppressed by a special effort. When no such effort was made, the one subject with his ear at the focus of the mirror could hear the involuntary sounds produced by the other one, in spite of the fact that the mouth was kept tightly closed and a watcher standing near by could detect no sounds or movements whatever. The mirrors made the sounds 14 times stronger for the subjects, so that the involuntary nasal whispering was sufficiently 1 md enough to give a large percentage of successful transferences of thought. For thought-trans- ference, therefore, all that is required is to find a subject 1 Binet, Double Consciousness in Health, " Mind," 1890, xv. 46. 260 THE NEW PSYCHOLOGY. who has an abnormally sharp ear and, for your part, to think very intently on the word you wish transferred. It is not necessary that there shall be any intentional communication ; if the investigators are sufficiently untrained in scientific psychological experimenting, and are inclined to attribute results to occult powers rather than to their own incapacity, the proofs of thought-transference inevitably follow. A carefiil study of the mistakes in the transferred figures, e.g., 10 for 1 8, 37 for 66, &c., proves that they arise from close similarities of the sounds in nasal whispering. One subject of a thought-transference experiment remarks that something seemed to tell him that the number was so and so. This something apparently never told him right, yet in the whisper language the mistakes are those of very similar sounds. It is quite evident what this " something " was. Thus ends the great mystery of thought-transference. The transference by contact proved to be the communi- cation of involuntary, unconscious movements of the hand ; the transference without contact proves to be the production of the involuntary, unconscious move- ments employed in nasal whispering. CHAPTER XVIII. RESISTANCE AND HEAVINESS. IN this chapter we shall consider two different sensa- tions, resistance and heaviness, with their variations in intensity. When we touch an object with a stick held in the hand, we notice a peculiar sensation which is referred to the extreme end of the stick. We apparently feel the resistance to the movement of the stick. It is this sensation that we are first to consider. Before proceeding to further treatment, it is necessary first to prove that resistance is not simply a complex of pressure-sensations from the skin, and sensations from the muscles. This has been done by Goldscheider. 1 In the first place, the skin sensations are not the essential factors. If they were, an increased pressure on the skin would disturb the sensation of resistance. Let the table be touched with a pencil held lightly in 1 Goldscheider, Untersuchungen uber den Muskelsinn, " Archiv f. Physiologic" (Du Bois-Reymond), 1889, Suppl. 165. The accounts of Goldscheider's work as presented in this chapter, are taken from the article just cited and from a summary, by Goldscheider him- self, of this and another article in the "Zeitschrift f. Psych, u. Physiol. d. Sinnesorgane," 1889, i. 145 ; Goldscheider's own words are used as often as practicable. 261 262 THE NEW PSYCHOLOGY. the fingers ; a resistance is felt. Now let the experi- ment be repeated with the pencil gripped as tightly as possible with the fingers ; the pressure sensations may be so strong as to be painful, yet the sensation of resis- tance is apparently unchanged. If resistance consisted in slight additional pressure on the skin this result would be contrary to all our experience, according to which slight additions to strong sensations have less effect than to weak ones. Again, let a rubber air- cushion be placed on the end joint of a finger, and a string carrying a weight be placed around the cushion. Such a cushion reduces the sensation of pressure to an extremely small amount, yet when the weight begins to draw on the string as the hand is raised from beside it, the resistance is plainly felt. Finally, when by an electric current the sensitiveness of the end section of the finger is so far reduced that the skin cannot feel less than a strong impression from a blunt scissors point, even then a touch of the finger on a table is felt with very little loss of intensity. It is very clear, therefore, that the sensation of resistance may be independent of pressure. This independence is emphasised in cases of anaesthesia of the skin such as occurs in tabes, as is illustrated by the following case. The skin of the patient's heel was so completely insensitive, that he did not feel the pinching of the skin or deep pricks with a needle. Yet he felt with the greatest sureness and regularity the lightest tapping of a finger in the direc- tion of the axis of the limb. The actual relation of pressure-sensations to sensations of resistance is brought out in the " resistance para- doxes." Let a heavy weight be held by a string from the fingers or from a stick held in the hand. Lower the weight rather rapidly till it rests on a cushion or a box RESISTANCE AND HEAVINESS. 263 of sand. As it strikes, a vivid sensation of resistance to the movement is felt, somewhat as though the hand were suddenly supported by a rod. The illusion is most marked when the length of the string is unknown to the person holding it ; this is readily brought about by having some one to prepare the weight and hand it to another person with eyes closed. This illusion is due to the sudden release x)f muscular strain, whereby the muscles themselves produce a pressure on the joints similar to one that would be produced by actually strik- ing an object. A similar sensation is produced by stretching a thin elastic band with the two hands, then relaxing it. As soon as the strain is completely relaxed a sudden blow is apparently felt on the ringer ends, This phenomenon has been used to investigate the relation between resistance-sensations and pressure- sensations. 1 The apparatus consisted of a string passing over two pulleys, to avoid side-movements, and carrying a weight. The string was fastened to a band which passed around a rubber cuff filled with water. Different cuffs were used for finger, hand, forearm, and upper arm ; they greatly reduced the sensation of pressure. The weight was lowered with a velocity of about 6 cm. per second ; it came to rest on a sancl-bag. The weight used was an aluminum pan filled with shot. The weight was increased from an imperceptible value until it was first noticed ; then it was decreased from a more than perceptible value till it ceased to be noticed. The following are some typical results : For movements around the shoulder joints ; (a) string 1 Goldscheider and Blecher, Versnche fiber die Empfindung des \'idcrs1andes t "Archiv f. Physiol." (Du Bois-Reymond), 1893, 536. 264 THE NEW PSYCHOLOGY. on the end of the index finger, 8.1 g. ; (6) on the second phalanx, n.og. ; (c) on the first phalanx, 15.1 g. ; (d) on the hand, 25. 3 g. ; (e) on the forearm, 44-8g. to 58.5 g. ; (/) on the upper arm, 77.4 g. For movements around the elbow; (a) on the end phalanx, 9.7 g. ; (6) on the second phalanx, 11.4 g.; (c) on the first phalanx, 17.8 g. j (d) on the hand, 31.2 g. ; (e) on the forearm, 7i-9g. These results were obtained by a movement of the forearm from a position vertically downward to a horizontal one ; for other positions they differed somewhat. For movements around the metacarpo-phalangeal joints ; (a) on the end phalanx, 22.6 g. ; (6) on the second phalanx, 66.3 g. After the sensitiveness was determined under these conditions for the various joints, pressure sensations were allowed to enter. The band was placed directly on the skin, the rubber cuff being omitted. The result was unexpected ; a sensation was always perceived with a weight of 10.6 g. to 12. 8 g.; regardless of where the band was placed and of which joint was moved. In fact, two sensations were present ; one of resistance which was localised where the weight struck, and one of pressure localised where the band touched the skin. This separation of the two sensations was lost with the smaller weights, with which the pressure-sensation was absorbed into the sensation of resistance. Even when thus absorbed, the pressure-sensation influenced the sensation of resistance as was proven by the following experiments. In one set the band was placed tightly around the finger, in another it was left loose, and in a third the skin was strongly com- pressed by a metal covering ; thus the pressure- sensations from the band were most delicate in the second set, somewhat overpowered in the first set, and RESISTANCE AND HEAVINESS. 265 strongly overpowered in the third set. The results were as follows.: Joint moved. Tight band. Loose band. Compression of skin. Metacarpo-phalangeal Wrist Elbow Shoulder 6o.O 45-0 IO.O 94 47-3 I 7 .8 13-8 134 over 300 33-8 20.5 14-5 In this table the two influences are apparent. Reading vertically downward we find increase^ sensitiveness as depending on the sensations o re- sistance from the various joints. Reading horizontally we see the influence of the pressure-sensations. The pressure-sensations, therefore, under ordinary circumstances, enter into our experiences of resisting bodies to a certain degree, although they are quite distinct from the sensations of resistance themselves. Goldscheider's investigations also plainly prove x that none of the other kinds of sensation, such as those derived from the muscles and the sinews, take any part in the feeling of resistance. They also prove that, on the physiological side, the concomitant processes are started in the joints. Another one of our sensations is that of heaviness. When we lift a weight fastened to a string we notice a certain feeling which we describe by saying that the weight is heavy ; what we actually feel is a more or less complicated sensation that we call heaviness. Weights can be lifted by movements where only one joint is involved, or by movements where several are involved. The former class includes those by the end joints, or by other joints when the more extreme ones 1 Goldscheider, Untcrsuchttngen ubcr den Muskclsinn, " Archiv f. Physiol." (Du Bois-Reymond), 1889, 167 to 171. 266 THE NEW PSYCHOLOGY. are eliminated by a stiff bar. The latter class involve more or less complicated relations of all the joints beyond the one at which the movement is made. The sensations in the two cases are different. When the movement is so made that it starts at first free, but suddenly receives a weight, e.g., by lifting a weight with a loose string, the effect with a single joint is merely that of a hindered movement. When this is done with several joints there is a feeling of resistance at the moment the weight is lifted. In this latter case heaviness and resistance are both present, in the former only heaviness. Goldscheider's results prove that the sensation of heaviness is quite independent of the sensations of pressure and of resistance. Physiologically it is closely connected with the tension of the sinews. Psycho- logically it enters into frequent connection with sensa- tions of movement to produce ideas of moving heavy objects, with sensations of resistance to produce ideas of inertia, and with sensations of pressure to produce ideas of supporting heavy objects. Most of our judgments of heaviness are made with the aid of movements ; we can best consider the particular experiments in a chapter on lifting weights. CHAPTER XIX. LIFTING WEIGHTS. ALL movements require the expenditure of energy in transferring the object moved. The amount of work done depends on the mass of the object moved and the distance of the movement. In moving a portion of the body we move a larger or smaller mass of bone, muscle, &c. When moving, an object the weight of this object is added to that of the portion of the body involved. The simplest case for investigation of the work involved in moving objects is that found in lifting weights. This case is of peculiar interest from the fact that with Weber and Fechner it played an extremely important part in establishing the new psychology. Weber's experiments * consisted in rinding how much a weight must be decreased in order that the difference shall be just noticeable. He found that for a \veight of 32 drachms the average difference for four persons was 3 drachms, and for a weight of 32 ounces it was not 3 drachms, but 3 ounces. In other words, the just perceptible difference for a lifted weight was not a constant amount, but was a constant fraction of the 1 Weber, " Annotationes anatomicoe et physiologicee," 81, Leipzig, 1851. Weber, Tastsinn und Gcmeingefuhl, "Wagner's Handworter- buch der Physiol.," iii. (2) 559 ; also separate, 104. 268 THE NEW PSYCHOLOGY. weight lifted. This fact of proportionality of the just perceptible difference received from Fechner the name of Weber's law. 1 Fechner began his experiments for the purpose of more accurately testing Weber's law. He soon found that the problem required a previous development of the method of experiment itself and the rules of com- puting its results. For several years Fechner regarded it as a kind of daily work to perform experiments for about an hour for this purpose. The results, as far as determining the just noticeable difference, are not of very great value, owing to the extremely complicated character of the judgments involved in comparing lifted weights. They furnished, however, for the first time, a carefully developed method for measuring judgments of this character. This method x)f right and wrong cases, as it was called, was worked out by Fechner 2 and Muller ; 3 it maintains its place as a foundation-stone of the new psychology. The method of right and wrong cases is, briefly stated, as follows : When the difference between the two weights is very small, the person lifting them will frequently judge the lighter one to be the heavier, and the reverse ; the greater the difference between the weights, or the finer the sensitiveness of the person, the greater will be the proportion of correct judgments to wrong ones. The method of right and wrong cases consists in determining the amount of difference re- quired to produce a given relation of right cases to the total number. The sensitiveness of the person lifting these weights is to be considered as inversely propor- T Fechner, "Elemente der Psychophysik," 134, 2 ed., Leipzig 1889. Muller, "Zur Grundlegung der Psychophysik," Berlin, 1878. This contains a full account with discussion. 3 Fechner, as before, 69, &c. 3 Muller, as before. LIFTING WEIGHTS. 269 tional to the difference thus found. Moreover, if Weber's law be true, this difference should be a constant fraction of the weight lifted. Take the case of two lifted weights, R, and R 2 , with a small difference, D = R r R 3 . The subject will on each occasion decide, " First greater than second," " Equal or doubtful," or " First less than second;" that is, he passes one of the three judgments D > o, D = o, D < o. Let r, g, and /, be the number of judgments thus passed in a series of n experiments ; how shall we state the results ? If there were only two judgments, the case would be simple enough ; the existence of three has led to an immense amount of discussion and to all kinds of opinions. Some people have thought it sufficient to state the percentage of right answers alone or of wrong answers alone ; this procedure can hardly be justified. Fechner and most others have divided the g cases equally between the right and the wrong, and have established a table whereby we can find, for any desired value of D, the number of right answers (including half of the g cases) for experiments under the same circum- stances, provided we know the number for any one value of D (see Appendix VIII). The troublesome question of distributing the g cases between the r cases and the / cases we can pass over entirely. The whole question has arisen solely from the fact that of two possible methods of computing results, the least appropriate one was chosen. It remained for an astronomer to put an end to the apparently endless discussion by showing that the standard methods for adjusting measurements, as employed in astronomy, physics, &c., were able to cover this case also. 1 The 1 Brims, Ueber die Ausgleichung statistischer Zdhlungen in der Psychophysik, "Phil. Stud.," 1893, ix. I. 2/0 THE NEW PSYCHOLOGY. formulas for computing the results are of interest only to the specialist, but the general idea of the method can be illustrated as follows. Suppose the true difference OD to be laid off in the line AB from the zero-point o. The difference, as observed by the subject, varies continually. There is a region Z u to Z , in which he judges D = o ; another region, Z to + oo, in which he judges D > o ; and a third, Z u to oo, in which he judges D < o. Bruns's method determines the values for Z and Z u , or the limits of the region of uncertainty, Z u to Z . This index of uncertainty is what is desired. Fechner's results I showed an approximately constant fraction only for moderately heavy weights. Later ~ i 1 I [ A Z tt O 2 Zo j Fig. 63. BRUNS'S METHOD FOR RIGHT AND WRONG CASES. experiments by Merkel, 2 whereby the just perceptibly different weight was selected from a series, showed that the fraction changed greatly for both very heavy and very light \veights, but was fairly constant for medium weights. We can thus accept Weber's law as valid, with fair approximation, for moderate weights. By making two noteworthy assumptions Fechner transformed Weber's law into a general form. The first assumption is that the just perceptible diffe- rence is a constant psychological quantity ; e.g., if the just perceptible difference is found for a weight of 10 grammes, and the just perceptible difference is found 1 Fechner, as before. 3 Merkel, Die Abh&ngigkeit zw. Reiz u. Empfindung, '/ Phil. Stud.," 1889, v. 253. LIFTING WEIGHTS. 2/1 for one of 10 kilos., the two differences mean the same thing to us mentally. If we denote the just perceptible difference in sensation by A E, Weber's law becomes, on this assumption, A E = C -p- , where C is a constant quantity. This holds good for all values of R. The second assumption is that what is true for the finite differences, A E and A R, is also true for the infinitely small differences, d E and d R. Then it X Fig. 64. FECHNER'S LAW OF THE RELATION BETWEEN STIMULUS AND SENSATION. follows that d E = C , which is Fechner's funda- mental formula. From Fechner's formula it follows by integration that E = C log R + A. At the threshold of sensation we have E = o, with a value a for R ; this gives A = C log rt; and E = C (log R log a). Using a = i as the unit by which to measure R, we have Fechner's law E = C log R. This law is represented by the curve in Fig. 64. 2/2 THE NEW PSYCHOLOGY. The intensities of the stimulus are laid off on the axis of X, and those of the sensation in the axis of Y. At a is the point where the stimulus first becomes noticeable. The intensity of the sensation thus varies as the logarithm of the stimulus. In investigating our judgments of heaviness we find that a judgment is greatly influenced by preceding judgments. Fechner noticed that after a long series of experi- ments with heavy weights, a lighter weight appeared unusually light. 1 The experiments were extended by Miiller and Schumann, who proved that as the difference between the weights lifted was made greater, the change in the estimates became greater, and that the influence of such differences diminished with the lapse of time. 2 The expected heaviness of a lifted weight depends not only on our acquaintance with it by actual lifting, but also on our general acquaintance with the looks and feeling of light and heavy bodies. When a weight looks large we expect it to be heavy. We consequently pre- pare for strong sensations when we lift it. If we do not realise these sensations, we believe it to be lighter than it really is. The reverse likewise holds true. The amount of this illusion was measured by Gilbert. 3 His object was to determine its relation to age ; his apparatus, therefore, provided for a single case, which was kept constant throughout. It consisted, in the first place, of a series of fourteen round blocks painted black ; 1 Fechner, Uebcr die Contrastempfindung, " Ber. d. k. sachs. Ges. d. Wiss., math. phys. Cl.," 1860, xii. 76. 3 Miiller and Schumann, Ueber die psycholog. Grundlagen der Vergleichimg gehobener Gewichte, " Arch. f. d. ges. Physiol." (Pfliiger), 1889, xlv. 37- ' "3" Gilbert, Researches on the Mental and Physical Development of School Children, " Stud. Yale Psych. Lab.," 1894, ii. 43, 59. LIFTING WEIGHTS. 2/3 in appearance they were all just alike, but in weight they were different. There were two other blocks, one much larger, and one much smaller than the series. The person was required to pick out that block of the series which felt equally heavy with the large block, and also that block which felt equally heavy with the small one. The true weights were, of course, unknown to him. Both the large block and the small block weighed 55 grammes, the blocks of the series ranged from 15 grammes to 80 grammes. The difference between the weight picked out for the larger one, e.g., 20 grammes, and that for the smaller one, e.g., 70 grammes, would give the effect of the difference in size between the two blocks. The difference in weight in this example would be 50 grammes, which would be the result of the difference of six centi- metres in the diameter of the blocks. The effect of the suggestion depends upon the age. In New Haven about 100 children of each age from 6 to 17 were tested by Gilbert. The average effect of the suggestion was as follows : 6 years, 42 grammes ; 7 years, 45 grammes ; 8 years, 48 grammes ; 9 years, 50 grammes ; 10 years, 44 grammes ; n and 12 years, 40 grammes ; 13 years, 38 grammes ; 14 to 16 years, 35 grammes ; 17 years, 27 grammes. For all ages the average was above 25 grammes. The suggestibility slowly increases from 6 years to 9 years ; after 9 years it steadily decreases as the children grow older. The results, when separately calculated for boys and girls, show that at all ages the girls are more susceptible to suggestion than the boys, with the exception of the age 9, where both are alike extremely susceptible. These are the average results for large numbers of children. Many young people, however, were so sus- 19 274 THE NEW PSYCHOLOGY. ceptible that the set of middle-sized blocks did not range far enough to suit them. At the age of 7 years 37 per cent, of the children declared that the large block was lighter than the lightest block, and that the small block was heavier than the heaviest. The actual difference between them was 65 grammes ; thus the effect of sug- gestion was more than the weight of the suggesting blocks. The idea involved in Gilbert's experiment has been made a subject of an extended investigation by Sea- shore. 1 Fig. 65. BLOCKS FOR MEASURING THE SIZE-WEIGHT ILLUSION. Seashore's apparatus consisted of two sets of cylin- drical blocks 31 mm. in length. Each set consisted of 17 blocks. Set A varied in size and had a uniform weight, while Set B varied in weight and had a uniform size. The blocks in Set A varied in diameter according to a series in which the regular increment is one-tenth. Those in Set B were arranged in a 1 Seashore, Measurements of Illusions and Hallucinations in Normal Life, "Stud. Yale Psych. Lab.," 1895, ii-i. I. LIFTING WEIGHTS. 275 series according to weight with a constant difference of 5 g- In the following account the blocks will be distin- guished by the names A and B with their respective numbers in the series. The blocks of Set A were of a constant weight, 80 g, and of diameters in millimetres as follows, beginning with the smallest : 20.0, 22.0, 24.2, 26.6, 29.3, 32.2, 35.4, 39.0, 42.9, 47.2, 51.9, 57.1, 62.8, 69.1, 76.0, 83.6, 91.9. The blocks of Set B were of a constant diameter, 42.9 mm., and of weights in grammes as follows, begin- ning with the lightest : 40, 45, 50, 55, 60, 65, 70, 75, 80, 5, 9> 95, 10, I0 5> no, "5, I2 - It is to be observed that the uniform weight for Set A is the same as the weight of B (9), the middle block in Set B ; and the uniform size in Set B is the size of A (9), the middle block in Set A. The observer placed himself by the table, on which the blocks were arranged in order, in such a position that by moving back and forth he could lift any block from its place in Set B and still retain approximately the same angle of the arm and hand. He was requested to select for each block in Set A a corresponding one in Set B, by taking one at a time from A and placing it by the side of successive blocks in B with which he wished to compare it, lifting one at a time until he found the one in B which he thought had the same weight as the one from A. The results are given in the following table : ILLUSION OF WEIGHT WHEN THE BLOCKS ARE SEEN DIRECTLY. A, size of the block in Set A (having a weight of 80 g.). B, weight of the block in Set B (having a diameter of 42.9 mm.) chosen as equal in weight to the block of Set A. C, number of millimetres by which the diameter in Set A differed from that in Set B. 2/6 THE NEW PSYCHOLOGY. D, grammes by which the estimated weight of the block in Set A differed from its true weight ; average of a total of twenty-five experiments on fifteen persons. MV } mean variation ; to obtain the mean variation for the series each result is to be divided by five. A B C D MV 20.0 1 10.2 22.9 + 30.2 7-5 22.0 103.8 20.9 + 23.8 7.0 24.2 98.2 -18.7 + 18.2 5-0 26.6 944 -16.3 + 14.4 6-5 29-3 94.0 -13-6 + 14.0 6-5 32.2 89.2 -10.7 + 9-2 8.0 354 86.3 7-5 + 6.3 5-o 39-o 854 3-9 + 54 4.0 42.9 83.8 + 3-8 6.0 47.2 80.4 + 4-3 + 0.4 5-0 51-9 75-6 + 9-0 4.1 4.0 57-1 71.6 + 14-2 - 8.9 5-5 62.8 69.0 + 19.9 II.O 6.5 69.1 65.8 + 26.2 14.2 6-5 76.0 64.2 + 33-1 -15-8 6-5 83.6 61.2 + 40.7 18.8 6.0 91.9 58.6 + 49-0 21.4 6-5 The general course of the illusion is shown in Fig. 66. The amount by which each 8o-gramme block differed from the middle size is laid off along the horizontal axis ; the values are taken from column C of the table. The amount by which each 42.9mm. blocks differed from the standard of 80 g. is laid off on the vertical axis. The arrangement is thus the same as that of Fig. 65. The amount of the illusion for any block is expressed by erecting an ordinate indicating the number of grammes by which it appeared to differ from the standard set. Thus the block 10.7 of column C, which weighed 80 g., appeared to be the same as a block of Set B weighing 9.2 g. more than 80 g. ; above the point - 10.7 of the horizontal axis we erect an ordinate equal to 4- 9.2 of the vertical scale. Pro- ceeding thus for all the blocks we obtain the curve of LIFTING WEIGHTS. 277 illusion as in Fig. 66. If size had had no influence, all the blocks would have been found to correspond with the weight of 80 grammes ; the curve would have coincided with the horizontal axis, as is practically the case with the G curve of Fig. 68. It is evident that there is a definite law governing the suggestive influence of size on judgments of heaviness. For the case here involved I have found l the law to be + Y INFLUENCE OP size ON JUDGMENTS OF WEIGHT DIFFERENCE IN siZE,xA-B IM MM. DIFFERENCE IN WEIGHT, v=B- A M c. ACTUAL RESULTS IDEAL RESULTS 20 Fig. 66. CURVE OF THE SUGGESTION BY SIZE. k i = ^r~ c d, where i is the amount of illusion, s is the difference in size acting as a suggestion, c is the diameter of the blocks of constant size (B series), d is the weight of the blocks of constant weight (A series), and k is a constant depending on the nature of the experiment. Thus in these experiments c was 43 mm., d was 80 g., and k was determined by the fact that the blocks were looked at while lifted, that the subject was ignorant of the illusion, &c. When the circumstances of the 1 Scripture, The Law of the Size-Weight Illusion, " Science," 1897, N.S., v. 227. THE NEW PSYCHOLOGY. experiment are changed, as in the following cases, the factor k changes ; the curve, however, still retains its character as a portion of a hyperbola, as is seen in Figs. 67, 68, and 69. Further experiments were made concerning the per- sistence of the illusion. In one set of experiments the observers were subjected to careful and attentive prac- PERSISTENCE OF THE ILLUSION OF WEIGHT A&B.FACT OF ILLUSION UNKNOWN C.FACT OF ILLUSION KNOWN 10 15 20 25 30 Fig. 67. PERSISTENCE OF SIZE SUGGESTION. tice. Iii another set the facts concerning the blocks were told to them. The results are shown in Fig. 67. A is the curve taken from Fig. 66 ; it represents the usual course of the illusion. B represents the results when each observer tried the same complete experi- ment twenty times, under similar circumstances, making two experiments each clay. No suggestion as to the degree of accuracy or success was given during the pro- gress of the experiments. The instructions emphatically LIFTING WEIGHTS. 279 expressed were : " The object of these experiments is to determine whether you can improve in the accuracy of this discrimination by practice. Do not allow yourself to be influenced in the least by memory of previous judgments or any theory of order or expected results." C is the curve when the observer knew the truth concerning the blocks, but judged them as fairly as possible. The immediateness with which the blocks were seen Ox 25 V 2 ^6^-te INFLUENCE OF size ON JUDGMENTS OF WEIGHT It. DIRECT VISIOW E INDIRECT VISION F. VISUAL MEMOHr G NO KNOWLEDGE. OF SUE Fig. 68. SIZE SUGGESTION INFLUENCED BY DIRECTNESS OF VISION. influences the amount of the illusion. When the observer looked directly at the blocks the illusion ran as in curve D Fig. 68 ; when he saw them by indirect vision the results ran as in E ; when he looked at them and closed his eyes the results ran as in F ; when he was blindfolded there was, of course, no illusion, as is shown by G. This influence of expectation is derived not only from sight, but also from other senses. Seashore made 280 THE NEW PSYCHOLOGY. experiments in which the idea of size was acquired by different means : (i) by grasping the block round its circumference (muscle sense) ; (2) by feeling it laid on the palm of the hand (touch) ; (3) by sight ; (4) by grasping it around the circumference and looking at it also. The results are shown in Fig. 69. Finally, a knowledge, or a supposed knowledge of the material of which the blocks are made also influ- IlLUSlON OF HEIGHT FROM DIFFERENT SENSES SlZE ESTIMATED BY H. MUSCLE SENSE I , TOUCH J. SIGHT D. MUSCLE SENSE TOUCH & SIGHT Fig. 69. SIZE SUGGESTION FROM DIFFERENT SENSES. ences the result. Experiments made with deceptive cork, wood, and leaden weights showed over- and under-estimation according to the disappointment of the expectation. To demonstrate such experiments before large audiences I have made a set of very large blocks. It consists -of cubical wooden boxes loaded with lead to the desired weights. The small block is a. cube LIFTING WEIGHTS. 28 1 of 8.2 cm. and the large one a cube of 60 cm., each weighing 8f Ibs. The standard set consists of cubes of 15 cm. ranging by f Ib. for each step from 2 Ibs. up to 17 Ibs. Seashore tried the experiment with this apparatus on four men with the following result : The large box was matched with boxes of 5.75 Ibs., 4.25 Ibs., 4.25 Ibs., and 2 Ibs., by the respective observers average 4 Ibs. that is, there was an under-estimation of 3 Ibs., 4.50 Ibs., 4.50 Ibs., and 6.75 Ibs. respectively average 4.69 Ibs. The small box was matched with 8.5 Ibs., 14.75 Ibs., 13.25 Ibs., and 10.25 Ibs. respectively average 11.96 Ibs. that is, there was a corresponding over-estimation of 0.25 Ib., 6 Ibs., 4.50 Ibs., and 1.5 Ibs. average 3 Ibs. This means that mainly on account of the differ- ence in size the observers made a difference of 2.75 Ibs., 10.5 Ibs., 9 Ibs., and 8.25 Ibs. respectively average 7.6 Ibs. between the two boxes, which both had the same weight, 8.75 Ibs. That is, the smaller is judged to weigh 2.9 times as much as the larger. This, it will be observed, slightly exceeds the average amount of the illusion between the extremes in Seashore's blocks. This illusion is based upon the difference in volume, but a comparison between my set and Seashore's shows that it depends very much upon the shape of the weights and whether two or three dimensions are varied. The diameters of the smallest and the largest of Seashore's blocks are in the ratio of 20 : 91.9 ; \vhile the one dimension of the boxes stands in the ratio 8.2 : 60, and still the illusion is not much stronger in the latter case. It is therefore evident that it does not vary directly with the volume. In these experiments of Gilbert and Seashore " the factors that produce such a deception of judgment seem to consist in a suggestion or, rather, a disap- 282 THE NEW PSYCHOLOGY. pointed suggestion of weight. Big things are, of course, heavier than little things of exactly the same kind. When we find two things of the same appear- ance but differing in size, the big thing must be heavier. This reasoning is all done without our suspecting it, and we unconsciously allow our judgment of weight to be influenced by the size as seen. When the eyes are closed and the weights are lifted by strings, of course there is no illusion. " Which is the heavier, a pound of lead or a pound of feathers ? A pound of lead, says the unsuspecting person, and then you guy him for his stupidity. But this poor fellow, who has been laughed at for centuries, is right. A pound isn't a pound all the world over ; it all depends on how the pound looks. A pound of lead is heavier than a pound of feathers. Try it with a pillow and a piece of lead pipe. No matter if the scales do say that they weigh just the same, the pound of lead is much the heavier as long as you look at it." 1 1 Scripture, "Thinking, Feeling, Doing," 260, Meadville, 1895. CHAPTER XX. PRESSURE. THE sensations of pressure, of which we have so frequently spoken in the last few chapters, have been made the subject of special investigations. Just as in the case of volition, we can compare our mental scale of pressure with the standard scale of weight. This has been done by Grimng 1 for several persons who gave their opinions concerning the relative heaviness of different weights. Characteristic results are shown in the figures for the two subjects. Series of weights 2 I OS 5o g 2502 1,2506 i,8oos Standard scale i 5 25 125 625 900 Mental scale, P i 2 6 17 93 315 Mental scale, K i 2 4 8 26 43 The remarkable differences between the standard scale and the personal scales are apparent. These results and those of two other subjects indicate the presence of a definite law of relation with personal constants. An important problem concerns the minimum amount of energy requisite for rousing the sensation of pressure. 1 Griffing, On Sensations from Pressure and Impact, " Psychol. Rev./' 1895, Monogr. Suppl. No. i. 283 284 THE NEW PSYCHOLOGY. A simple method of doing this is to lower small weights on the part to be tested, e.g., skin, mucous membrane, &c. x A convenient arrangement comprises 20 to 40 small discs of cork suspended from handles by fine cocoon fibres ; the discs are 3 mm. in diameter, and range in weight from i mg. upward by steps of i mg. The usual way of performing the experiment has been as follows. The discs are lowered in succession softly on the skin until one of them is felt. The lightest one felt is the least noticeable weight : the sensation from it is said to be just above the "threshold of sensation." The threshold of sensation, in this sense, lies, under these conditions, according to Weber, at about 2 mg. for forehead, temples, and back of forearm and hand ; 3 mg. for inner side of forearm ; 5 mg. for nose, hip, chin, and abdomen ; 5 mg. to 15 mg. on inner surface of fingers ; and 1,000 mg. on heel and nails. In my own experience I have found that these figures are quite too low for most people. For the inner side of the hand, for example, the threshold ranges from 12 mg. to 20 mg. Some people cannot feel even the 20 mg. disc on the hand or fingers. Tests with these discs do not afford a measurement of one of the factors involved in applying them, namely, the velocity with which they strike the skin. A disc will sometimes be felt, or not, according as it is lowered more or less gently. The energy involved in the application of the disc depends not only on the mass of the disc, but also upon the velocity of its motion. 1 Aubert and Kammler, Untersuchungcn ubet den Druck' und Raumsinn dcr Haut, Moleschott's " Untersuchungen," 1859, v. 145- PRESSURE. 285 Measurements of the energy of the stimulus corres- ponding to the threshold of pressure have been made by Blix. 1 The apparatus used comprised a straw 10 cm. long, fastened to a light horizontal axis. On the end of the straw, a piece of horsehair was fastened with wax. This was perfectly balanced by a wire. When the wire was bent sidewise over the scale, the centre of gravity was thrown out of the axis along the line of the straw. When the straw was raised to a certain height, and then allowed to fall, the hair struck the skin with an energy depending upon the position of the centre of gravity and the height of fall. The scale served to in- dicate the position of the centre of gravity. The scale for the apparatus was established by deter- mining how stiffly a spring had to be stretched in order to just yield when the horsehair struck it ; and by then finding how many grammes of weight were required to make the spring yield. Blix found that, on the most sensitive spots on the back of the hand, the threshold was at a point indicated by a pressure of 0.20 g., while on the middle of the lower arm it was 0.33, and on the thigh 1.30. These most sensitive spots he calls pressure spots. In the spaces between these spots, the threshold is very much higher.- For example, at a certain group of spots on the back of the hand, the threshold was at 0.23 g., while just between these spots 1.5 g. produced no noticeable sensation. What is this threshold ? Is it the sensation from a certain weight such that all heavier weights are felt, and all lighter ones not felt ? No, there is no such 1 Blix, Experimentclle Beitrdge zur LQsung dcr Frage fiber die spcdfische Energie der Hctutnervcn, "Zt. f. Biologic," 1885, xxi. (X. F. iii.), 145. . 286 THE NEW PSYCHOLOGY. weight ; the weight that is felt in one experiment is not felt in another. To illustrate what is meant by the threshold let us suppose the results of thousands of experiments to lie before us. Each experiment consisted in the appli- cation of weights in succession, from i mg. to 20 mg, We would have records similar to the following one, /.OO o.fo $ so & zo Fig. 70. PROBABILITY CURVES FOR THE PRESSURE THRESHOLD. where a star * means that the weight was felt, and a dash that it was not. Weights i 2 3 4 5 6 7 8 9 10 ii 12 13 14 15 16 17 18 19 20 Exper. i *_***__**_**** The total number of occurrences for each weight is to be written at the bottom. On the horizontal line PRESSURE. 287 in Fig. 70, we lay off the weight units in milligrammes. We then erect ordinates proportional to the number of times each was felt ; as a basis for this proportion it is convenient to take i.oo, and we therefore express the percentage of times each was felt. Connecting the ends of the ordinates, we get a curve of the form I. Each weight has been felt a certain proportion of the time. Certain extreme weights have been felt all the time. Shall we take the weight that is felt all the time as the threshold ? As we increase the number of experiments, we find that this weight is liable to slowly become greater ; we could not point to any particular weight as the first one that would be always felt as the lightest one. We assume, however, just as in Chap. II., that anything that happens 0.999988 times out of a i.oooooo is practically certain to happen j we therefore pick out this weight as practically sure to cause a sensation ; it may be called the " upper thres- hold." In like manner we pick out the weight that fails to be felt, 0.000022 times out of i.oooooo ; this is the "lower threshold." There is still another value entitled to be called the threshold ; this is the one corresponding to the weight that is felt half the time, or the " median threshold." This median threshold holds a peculiar position. We may conceive the threshold of sensation as really a constant quantity, and the par- ticular values obtained in the experiments to be brought about by a multitude of interfering phenomena, which cause the results to fluctuate. The threshold is hereby treated as analogous to the true value of a quantity in physical measurements. In measuring the length of a line the results will disagree, provided the method be fine enough, as explained in Chap. IV. ; we assume that there is some true value, which would be attainable with in- finitely accurate methods. In a statistical problem we 288 THE NEW PSYCHOLOGY. assume that there is an ultimate value toward which, with finer methods and greater numbers, the quantity tends. The upper, the median, and the lower thres- holds are similarly quantities toward which the 0.0022 %, the 50 %, and the 99.9978 % values tend to settle as the number of experiments increases. Aside from this there are no reasons for considering any values rather than others as the thresholds. The three thresholds will differ under different condi- tions for different persons, &c. For one condition the curve may run as shown in I. (Fig. 70), for another as in II., for still another as in III. Persons or conditions whose thresholds are lower are said to be " more sensitive," and likewise the reverse. We. have every reason to believe that the curve of results for an extended series of careful experiments would follow the law for *'(>) (see Appendix I.), where y-h D, D being the amount of the weight and h a quantity indicating the subject's fineness of sensation. For any given subject or condition we would, therefore, know the frequency of occurrence for each value as soon as we had determined it for one of them. In this explanation of the threshold we have supposed the number of experiments to be practically unlimited. In actual work, the number of experiments is not large. It is thus impossible to pick out directly the upper and lower thresholds. The median threshold can be picked out directly as the middle value M (p. 46). Of course, as the number of experiments is limited, there is a degree of uncertainty attached to it. This degree of uncertainty can be indicated, as in Chap. II., on the supposition of the validity of the * (r) law for this case. On a similar supposition we can also deduce the upper and lower thresholds as follows. The general experience of science since the* time PRESSURE. 289 of Gauss, 1 in dealing with fluctuations of the kind \ve find here, has tended to the universal justification of $ (y) ; we are therefore entitled to assume its validity here, until experimental evidence to the contrary is produced. To find the upper threshold we refer to the table for * (y)- For the value occurring 50 % of the time we find y' = 0.4769, and for that occurring 99.9978 % we find y" = 3.0000. If the median threshold M corresponds to y', the upper threshold will be V M = 6.2906 M ; and by analogous reasoning the lower will be 0.00004 M. A very useful practical threshold is the quartile value. 2 The over- and the under-quartiles are those values above or below which 25 % of the results lie. With a very uncertain median the quartiles will be very distant, and likewise the reverse. With $ (y) as valid for the particular set of experiments, the over-quartile Q will be equally distant with the under-quartile q, from the median M, i.e., Q M = M q. The usual method of determining the threshold differs from those we have used by stopping at the first weight felt. Thus, in the example given above, the experimenter would stop with the weights 4, 3, 5, . . ., 3 and would not use any beyond the first one felt. The results for the smallest weights are then averaged. What is meant by the value thus obtained ? If in all cases every weight were felt beyond the first one, the average for the first ones would as a consider- ation of the * (y) curve will show be theoretically, for an unlimited number of experiments, the same as the median threshold. But the weights beyond the lightest 1 References and psychological applications are to be found in Scripture, On Mean Values for Direct Measurements, " Stud. Yale Psych. Lab.," 1894, ii. i. 2 Galton, Statistics by Intercompnrison, "Phil. Mag.," 1875 (4), xlix. 33. 2O 2QO THE NEW PSYCHOLOGY. one are not all felt. Just what is the relation between the first weight felt and the median threshold, I am at present unable to say. Theoretically, I suppose, this weight corresponds to the smallest one in a series of observations, and holds to the median threshold the relation expressed by 5 = -~ i M where s is the average first weight, M the median threshold, and n the number of experiments. At any rate it is a questionable quantity. The next problem in investigating sensations of pres- sure is that of the just noticeable difference. This is the amount of difference that can be made in a given pressure before the difference is noticed. Most experiments have been made (i) by applying weights in succession to the same spot until two weights were found whose difference was great enough to be noticed ; (2) by applying in succession weights having certain small differences, and noting the proportionate number of times in which this difference was noticed. The latter method is similar to the method of right and wrong cases described in Chap. XIX. The former method will now be described ; it brings out many prominent characteristics of psychological procedure. The experiments are generally made in the following way. Weights just alike in size are provided, but in- creasing and decreasing in weight regularly from a given standard. For example, from a standard of loog. the set will run upward and downward by steps of i g. The standard is applied, say, to the palm of the hand, the hand being supported on a cushion ; it is removed, and, after about 2 sees, the next weight, 101 g., is likewise applied for an instant. The subject immediately states whether the second weight felt lighter than, or heavier than, or the same as the first. After a short rest the standard is again used ; then the 102 g. weight is applied. PRESSURE. 291 In a similar way the weights 103 g., 104 g., &c. are used, till a difference has been detected several times in succession. Then the experiments are repeated, begin- ning with a definitely heavier weight than the standard, and proceeding downward till the difference has re- mained unnoticed several times in succession. In a similar manner the weights lighter than the standard are used. The record will look like the following : W 101 IO2 I0 3 I0 4 IO, 106 107 108 109 no >4 I 5 \1/ -t w 99 98 97 96 95 94 93 92 9 1 90 f : = \j A - Standard : 100 g. ; standard first. W= weight applied. The signs =, >, < indicate the judgments of W as compared with standard ; ^ indicates the order in which the weights of W were used. The short lines indicate the limits within which the subject seems to be uncertain as to the difference. The weight, which is just at this limit is to be considered as just perceptibly different. The difference between it and the standard is the just perceptible difference. In the record given the just perceptibly greater differ- ence when going away from the standard is do=6, when going toward it d^=5; the just perceptibly smaller difference is cV, = 8 away and d^ = 6 toward. We notice that when going away from equality, the difference remains longer unnoticed. Experience proves this to be a regular phenomenon ; the law governing it in its 292 THE NEW PSYCHOLOGY. dependence on the standard, the size of the successive differences, &c., has not been established. The just perceptibly greater difference is d = d + d =5 ; the just perceptibly smaller difference is d u du + d " - 7. We 2 cannot, however, compare d with d u until we perform another experiment with the standard weight last. The record for the second set will have this appear- ance : W 101 102 103 104 105 106 107 1 08 109 no = > W 99 98 97 96 95 94 93 92 90 Standard: ioog.; standard second. It therefore makes a difference whether the standard is placed first or second. If we wish to eliminate this difference in order to obtain the just perceptibly greater and smaller differences, we take D =- : =7, i I $ and D u = ""* u = 6. This illustrates a generally observed fact that the just perceptible difference is less on the side of smaller than on the side of greater. If, however, we wish to determine the relation of the second weight to the first one, we remember that adding d to ioog. gives the just noticeably greater weight and subtracting PRESSURE. 293 d u from loog. gives the just noticeably smaller weight. Thus 105^-g. and 93 g. are the just noticeably different weights ; the weight lying midway between them is 99 J g. when the standard is first. When the standard is second the weights are io8Jg. and 95, and the middle weight is ioi}g. This illustrates the general law that when tw r o weights are compared the second is over-estimated. The psychological processes involved in experiments on the just noticeable difference can be brought out by various methods of procedure. In fact, the chief interest of these experiments lies, not in finding a definite figure for the just noticeable difference, but in observing how this difference changes with the varying mental attitude. What is measured in such experiments is not a fact of sensation, but the accuracy of judgment, the attitude of expectation, the quality of self-reliance, &C. 1 These facts have been generally overlooked, and the experimenters have sought to eliminate the influence of the mental attitude. Consequently, in discussing the just noticeable difference, we seldom have the necessary data for a full understanding of it. In the records just given, the subject knows how the experiments are carried out, or carries them out himself : this is the " conscious " method, approved by Fechner. By changing the method of experimenting we can change the subject's mentttl condition. A mere glance at a record sheet frequently suffices to tell what this attitude was. Suppose we say to the subject : the weights are to be 1 It may seem a strange statement, but it is true that in these methods we possess the means of measuring such apparently inaccessible mental processes as faith, honesty, and the like. The proper development of the methods is still in the future. 294 THE NEW PSYCHOLOGY. given you in regular order, but you will not know whether they will run toward greater or toward less. We get a record of this sort where, for brevity, only d^ and d t ', are given : W 101 102 I0 3 IO4 105 106 107 108 109 no W 99 98 97 96 95 94 93 92 9 1 90 We see at once the effect of uncertainty as to which way the weights are to change. This is called the " partly unconscious " method. Suppose, again, we say : the weights are to be given you in an utterly irregular order. Then, if we actually carry them out in regular order, unknown to the subject, \ve get a record where the mind is in an unprejudiced condition. The judgments will be more irregularly distributed ; for example : W TOI 102 103 IO4 105 I O6 107 1 08 109 no W 99 98 97 96 95 94 93 92 9 1 90 This is the " unconscious method." The values for the PRESSURE. 295 just perceptible difference may be the same as those with the partly conscious method ; they will be larger than with the conscious method. The decrease of the values from the just perceptible differences in the con- scious, as compared with the unconscious, method gives us the effect of the mental attitude of confident expec- tation. Let us now consider the relation between the method of finding the just perceptible difference and the method of right and wrong cases explained in the previous chapter. Within the doubtful region marked off by the short lines, the values with the unconscious method are very irregular. The various influences that hinder us from detecting small differences are continually changing. If, instead of changing the weights in the last experiment, we always give to the unsuspecting person the standard of 100 g., we get a record of this character : =, <, <, = , >, =, = <, >, >, =. We have here passed to the method of right and wrong cases. We get a number of judgments in which the first weight is judged to be > , others in which it is = , and others in which it is < the first. Now, suppose that we use the two weights 100 g. and 101 g., the subject will, in a long series of experiments, show an excess for >, with less for <, together with a certain number of = . If 102 g. be used, the differences will be still greater, and, as the weight compared with the standard becomes 103 g., 104 g., and still more different, the > prepon- derate still more at the expense of = and <, till finally all judgments are >. Instead of carrying out the experiment with suc- cessively different weights, as just described, we might select a certain pair of weights, say, 100 g. and 296 THE NEW PSYCHOLOGY. 105 g., and determine the relative proportions of >, =, and <. This is the method which has been called the method of right and wrong cases. It is evident that, if one person is more sensitive than another, he will give more > judgments, or "right cases." 1 We must now turn to a new psychological quantity ; the least noticeable, or just perceptible, change in pressure. Experiments on the just perceptible change in pres- sure from o, i.e., on the least perceptible pressure, have been made by Hall and Motora, 2 who used a little car running along a scale-beam at definite rates. The pres- sure was thus regularly increased or decreased from any desired initial pressure. The following is a charac- teristic result. With a rate of change of yf^- per second, the just perceptible change (average of increase and decrease) was found for Motora to be Initial weight . . . . 5 10 20 30 40 50 60 65 70 75 too 200 500 Just perceptible change 3.5 5.15 7.8 7.9 13.3 13.0 14.0 14.5 15.4 17.5 27.9 54.4 163.4 Ratio 1.7 1.5 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.3 1.3 The just perceptible change was thus almost exactly a constant fraction of the initial weight. Starting with an initial weight of 50 g., the just per- ceptible changes with different rates for Motora were Rate T VV its ii'3 T-IO i^rs aTo ^no Just perceptible change 22.0 14.6 13.0 9.3 9.1 6.8 6.6 Ratio 1.4 1.3 1.3 1.2 1.2 I.I i.i There is thus a decrease in the amount of the just per- ceptible change as the rate was made slower. 1 The rules for calculating the results obtained by this method are to be found in Bruns, Ueber die Aiisgleichrung statistischer ZiiJil- ungen in der Psychophysik, "Phil. Stud.," 1893, ix. i. See p. 268. 2 Hall and Motora, Dermal Sensitiveness to Gradual Pressure Changes, "Am. Jour. Psych.," 1887, i. 72. PRESSURE. 297 The problem has been taken up for further treatment 1 by Dr. C. E. Seashore, of the Yale Laboratory. His apparatus is constructed on the principle that a body immersed in water decreases in weight in proportion to the extent to which it is immersed. A light and care- fully balanced scale-beam has a brass rod suspended on each end. On the lower end of one rod stimulating points of any size may be placed ; the other rod hangs inside of a large glass tube, in which a column of water may be raised or lowered at any desired rate. At the lower end of the glass tube is a U-shaped tube in which nozzles of various sizes may be inserted to regu- late the size of the flowing stream. Water is conducted through a hose from a reservoir on an upper floor. The head of the stream being kept constant, the rate of flow is regulated by the size of the nozzles. As the immersed rod becomes lighter owing to the rise of the water, the other rod becomes proportionately heavier. The height of the column of water is read off on a mm. scale, and the amount of change in pressure may easily be com- puted from the known amount of water displaced by the rod. This apparatus solves the problem of getting a gradual change of pressure at any desired rate with- out jarring the stimulating point. The first series of experiments was made to find the least perceptible change for various rates of increase. The spot investigated was the outer side of the index finger at a point midway between the second and the third joints, with a circular area of stimulation 5 mm. in diameter. The initial stimulus was 5 g. Hence the only varying quantity was the rate of increasing the 1 The account of the extensive investigations of Stratton, Ucbcr d. Wahrnehmung v. Drnckiinderungcn bei verschicdcner Geschiviu- digkciten, " Phil. Stud.," 1896, xii. 525, was consideration here. W OF THE UNIVERSITY 298 THE NEW PSYCHOLOGY. pressure. The method of experimenting was as follows : The observer having adjusted his hand on a special hard rubber support, by which the index linger would be kept still and yet be free from any surrounding con- tact, the stimulating point (having a pressure of 5 g.) was placed on the selected spot as gently and quickly as possible after a signal. About two seconds after the point had been placed a second signal was given, and the stimulus began to increase. The observer knew nothing about what rate was to be chosen in any trial ; he was simply asked to give a signal when he was sure the stimulus had increased. Five rates were used, and the trials were so distributed as to eliminate the effect of fatigue in summing up the results for comparison. TABLE. A 0.036 0.220 0.570 0.965 1.326 B 3-2(1.8) 6.5(2.4) 94(2.8) 10.6(2.4) 12.1(2.9) C 17.7 5.9 3.2 2.2 1.8 The table gives the results r of the experiments on thirteen observers, being the averages from ten trials by each observer on each rate. Thus each figure in the record represents 130 single trials. The figures in the horizontal line A give the part of the initial stimulus by which the pressure increased per second ; B gives the number of grammes to which it was necessary to increase this stimulus in order that the increase should be felt. The mean variations are indicated by the figures in parentheses. C indicates the number of seconds during which the stimulus increased before the change was perceived. These results are represented in Fig. 71, where the amount of increase per second is marked off proportionally on the abscissa. It also represents the proportional part which the increase per second 1 To be found in detail in " Stud. Yale Psych. Lab.," 1896, iv. PRESSURE. 299 12.1 10.6 9.4 6.5 3,2 was of the initial stimulus. The amount of increase in grammes is indicated on the vertical axis. The previously noticed law is here confirmed. Within the region here investigated the sensitiveness to change increases as the rate decreases. But this is true only for moderate rates. It is interesting to note how the curve must be deflected at both ends if continued. The slowest rate here used is the slowest rate by which the pressure can be increased and yet be detected by the observer. From other experiments we may infer 0.036 0.220 0.570 0.965 1.327 Fig. 71. DEPENDENCE OF THE LEAST NOTICEABLE CHANGE ON THE RATE OF CHANGE. that in the short distance between rate 0.036 and o the curve must rise abruptly to a very high or indefinite point, i.e., when the increase in pressure is sufficiently slow it may be continued indefinitely, or until it becomes painful without a distinct sensation of pressure. The fastest rate is the fastest rate that can be used in accurate measurement by the present method. To investigate the variation with the rate between this rate and instan- taneous increase of the pressure, Dr. Seashore has constructed two compound scales, by means of which very rapid rates of increase may be produced and 300 THE NEW PSYCHOLOGY. measured, and by the other an instantaneous increase of the initial stimulus may be made without taking off or placing any weights on the stimulating point. Suffi- cient results have not been obtained on the former point to allow any generalisation, but for instantaneous addition of weight to 5 g. two seconds after it was applied seven of the thirteen observers in the previous experiment perceive on the average 0.35 g. This amount is indicated by the mark over the dotted line in the curve, which shows that the curve must descend abruptly from the highest point to this, the lowest. These two abrupt deflections of the ends of the curve in opposite direc- tions show how important and complex the one factor of the rate of change in pressure may be. How great the just perceptible change can be made to become by making the rate of change extremely slow is a matter that still remains for investigation. It is worthy of note that it has been found possible in 5J hours to actually crush a frog's foot, without a sign that the pressure was felt, by screwing down a button at the rate of 0.03 mm. per minute. A similar experiment showed that a live frog can actually be boiled without a movement if the water is heated slowly enough ; in one experiment the temperature was raised at the rate of 0.002 C. per second, and the frog was found dead at the end of 2j hours without having moved. 1 If a frog can be crushed or boiled without any evidence that he has noticed it, it is at least an interesting 1 The literature on these experiments with frogs includes Heinzmann, Ueber die Wirkung sehr alluutliger Aendenuigen thermischer Reize aitf die Empfinduugsnerveu, " Archiv f. d. ges. Physiol." (Pfluger), 1872, vi. 222. Fratscher, Ueber conti nuirUche und langsame Nervenreizung, " Jenaische Zeitschrift," 1875, N. F. ii. 130. Sedgwick, On the Variation of Reflex Excitability in the Frog induced by changes of Temperature, " Stud. Biol. Lab., John Hopkins Univ.," 1882, 385. PRESSURE. 301 question of what can be accomplished in this direction with human beings. This whole question of the just perceptible change and its dependence on the rate has just begun to receive recognition as one of the most fundamental questions of psychology. The general problem can be stated in the following way. Starting with the initial stimulus r (pressure, tone, light), we cause one of its properties, i (intensity, extent), to change at the rate of u = ^. The just perceptible change will be D = f (r, ^). This is the problem of the law of the just perceptible change J ; its particular form remains to be determined. It is a fundamental law of mental life and has far- reaching consequences. 2 Finally, there is another mental quantity closely related to the just perceptible change, namely, the just percep- tible acceleration of the change. Suppose the pressure in the experiments mentioned above to be steadily changing at a noticeable rate ; how great an accelera- tion or retardation in this change is required in order to be noticed. This acceleration to continue the example just given is u' = ^, and its law would be given by the determination of A= f (r, v*' S A J. I have observed this quantity A in experiments on the pitch of tones,3 but have not yet been able to measure it. No data are at hand concerning the just perceptible acceleration for pressure. 1 Scripture, The Method of Minimum Variation, "Am. Jour. Psych.," 1892, iv. 577. Ibid., Ueber die Aenderungsempfindlichkeit, "Zt. f. Psychol. u. Phys. d. Sinn." 1894, vi. 472. 2 Preyer, Die Empfindung als Fnnktion der Reizfliidentng, " Zt. f. Psychol. u. Phys. d. Sinn.," 1894, vii. 241. 3 Scripture, On the least Perceptible Variation of Pitch, "Am. Jour. Psych.," 1892, iv. 579. CHAPTER XXI. PAIN. PAIN has been asserted to be a special kind of sensation, or a noticeable degree of the obscure sensations from the bodily tissues, or the exaggerated degrees of all sensations, or the extreme degree of dislike, &c. We must here, however, treat the not very extensive collection of experimental data in a manner independent of theories. As the intensity of a sensation is increased from zero upward it generally reaches a point at which it becomes disagreeable (or agreeable), and still further onward a point where it becomes painful. The relations between the threshold of sensation, the threshold of disagree- ableness, and the threshold of pain, can be illustrated by the following experiment : The current from a battery runs through the primary circuit of an inductorium with its vibrator ; the cords from the secondary circuit end in' two electrodes, a large one to be held in the hand, and a small one to be applied to the point of the finger. The secondary coil is started at some distance from the primary, and is slowly moved toward it. Instructions are given to the subject to say, (1) when he first feels a sensation from the electrode ; (2) when the sensation first becomes disagreeable ; and (3) when it first becomes painful. The experimenter records the position of the secondary coil, and conse- quently the strength of the current at each of these points. The reader has probably made to himself the remark usually made by persons before beginning the 302 TAIN. 303 experiment : namely, that it will be easy enough to tell when the sensation is first felt, and also when it becomes painful, but that disagreeableness is too indefinite to be determined. Let us suppose, however, that ten experi- ments have been made on such a person ; we have the means of obtaining a numerical expression for this indefiniteness namely, by finding the mean variation. The following is a characteristic average of ten ex- periments on one subject : threshold of sensation, 105, MV 4.2 ; threshold of dislike, 95, MV 3.7 ; threshold of pain, 82, MV 4.2. The figures indicate the number of millimetres by which the secondary coil was distant from its most effective position. Experiments on over twenty students gave very similar records ; the mean variation was generally about the same fraction of the threshold in all three cases. The conclusion is amply warranted that " dislike " is as clear and definite a result of a stimulus as sensation or pain. The further consideration of the feelings of dislike and liking will be found in the following chapter. Experiments have been made on pains produced by pressure. The pressure algometer consists essentially of a strong spring by means of which a rubber disc or point is pressed against the surface to be tested. Some experiments of this kind made in New York City gave the following results in kilogrammes I : Subjects 50 boys. 40 College 38 law 58 40 college stu- students (men) students women dents (women) Ages 12 to 15 16 to 21 19 to 25 l6t022 Average 4-8 5-1 7.8 3-6 3-6 1 Griffing, On Sensations from Pressure and Impact, 14, "Psych. Rev.," 1895, Suppl. i. 304 THE NEW PSYCHOLOGY. The question of the relative sensibility of men and women to pain is of interest in connection with the greater power of recovery from injury that is found in women. The facts reported have been summarised by Ellis. 1 Sensations of pain, as well as of pressure, can be produced by the impact of falling bodies. A box containing a weight is allowed to fall upon the palm of the hand. It is guided by grooves without appreciable friction ; the part that strikes the hand is i cm. in diameter. Experiments by this method 2 gave for one observer an average 1,670 gramme-centimetres, and for another observer 935 gramme- centimetres as the energy necessary to just produce pain. At this point we must leave the subject of pain. Practical acquaintance with its various forms and com- plications is a part of the duty of every physician ; but a scientific study of its psychological laws has only been begun.s 1 Ellis, Man and Woman, 120, London, 1894. 2 Griffing, as before, p. 55. s A summary of the present knowledge concerning pain is to be found in Goldscheider, "Ueber d. Schmerz," Berlin, 1894. CHAPTER XXII. FEELINGS. UNDER the head of " feeling" we shall consider the two mental states which we express as " dislike " and "liking," or "disagreeableness" and " agreeableness." The various views concerning these phenomena: that they are properties of sensations like intensity and quality, that they are separate sensations, that they are unconscious reasonings, that they are relations between ideas, &c., are not, in the present state of our experi- mental knowledge, proper subjects of discussion here. It is the duty of the psychologist to present the thoroughly proven data concerning " dislike " and " liking " as far as possible, and to suspend judgment concerning the various theories until further data are obtained. In the previous chapter an experiment was described wherein it was shown that an electrical stimulus at a certain intensity aroused a sensation of touch, that as it increased in intensity a feeling of disagreeableness was added, and that beyond a still higher point a sensation of pain was also added. Similar experiments might be but have not been made on the various stimuli that produce disagreeableness and pain. The question now arises concerning agreeableness. Agreeableness is connected with disagreeableness by 21 3 c5 306 THE NEW PSYCHOLOGY. many facts of every-day life, by language, &c., neverthe- less they are two distinct phenomena. The electrical stimulus described may not at any intensity become agreeable, although at a certain intensity it does become disagreeable. On the other hand, another stimulus, e.g., a colour from the spectrum, may, as its intensity is increased, become agreeable at a certain point and remain so until it becomes painful. Again, there are certain sensations that are always agreeable. Finally, there are portions of the body to which the application of an object produces simply and solely a feeling of agreeableness without any sensation of pressure. The method for measuring disagreeableness and agree- ableness has not yet been found. All that we can do is to pick out what stimuli are accompanied by agreeable- ness or by disagreeableness, and also to pick out those that are most agreeable or disagreeable. According to general observation bright colours, clear sounds, certain tastes, odours, and touches are agreeable, while dull colours, harsh sounds, other tastes, odours, and touches are disagreeable. Moreover, various forms and combinations of colour, as in architecture, painting, and decoration ; various combinations of sounds, as in music ; and various combinations of odours and tastes, as in a well-arranged dinner, are considered agreeable, while others are not. The first to attempt to obtain systematic data on what are the most agreeable subjects was Fechner. 1 Experimental aesthetics, as these investigations have 1 The following account of his work is taken as far as possible in the original words from Fechner, Zur experimentalcn Aesthetik, " Abhdl. d. k. sachs. Ges. d. Wiss., math.-phys. Cl.," 1871, ix. 555 ; Ibid., " Vorschule der Aesthetik," ch. xiv., Leipzig, 1876 ; Ibid., Wie es der expcr. Aesthetik seither ergangen ist, " Im neuen Reich," 1878, Nos. 28, 29. FEELINGS. 307 been called, arose from discussions concerning the "golden cut." The " golden cut" is an expression of the relation between two quantities whereby the smaller bears the same relation to the larger as the larger bears to the sum of both, i.e., as i to 1.618. This relation has been asserted to be the fundamental law in the divisions of the human form, in the proportions of the higher animals, in the construction of the plants, in the forms of various crystals, in the arrangement of the planetary system, in the proportions of the most beauti- ful productions of architecture, sculpture, and painting, in the most satisfying accords of musical harmony and, finally, in the construction of a great universal compara- tive science of nature. 1 Is the " golden cut " really the most agreeable relation for forms ? this is the question that Fechner asked. To answer it he used three methods. For the " method of choice " he placed thin rectangles of white cardboard with a constant area before many persons and required each subject to point out which impressed him as the most agreeable one, and which as the most disagreeable one. For the "method of application" he measured the most various rectangular objects to be found in daily life where the relation between the parts was not determined by the use, e.g., visiting cards, paintings. For the " method of production " the subject drew figures in the proportions most agreeable to him. Fechner's results have been briefly stated by himself as follows : 1. The aesthetic value of the "golden cut" has been much exaggerated, but nevertheless it is to be recog- nised as valid under certain limitations. 2. That for the sides or dimensions of rectangles it 1 Zeising, " Das Normalverhaltniss der chemischen und morpholo- gischen Proportionen," Leipzig, 1856. 308 THE NEW PSYCHOLOGY. has an indubitable precedence before all other relations, but yet not so emphatically before relations that differ slightly from it. 3. That the " golden cut" is decidedly at a disad- vantage as compared with the relation of i to i for the division of horizontal objects and of i to 2 for the relation of the upper to the lower part of crosses. An example of the modification of forms in the tendency toward this relation is found in the grave- crosses (in- stead of grave-stones) of Germany and in ornaments in the form of a cross. The model for all these is the crucifix. Fechner's measurements of jewellers' crosses showed that the cross-piece of the crucifix stands too high to produce a pleasing division between the upper and the lower parts of the upright and that the relation in the ornamental crosses was as i to 2. In the grave- crosses the crosspiece stood a little higher than in the ornamental crosses, but still not so high as in the crucifixes. These experiments by Fechner remained the only ones until the problem was taken up by Witmer, who made use of an improved method of choice. 1 It was found possible to establish the main points of the curve of aesthetic pleasure for simple forms. For example, a series of rectangles was submitted to a subject with the demand as to which were the most displeasing ones, which the most pleasing, which the apparent square, which the figures just as pleasing as the apparent square, &c. Experiments on seven persons gave, for the rect- angle, closely agreeing results. If on the X axis we start with a true square and suppose this to gradually lengthen, we can indicate the curve of resulting aesthe- tic pleasure as in Fig. 72. The real square i : i is 1 Witmer, Znr experimcntellcn Aesthetik einfaclicr riiumlidicr Formverhc'iltnisse, "Phil. Stud.," 1893, ix. 96, 208. FEELINGS. 309 disagreeable, the apparent square i : 1.030 is very agreeable ; the most agreeable figure is i : 1.651 ; the figures just as agreeable as the apparent square are i : 1452 and i : 2.201 ; the most disagreeable figure is i : 1.181 and the next most disagreeable one is i : 3.090. These and similar experiments on crosses, ellipses, &c., showed with substantial agreement that the most agreeable figure is better expressed on an average by i : 1.65 than by the " golden cut" i : 1.62. There is no reason for preferring the " golden cut " to the empiric- ally established relation unless a mathematical mysti- cism be such. We can therefore accept i : 1.65 as in general the best value. Fig. 72. CURVE OF AGREEABLENESS FOR RECTANGLES. The investigations of Fechner and Witmer were followed by Cohn's experiments on the feelings con- nected with colours. 1 Pure, brilliant colours were obtained from light trans- mitted through various combinations of coloured gelatine. The colours appeared in pairs as small rectangles in the wall of a darkened chamber. The subject stated which of two colours or combinations produced the stronger feeling of agreeableness. From the results it was possible to determine the relative degrees of agreeable- ness of the various colours and their combinations. The conclusions were drawn from experiments on fifteen 1 Cohn, Expert mcntdle Untersiichungcn fiber die Gcfiihlsbetonnng dcr Farben, Hclligkelien und ihrer Combinational, " Phil. Stud.," i8i;j, x. 562. 3IO THE NEW PSYCHOLOGY. subjects. With colours of the same purity and brilliancy the relative agreeableness of one colour as compared with another seemed to be a purely individual matter. The law of agreeableness for pairs of colours can be expressed in the following manner. If the colours be arranged in a circle with complementaries (pairs of colours that in certain proportions produce white) at the ends of diameters, a combination of two colours increases in agreeableness as the colours are chosen further apart, the maximum agreeableness appearing for complementary colours. This is expressed in Fig. 73, in which the circumference of the circle is supposed to /80 360 Fi g- 73- CURVE OF AGREEABLENESS FOR PAIRS OF COLOURS. be rolled out into a straight line. One of the colours is supposed to be stationary at o ; the curve of agree- ableness rises as the other colour changes to more distant hues, reaches a maximum for 180, and sinks as the second colour again approaches the hue of the first. Experiments with colours mixed with white (light grey) and black (dark grey) showed that of two shades of the same colour the purest one was preferred. As for combinations of greys, the results were the more pleasing as the greys became more different. This held good as far as the limits of the experiment extended, namely, for white cardboard combined with black paper, the relative intensities being as 40 to i. FEELINGS. 311 The general law seems to be : the greater the differ- ences between colours the greater the feeling of agree- ableness. " Of course this is valid simply as a matter of sensory pleasure without secondary factors. Now the preference for strongly contrasting combinations is considered to be in general the mark of the more savage nations, and of the uncultured classes of society. When we find the same preferences among cultivated persons whose eyes have been accustomed to dull colours and small contrasts in clothing, &c., we have a passable justification for considering the rule as a general one. Former philosophers and aesthetical theorists were inclined to consider the highest ideals of beauty as universal for mankind, whereas the sensory pleasures were regarded as fluctuating and dependent on in- dividual caprices. Is not our psychological knowledge leading us gradually to the opposite result ? It seems entirely plausible that the sensory constitution of man is a fundamental and original one, whereas those com- plicated mental relations, on which higher sesthetical pleasure rests, vary with race, civilisation, and culture. But we have here already left the domain of facts and have anticipated future investigations." x It is a noteworthy fact that, in contradiction to these psychological laws, to the natural tastes as exhibited by children and by the southern nations, we people of the English race decorate our towns, our homes, and our persons with the dullest combinations we can find. Any one who attempts to put a little life into our colours is decried as an uncultured being. As Ruskin says : "The modern colour enthusiasts who insist that all colours must be dull and dirty are just like people who eat slate-pencil and chalk and assure everybody that they are nicer and purer than strawberries and 1 Colin, as before, p. 601. 312 THE M;\\ PSYCHOLOGY. plums. The worst general character that decorative colouring can possibly have is a prevalent tendency to a dirty yellowish green, like that of a decaying heap of vegetables. It is distinctively a sign of a decay of colour appreciation." We may remark in passing that the instinctive love of the child for bright colours is, in many American schools, systematically subjected to a process of deformity-making till he learns to prefer the dull and dirty combinations. With the facts related in this chapter our experimental knowledge of the psychology of feeling comes to an end. As "for the mental states known as " emotions," e.g., fright, joy, &c., which are closely connected with strong feelings, we have no accurate knowledge what- ever. The effects of various emotions on the circulatory system have been investigated by Mosso and others ; but the methods have not been arranged so as to obtain any facts concerning the psychology of the emotions beyond ordinary qualitative knowledge. The sphygmo- graph, plethysmograph, pneumograph, sphygmanometer, and galvanometer may offer great possibilities for the analysis of the confused mass of mental phenomena known as the emotions ; but to attain these possibilities the investigations must be pursued according to psycho- logical methods. These methods e.g., establishing scales of emotional intensity, finding the just percep- tible difference in an emotion, &c. have not yet been found. CHAPTER XXIII. SOUND. THE innumerable sounds that we hear are by common consent roughly classed into noises and tones. The tones include sounds such as those from most musical instruments ; the noises include such as rasping, hissing, banging, &c. This division cannot be carried through in all cases ; the passage from tones to noise is gradual, many noises have the character of tones and likewise the reverse. Many sounds are considered as noises or as tones according to the relations in which they are found. The various blocks in a xylophone appear as noises when struck separately, but as the tones of a tune when struck in appropriate time and succession. The tones of a piano produce a noise when struck in a jumble together. Properly speaking, "noise" is a convenient term applied to such sounds as are not considered to be tones. In the first place, let us consider a tone, e.g., from a violin string when the string is snapped. If the finger or a brush is applied to the middle of the string while it is vibrating, the original sound disappears, but a fainter one an octave higher is heard. In a similar manner still higher tones can be heard by touching the string at J, ^, &c., of its length. If the string be now set in vibration, the person listening will hear the violin 313 3H THE NEW PSYCHOLOGY. tone as composed of one loud tone with faint higher tones. These higher tones are the so-called overtones. Physically they are produced by the string vibrating in sections in addition to its total vibration ; psychologically they are, with the main tone, simply components of the violin tone. Such a tone is a complex one. If we search for simple tones, that is, those in which only one com- ponent is found, we find them best in the tones of carefully made tuning-forks. Simple tones have three properties : pitch, intensity, and duration. Tones have thus three dimensions ; the common statement that "tones have one dimension and lie in a line" arises from the fact that in most musical instruments the property of pitch is represented by a keyboard, while the two other properties are varied by the action of the performer. The property of pitch can be illustrated by running the voice from low to high notes, by sliding the finger up a violin string, &c. The property of intensity is that which we vary when we sing more or less loudly. The property of duration is that which characterises a tone maintained for a longer or a shorter time. In regard to pitch it must not be thought that the terms " high " or "low" have any reference to space. They might just as well be reversed, so that base tones would be called high ; or utterly different names might be used. In fact, the Sanskrit terms meant "loud" and "soft"; the Hebrew meant "audible " and "deep." The Greek terms were " sharp " and " heavy," and also referring to the strings of the lyre " low " and " high " in exactly the opposite meaning to ours. The Latin was simply a translation of the Greek words into "acute" and "grave"; and the modern Romance languages, like the French, retain the Latin terms in modified forms, In the Middle Ages it was customary to speak of SOUND. 315 ascending and descending ; it is from this that German and English probably derive the highness and lowness of tones. 1 Pitch is continuous. Starting with the finger at ;i certain place on a violin string, we can change the pitch of the tone continuously by sliding it one way or the other. As usual, we first look for the two different quantities : the least perceptible change and the least perceptible difference in pitch. Following some preliminary observations, 2 the least perceptible change has been investigated by Stern.3 The tone is produced by a current of air blowing over the mouth of a bottle. The change in pitch is brought about by a current of water flowing in at the bottom of the bottle and thus, by changing its length, raising its pitch. It is necessary that this change in pitch shall proceed at some definite rate ; this is accomplished by means of a variator attached to the bottle as shown in Fig. 74. The water runs at a definite rate into the variator instead of directly into the bottle, because the pitch of the tone does not rise proportionately to the rise of the water in the bottle. The variator receives a carefully determined form, such that the rise of the water in the bottle produces an even rise of pitch. The various rates at which the tone is altered are produced by nozzles of different sizes in the tube from which the water enters. The experiment was performed as follows : the tone 1 Slumpf, " Tonpsychologie," i. 189, Leipzig, 1883. 2 Scripture, On the Least Perceptible Variation of Pitch, "Am. Jour. Psych.," 1892, iv. 580. Ibid., Ueber die Aenderutigscmpfiiidlichkeit, "Zt. f. Psych, u. Phys. d. Sinn.," 1894, vi. 472. 3 Stern, Die Wahrnehimmg von Tonverftnderungen, "Zt. f. Psych, u. Phys. d. Sinn.," 1896, xi. i. THE NEW PSYCHOLOGY. was turned on and then gradually raised in pitch until the subject detected the change. The tone used was one of 400 complete vibrations per second. The results ran generally in a manner similar to the following specimen : with a rate of change of 0.40 vibrations per second the just perceptible change was 2.70 vibrations, with 0.50 it was 3.50, with 0.58 it was 4.12, and with 0.77 it was 5.86. The results from the various observers clearly prove that the least perceptible change under these particular circumstances increases as the rate increases. Further experiments on tones of different Fig. 74. THE TONE-VARIATOR. pitch and on the least perceptible change in intensity, are to be awaited with interest. Still another question in regard to tone-changes, namely, as to the just perceptible acceleration of the change, must remain, apart from a single observation as to its existence, 1 unanswered. Possibly by using two variators in succession in Stern's apparatus the answer might be found. Quite a different problem from that of the just per- 1 Scripture, as cited, "Zt. f. Psych, u. Phys. d. Sinn.," 1894, vi. 473- SOUND. ceptible change is that of the just perceptible difference ; the general characters of these two phenomena have been illustrated in Chap. XX. In the present case a tone of a certain pitch is first produced, and then another of a slightly different pitch ; the subject states his judgment as to whether the two tones are the same or different. An apparatus for this experiment consists of two forks of the same pitch, with a small weight at the middle of one prong of each fork. Starting with the weights at the middle, whereby both forks give the same tone, one of the weights is moved upward and downward by successive steps in the manner described for pressure. The forks are sounded alternately. The figures for the just perceptible difference have the meanings attributed to them in Chap. XX. The dependence of the just perceptible difference on the pitch of the tone follows the general rule z that the just perceptible difference expressed in vibrations, is smallest with low tones and largest with high tones without the difference being very great, and that within the range of the tones usually employed in singing it remains practically constant. It thus differs completely from the law of proportionality known as Weber's law. A convenient apparatus for rapid experiments on the just perceptible difference, is found in the tone- tester, Fig. 75. It consists of an adjustable pitch-pipe B fastened to a plate A. To the regulating rod C a long arm D is fastened, which is moved by the handle E. As C is moved inward the tone of the pitch-pipe rises. As it is moved outward the tone falls. Each movement makes a change in the position of the pointer. The tone-tester is compared beforehand with a carefully tuned piano to determine the position of the pointer 1 Luft, Ucber die Untcrscliicdscmpfindlichkcit f. Tonholtcn, " Phil. Stud.," 1888, iv. 511. THE NEW PSYCHOLOGY. when the pipe gives A of concert pitch. This position is marked at A 435 in the illustration. The figures mean that at this point the whistle makes a tone of 435 vibrations per second. In the same manner the suc- ceeding notes are settled. The spaces are then sub- divided by the eye into thirty seconds of a tone. To make the experiment the pointer is placed at A and the pipe is blown for an instant. The pointer is Fig. 75- THE TOXE-TESTER. then moved upward one mark and after about two seconds the pipe is again sounded. The person experi- mented upon tells if he hears a difference. The experi- ment is repeated, starting with A every time and moving one step further for the second tone, till a difference is heard. In a similar manner the difference below A is found. The just perceptible difference between tones has been found to change with age. Experiments on SOUND. 319 school children have resulted in a curve of the kind shown in Fig. 76. 1 In singing, tones are produced by muscular efforts, whereby the vocal cords are stretched. Higher tones require greater tension than lower ones. In order to produce a tone of a given pitch the muscular effort put forth must be of a definite amount ; any failure to get the amount correct makes itself apparent in the lack of Fig. 76. SENSITIVENESS OF SCHOOL CHILDREN TO TONE- DIFFERENCES. correspondence between the pitch of the tone intended and that of the tone produced. Experiments on the accuracy with which tones are produced by the voice have been made by Kliinder. 2 Fine metal points attached to delicate membranes recorded on the smoked drum both the vibrations of an 1 Gilbert, Experiments on the Musical Sensitiveness of School Children, " Stud. Yale Psych. Lab.," 1893, i. 80. 2 Kliinder, Ueber die Genauigkeit der Stimmc, "Arch. f. Physiol." (Du Bois-Reymond), 1879, 119. 320 THE NEW PSYCHOLOGY. organ pipe and those of the voice. The subject of the experiment was to sing the same tone as the organ pipe. A comparison of the two sets of waves drawn by the points showed how accurately the voice agreed with the organ pipe. 1 A characteristic record for the tone G = 96 complete vibrations showed that the voice responded with a tone of 96.34 vibrations with a mean variation of 0.18 vibra- tions, the constant error being, 96.34 96 = 0.34. Of these quantities the constant error may be due to an error in the sensation of the tone or to a defective adjustment of the execution to the sensation. As the person hears his own voice together with the standard tone, it is probable that the constant error for an experi- ment lasting over some time is due to the ear. The mean variation, however, is a continual change from one side to the other, in which there is no time for any influence from the ear. The mean variation there- fore indicates the uncertainty of the control over the tension of the vocal cords ; it is an error of execution. Similar results were obtained for higher tones, the errors bearing about the same proportion to the number of vibrations of the tone itself as in the case mentioned. It can be concluded that a good voice will make an error of about 0.4 % of the number of vibrations in the tone. For a register extending from F with 88 to d ! with 297 vibrations, this allows about 40 distinctly separated tones that can be given with the voice. This interval contains 22 half-tones of the scale ; the voice could therefore hardly keep separate, with perfect satisfaction, intervals of quarter-tone. It is remarkable in this con- nection that the Oriental nations causing in quarter tones. 1 The apparatus of Hensen (Du Bois-Reymond's " Archiv f. Physiol.," 1879, 155) for demonstrating the accuracy of the voice is described with illustrations in Scripture, " Thinking, Feeling, Doing," 77, Meadville, 1895. SOUND. 321 The number of tones we can hear is limited ; if we run upward or downward indefinitely along the scale we finally arrive at a point where we no longer hear tones. To determine the upper limit of pitch we can most 60000 ssooo 50000 fSOOO wooo 3SOOO 30000 25000 20000 15000 10000 5000 Sft 156 * do 3 SO Fig. 77. DEPENDENCE OF THE UPPER LIMIT OF PITCH ON INTENSITY. conveniently use the Galton whistle. 1 This is a closed labial pipe with an end adjusted by a micrometer screw. As the end is pushed inward the pipe becomes shorter and the tone rises in pitch. The number of 1 Galton, Whistles for the Audibility of Shrill Notes, " Inquiries into Human Faculty," 38, New York, 1883. 22 322 THE NEW PSYCHOLOGY. vibrations can be calculated from the reading of the screw. As the tone rises there is finally a point at which it disappears for the person listening ; this is the upper limit of pitch, or the highest audible tone. The upper limit of pitch depends upon the intensity of the tone. 1 To determine this relation the whistle is sounded by a blast whose itensity can be regulated. This can be done in the following way. The blast from a rotary-fan blower is carried by a rubber hose to a distant room. The hose ends in a rubber tube having a stopcock and dividing into two branches. The adjustment of the stopcock regulates the force of the blast ; this force is indicated by a manometer at the end of one of the branches. The other branch of the tube ends in the Galton whistle. In this manner a constant blast of air can be maintained, and its intensity can be varied at will. The results of experiments on six subjects are shown in Fig. 77. It will be seen that for most intensities the upper limit of pitch varies almost proportionately with the intensity ; the deviation for the greatest intensity is probably due to the painful character of the tone. The upper limit of intensity descends with advancing age. 2 This dependence of the upper limit on age was remarked by Galton. " On testing different persons, I found there was a remarkable falling off in the power of hearing high notes as age advanced. The persons themselves were quite unconscious of their deficiency so long as their sense of hearing low notes remained unimpaired. It is an only too amusing experiment to test a party of persons of 1 Scripture and Smith, Experiments on the Highest Audible Tone, " Stud. Yale Psych. Lab.," 1894, ii. 105. 2 Zwaardemaker, Der Umfang des GehQrs in den verschicdenen Lcbcnsjahrcn, "Zt. f. Psych, u. Phys. d. Sinn.," 1894, vii. 10. SOUND. 323 various ages, including some rather elderly and self-satisfied personages. They are indignant at being thought deficient in the power of hearing, yet the experiment quickly shows that they are absolutely deaf to shrill notes which the younger persons hear acutely, and they commonly betray much dislike to the dis- covery." s The results of experiments on animals are remarkable. Galton relates : " I have gone through the whole of the Zoological Gardens, using an apparatus arranged for the purpose. It consists of one of my little whistles at the end of a walking-stick, that is, in reality, a long tube ; it has a bit of india-rubber pipe under the handle, a sudden squeeze upon which forces a little air into the whistle and causes it to sound. I hold it as near as is safe to the ears of the animals, and when they are quite accustomed to its presence and heedless of it, I make it sound ; then if they prick their ears it shows that they hear the whistle ; if they do not, it is probably inaudible to them. Still, it is very possible that in some cases they hear but do not heed the sound. Of all creatures, I have found none superior to cats in the power of hearing shrill sounds, it is perfectly remarkable what a faculty they have in this way. Cats, of course, have to deal in the dark with mice, and to find them out by their squealing. Many people cannot hear the shrill squeal of a mouse. Some time ago, singing mice were exhibited in London, and of the people who went to hear them, some could hear nothing, whilst others could hear a little, and others again could hear much. Cats are differentiated by natural selection until they have a power of hearing all the high notes made by mice and other little creatures that they have to catch. A cat that is at a very considerable distance, can be made to turn its ear round by sounding a note that is too shrill to be audible by almost any human ear. Small dogs also hear very shrill notes, but large ones do not. I have walked through the streets of a town with an instrument like that which I used in the Zoological Gardens, and made nearly all the little dogs turn round, but not the large ones. At Berne, where there appear to be more large dogs lying idly about the streets than in any other town in Europe, I have tried the whistle for hours together, on a great many large dogs, but could not find one that heard it. Ponies are sometimes able to hear very high notes. I once frightened a pony with one of these whistles in the middle of a large field. My attempts on insect- hearing have been failures." a Galton, as before. a Ibid. 324 THE NEW PSYCHOLOGY. There is likewise a lower limit of pitch which can be found by using enormous tuning forks, or slowly vibrat- ing reeds. At this lower limit the tone breaks up into a series of low puffs. This lower limit is generally found somewhere around twelve complete vibrations. Turning to the property of intensity x we first look for a means of measuring the intensity of tones. This is found in the Wien resonator. 2 This consists of a hollow brass sphere. On one side there is an opening of a definite diameter ; on the other, a thin metal plate, the top of a capsule from an aneroid barometer, forms a portion of the surface of the sphere. This resonator answers to a tone of a certain pitch. The vibration arriving at the opening sets the spherical mass of air contained in the resonator into strong vibration ; this produces a vibration of the thin plate. The stronger the tone the greater will be the vibration of the plate. To measure the extent of the plate's vibration, a minute mirror is arranged to move with it in such a way that it deflects a ray of light. The amount of this deflection is read off in a galvanometer telescope. By careful experi- ments the relation is determined betw r een the amount of deflection and the amount of energy contained in the sound vibrations at the mouth of the resonator.3 The sound used by Wien was a tone from a telephone 1 A musical notation for expressing steps of intensity in addition to the usual factors of pitch and duration was first proposed by Scripture, Notation for Intensity, "Am. Jour. Psych.," 1892, iv. 580. It was further developed in " Thinking, Feeling, Doing," 148-152, Meadville, 1895. The notation involves a system of changes in the heads of the notes, and does not interfere with the ordinary notation. 2 Wien, "Ueber die Messung der Tonstarke," Diss., Berlin, 1888. Ibid., Ueber die Mcssnng dcr Tonstitrke, " Annalen d. Physik u. Chemie," 1889, N. F. xxxvi. 834. 3 The resonators made for the Yale Laboratory have a special tuning adjustment designed by Prof. Wien. SOUND. 325 produced by electrical interruptions from a vibrating timing fork. With this apparatus the threshold of intensity or the faintest audible tone can be found. For several persons tested by Wien the result showed a fair agreement with his own ear. The intensity of the vibrations was Fig. 78. TONE MEASURER. 0.068 pp nig. 1 which means that the energy of the air vibrations for this faintest tone was equal to the energy represented in a weight of i mg. falling through a dis- tance of 0.068 pp. As the tympanum of the ear has a surface of about 33 square millimetres, the total energy expended in setting it in vibration was 2.2 ^ mg. This W = millionth part of a millimetre ; mg. = milligramme. 326 THE NEW PSYCHOLOGY. amount of energy would be just sufficient to raise 5.1 x io~ I2m &- f wa ter through iC. Wien also investigated the just perceptible difference for various intensities. If the intensity of the tone be indicated by R and the just perceptible difference be indicated by AR, Wien's results for various intensities agree approximately with Weber's law of proportionality -^- ; that is to say, the just perceptible difference is proportional to the intensity of the tone. As the Wien resonator has not come into general use, experiments on the intensity of sound are made with purely arbitrary scales. I will select two problems thus investigated : first, the threshold of hallucination, and second, the threshold of sensation during sleep. In measuring hallucinations of sound, 1 the person experimented upon was placed in a quiet room and was told that when a telegraph sounder gave a signal, he should listen for a very faint tone which would be slowly increased in intensity. As soon as he heard it, he was to press a telegraph key. The experimenter in a distant room had a means of producing a tone of any intensity in the quiet room. The apparatus for producing the tone consisted in an electric fork, interrupting the primary circuit of an inductorium in the experiment room, and a telephone in the quiet room (unknown to the subject), which was in connection with the secondary coil of the induc- torium. The intensity of the tone depended on the distance between the two coils of the inductorium. In the first few experiments a tone would actually be produced every time the sounder gave the signal, but after that the tone was not necessary. It was sufficient 1 Seashore, Measurements of Illusions and Hallucinations in Normal Life, " Stud. Yale Psych. Lab.," 1895, iii. 49. SOUND. 327 to give the signal on the sounder in order to produce a pure hallucination. The persons experimented on did not know they were deceived, and said that all tones were of the same in- tensity. The real tone could be measured in its intensity, and since the hallucination was of the same intensity it was also indirectly measured. It is to be clearly understood that the persons experi- mented upon were perfectly sane and normal. They were friends or students, generally in total ignorance of the subject, who supposed themselves to be undergoing some tests for sensation. 1 Another illustration of the application of psychological methods is to be seen in the investigations on sleep. A prominent characteristic of sleep, as of various other conditions of consciousness when compared with the condition of maximum consciousness, is the rise of the thresholds in the various senses. The law according to which the threshold for sound is changed with the pro- gress of sleep has been investigated by Kohlschutter, Monninghoff and Piesbergen, and Michelson. 2 In Michelson's experiments a measurable sound was produced by the falling of brass balls at various heights on an open board. The subject of the experiment retired to rest not knowing whether any experiment was to be made or not. The experimenter in another room manipulated the apparatus so that balls were dropped from successively greater heights until the sound was loud enough to awaken the subject. This sound can be con- 1 The principle of the method for measuring hallucinations was first stated by Scripture and Seashore, On the Measurement of Hallucinations, " Science," 1893, xxii. 353. A further application of the method to the measurement of the intensity of an imagination is described in Appendix V. 2 Michelson, " Untersuchungen iiber die Tiefe des Schlafes," Diss., Dorpat, 1891. 328 THE NEW PSYCHOLOGY. sidered as the just perceptible sound in the given con- dition of sleep. The experiments were made at different 25 0123456701 1234 Fig. 79. CURVES OF SLEEP ; L, M, H, THREE SUBJECTS ; N, NIGHT SLEEP ; D, DAY SLEEP ; S, SUMMER SLEEP ; W, WINTER SLEEP ; C, SLEEP FROM NARCOTICS. intervals of time after falling asleep, not more than two, however, being made in any one night. The general course of the threshold is represented in Fig. 79. With SOUND. 329 normal individuals the sleep as measured by the height of the threshold, is rather light during the first fifteen or twenty minutes after falling asleep, but thereafter rapidly becomes deeper, reaching its maximum at J to i hours. 1 In order to wake the person at the moment of deepest sleep, it was found necessary to let a brass ball of nearly -J Ib. weight fall through a distance of I metre. After this point the depth of the sleep decreases with considerable rapidity and reaches its first minimum at about the third hour. The further course of the sleep follows, with considerable regularity, an alternation between greater and less depth, the general average depth being steadily less. Day sleep is lighter, but follows the same course as night sleep (D, N in Fig. 79). Winter sleep is deeper than summer sleep (W, S). Narcotics produce strong but short sleep (C). Each person has his own peculiar curve of sleep (L, M, H), but all agree in certain general characteristics. 1 In Fig. 79 the numbers on the horizontal lines give the hours after falling asleep. The numbers on the vertical lines give the energy of the falling ball in thousands of gramme-centimetres, i.e., the weight of the ball multiplied by the height of fall. Although it cannot be said that the intensity of the sound was proportional to the energy of the falling ball, yet the scale can serve as a fair approximation to a scale of sound-intensities CHAPTER XXIV. COLOUR. ONE of the forms of energy which we perceive is that of colour. Under the term colour all our sensations of light are included. Our investigation, however, must start with the colours actually given us in nature. In the first place, we will define the spectrum colours by the wave-lengths of the physical vibrations corres- ponding to them. With the spectrum spread out as a band on the wall, we can tell by the Fraunhofer lines the wave-length for any particular colour. Such a method of defining colours is indicated in Fig. 80. By increasing and then diminishing the intensity of the light furnishing the spectrum we can cause these colours to pass from the fullest intensity attainable down to perfect blackness. For the present, however, we will disregard the matter of intensity and will confine our account to colours and their combinations of any moderate intensity. Even then, can we possibly bring the infinity of colours in nature into any system ? In the first place, we can conceive the mixture of any two colours to be represented by points along a straight line. Thus, if a colour R (red) be mixed in various proportions with another B (blue), the results will be represented by points in the line R B. 330 COLOUR. 331 ?zo tOQ tto 660 Rid Ot-anj 600. S80- A colour composed of spectrum colours is defined by the relative proportions of the components. Red of a certain wave- length 656.2 pji mixed in certain proportions with a greenish blue of , 492.1 HP- produced white for one subject ; in other proportions it produced whitish reds and whitish o - greens. In our colour system this particular red and this particular green must lie in a straight line with white, thus R W G. In a similar manner any other colour must lie on a line drawn between o - its two spectrum components. Each colour can have only one place. White, for example, can be produced by many pairs of colours ; such pairs are called complementary colours. All complementary colours must thus lie at the ends of lines intersecting at a point indicating white. Any other compound colour might be used for this purpose instead of white. As a result of the condi- tion that a colour can occupy only one place, the spectrum colours and their combinations form for each person a definitely united system, the geometric form of which is shown in Fig 81. The colours of such a system cannot be compounded of two elements used in various pro- Fig- 80. COLOURS IN portions. We can, however, sup- pose them to be compounded of three elements. These soo jrcrn too Violtt 332 THE NEW PSYCHOLOGY. three colours would be indicated by the corners of a triangle whose area would inclose all possible colours. The spectrum line of Fig. 80 is retained, but is bent around to a curve. It is at once evident that the three fundamental colours cannot be spectrum colours. No colour triangle can be drawn such that its corner colours shall lie in the curve of the spectrum colours and yet include the other colours. The closest that we can make any triangle conform to the spectrum curve is indicated by Fig. 8l. THE COLOUR SYSTEM ON THE SIMPLEST SUPPOSITION. the triangle BKV, whereby the violet of the spectrum is supposed to have been rendered slightly whitish by the fluorescence of the retina. If we assume that this triangle represents our mental colour system, our three fundamental colours are spectrum red, a yellowish- green that is not so whitish as the spectrum colour and a violet that is a trifle deeper than the spectrum violet. It is to be noticed that the colours of the spectrum and their combinations do not comprise all the colours we must be able to see. This triangle indicates that the COLOUR. 333 yellows and greens are more or less whitish as compared with the other colours. There is no necessity, however, for making our colour triangle as. close to the spectrum line as possible ; we are at liberty to draw it wherever we find reason to place it. We shall now consider some reasons that give it a definite place. We have treated the colour system as though it were valid for all persons. This is not the fact. The system we have described is simply typical of the great majority of persons. There are other colour systems ; and, more- over, even individuals of the majority show slight differ- ences. The colour system of an individual is determined by establishing for him equations between combinations of colours. To illustrate how this is done I prefer to describe one of the latest and best methods rather than the older and less accurate ones, although the latter are the universal ones for pedagogical and practical purposes. The Helmholtz spectrophotometer for mixing colours x is so arranged that the subject sees two coloured surfaces side by side. Each of these surfaces is illuminated by combinations of spectrum colours. The differences in hue are measured by the differences in wave-length and the intensities are considered as proportional to the quantities of physical light. The simplest form of " colour equation " is found for persons who can match any colour by merely varying the intensity of one colour. One of the colour-surfaces is taken from some place in the spectrum say the middle, or what to us is green and remains unchanged except for variations in intensity. The other surface is illumi- 1 Konig and Dieterici, Die Gmndempfindnngen und ihre Intcn- sihtfsverteilung im Spektrum, " Zt. f. Psychol. u. Phys. d. Sinn.," 1892, iv. 243. Helmholtz, " Physiologische Optik," 355, 2 Aufl. 334 THE NEW PSYCHOLOGY. nated in succession from the various parts of the spec- trum with light of a constant intensity. By simply increasing or decreasing the intensity of the first surface, the subject can make it appear exactly like any colour that may be thrown on the other surface. The results of such a series of measurements z are shown in Fig. 82, where the horizontal line represents the spectrum colours laid off according to wave-lengths, and the curved line H shows the relative intensities of the resulting sensations from different wave-lengths. Thus, the spectrum light of c o E D F G : H Fig. 82. PROPORTIONS OF THE ELEMENTARY COLOURS IN THE SPECTRUM, FOR MONOCHROMATS AND DICHROMATS. 540 ^ can be matched by the light of 570 pp by making the physical intensity of the latter ij- times stronger. Such persons see the whole world in shades of one colour ; as far as "colour" is concerned there is no more meaning in it than there is to normal individuals in a photograph or an engraving. These persons are " mono- chromatic" in the same sense as a photographic plate is monochromatic ; all the variations of the world of colour are reduced to a system of intensities of one colour. The arrangement of intensities is, however, not the same 1 Konig and Dieterici, as before. COLOUR. 335 as with the photographic plate. For the ordinary plate the blues are high lights, the reds are nearly the same as black, and the greens are quite dark. It is true that the so-called orthochromatic plates change the result to some extent by making the greens and reds brighter, so that the picture more nearly represents the relative intensities as they appear to the normal eye. Even this, however, does not correctly represent the appearance to the monochromat. The curve H in Fig. 82 shows that, for the monochromat from which it was obtained, the brightest colour corresponds to our green, that the blues and yellows were dark, and that the extreme reds and violets were absolutely black. This subject of Konig's measurements stated that for him the usual representa- tions of landscapes by engravings never gave a proper reproduction of the relations of brightness ; for him the fields and forests were almost always the brightest objects in a landscape, whereas in the drawings produced by other persons they were dark. It would be interesting to learn what colour of our system corresponds to the one colour of the monochromats ; there are, however, at present no data for settling this point. For another class of persons any colour of the spectrum shown on one of the surfaces of the spectrophoto- meter can be matched by a combination of particular intensities of two other spectrum colours. For these "dichromats" there are two sharply limited regions at the ends of the spectrum within which there are no changes of hue, but merely of intensity. All the other parts of the spectrum, the " middle region," can be produced by mixtures of the two end regions. The colours of the two end regions can be considered as the elementary colours ; they are most conveniently called the ''warm" colour for the red end, and the "cold" colour for the violet end. 336 THE NEW PSYCHOLOGY. Using colours from the two end regions Konig and Dieterici * have determined the proportions necessary to match any other colour in the spectrum. The proportions of the cold colour were nearly, but not quite, the same for all four subjects (Fig. 82, K). The proportions of the warm colour were quite different ; two of the subjects agreed closely in following a certain law, and the two others agreed fairly in following quite a different law (Fig. 82, W, and W 2 ). It was quite evident that the subjects belonged to two different forms of dichromasy. The whole world of colour thus appears to a dichromat as a mixture of two colours, somewhat in the same way as a landscape would appear to us if painted in red and violet or in green and violet. The most common class of people is that of the " trichromats " ; these include almost all women and about 96% of the men. When one of the surfaces in the colour-mixer is illuminated by a spectrum colour, it is not often possible to match that colour by a mixture of two other colours ; for most of the spec- trum a third colour must be employed. For the trichromats the end regions of the spectrum are of a constant hue and differ only in intensity. Just inside of each end region there is an intermediate region in which any colour can be produced by mix- tures of the end colour with a colour of the inter- mediate region. Between these intermediate regions lies the middle region, which requires the presence of some third colour in addition to colours from the end regions. These regions extend, with very small individual differences, over the spectrum as follows 2 : 'As before, p. 259. 2 Konig and Dieterici, as before, p. 283. COLOUR. 337 Warm end region, from extreme red to 655 up. Warm intermediate region, from 655 /i/i to 630 /*/*. Middle region, from 630 ju/4 to 475 up,. Cold intermediate region, from 475 /i/i to 430 //*. Cold end region, from 430 fi/j, to extreme violet. To establish the colour equations for a trichromatic system it is necessary to determine quantitatively the various complementary colours. This was done by Konig and Dieterici for over seventy persons, finding that all but three agreed closely on one system of results, B C D EbFG H ' Fig. 83. PROPORTIONS OF THE ELEMENTARY COLOURS IN THE SPECTRUM, FOR TRICHROMATS. while these three agreed on a different system. The former are justifiably called the " normal trichromats," and the others the " abnormal trichromats." Measurements on two normal and one abnormal tri- chromat gave results as indicated in Fig. 83. The proportions of red and violet corresponded closely for all three ; the results are indicated by the curves R and V. The proportions of green differed considerably for the two normal trichomats, G a and G b and still more for the abnormal trichromat G c . The colour curves which have been used up to this point represent the proportions of elementary colours 23 338 THE NEW PSYCHOLOGY. which are actually required to produce the spectrum colours and their combinations. From the equations for elementary and compound colours of the spectrum we can draw conclusions con- cerning the psychological, or fundamental, colours. In the first place, we must conclude that the number of fundamental colours must be the same as the number of elementary colours. 1 For the trichromats the fundamental colours will be derivable from various proportions of the three elementary colours. Thus, for the normal trichromats, the fundamental colours are derived from the elemen- tary colours R, G, and V, by = a' . R + b 1 . G + c' .V & = a" . R + b" . G-+c" . V 33 = a'" . R + b'" . G + c'" . V where the co-efficients a, b, and c may have any values, including o. Likewise for the abnormal trichromats the fundamental colours are derived by E' = a' t . R' + b; . G' + c' x . V ' = a; . R' + K . G' + c; . V 33' = a;' . R' 4- b;" . G' + c;" . V 1 For the dichromats we have for the first class aatti = * . w, + # . K And for the second m 2 = a' 2 . W 2 + (3 2 . K 1 Konig and Dieterici, as before, p. 324. COLOUR. 339 For the monochromats the fundamental colour will be $=aH, where H is the spectrum colour chosen as elementary. The relations between these systems are to be determined by experiment and by computation. 1 If such relations exist, the colour equations established experi- mentally for a more complex colour system, must seem correct for a less complex system. Then, by computa- tion, values can be found for a, b, c, , /3, in the equations a 8 C toF GH Fig. 84. PROPORTIONS OF THE FUNDAMENTAL SENSATIONS IN THE SPECTRUM. just given, such that the curves thereby deduced for $, m it m a , K 2 , &', ', 33', shall coincide with some or all of those deduced for E, whereas for simultaneous points it ranged from 20 mm. TACTUAL SPACE. 381 to 35 mm. (average 24 mm.), and for successive points 5 mm. to 9 mm. (average 7 mm., p. 373). It would thus be much easier to read a point alphabet than a line alphabet, provided the points were felt in succession. The actual experience in institutions for the blind has brought about a similar decision. The point alphabets consist of developments of a fundamental form. In the Braille system the fundamental form is , whereas it is : : : in the New York system. The forms for the first five letters are given in Figs. 95 and 96. Aside from various practical differences, such as the selection of the letter forms (e.g., in the New York alphabet the most frequent letter, e, has the simplest form, and so on), it is to be noted that the Braille system throws more work on simultaneous distinctions, whereas the New York relies more on successive distinctions. We might suppose the latter to have the advantage in this particular ; it would be rash, however, to express a definite opinion until extensive experiments have been made on the subject. In reading the signs, the end of the index finger is passed over them in succession. The other fingers act merely as supports and are not taught to read. In advanced cases the finger of the left hand also assists whereby the right hand gives an outline sketch of the contents of the line, and the left hand fills up the details, 1 in much the same way as the side parts of the eye make the first sketch before the actual reading by the central portion. Those who read most rapidly pass both fingers quietly over the lines, and the two hands differ only in the speed with which they do this. With some persons the hands separate in the middle of the line, the left 1 Heller, as before, 458. 382 THE NEW PSYCHOLOGY. hand going to the beginning of the next line, while the right hand finishes. In most of the blind both fingers are equally educated ; this is necessarily the case in reading music whereby the hands are alternately applied to the notes. 1 1 Heller, as before. CHAPTER XXVIII. MONOCULAR SPACE. IN considering monocular vision we should suppose one eye to be closed or covered, in order to be rid of the influence of binocular combination of the two monocular fields. We are also to distinguish as clearly as possible what we actually see from our knowledge, gained in various ways, concerning what is seen. Looking at the world with one eye, we see the top of the ink bottle as an ellipse whose size and shading can be varied greatly by placing our hand into the field of vision and moving the bottle. In one position this ellipse becomes a circle ; and in any position the ellipse can be made to increase or decrease in size by altering the muscular adjustments of the arm. For monocular vision, how- ever, all conclusions regarding a constant shape, size, &c., are matters of inference, from relations to other senses. We can get some idea of what we actually see monocularly by supposing ourselves to be immovably fixed, and to have no other sensations than those of one eye, i.e., no touch, no heaviness or resistance, &c. The whole world would then appear to us like the picture on the ground glass of a camera. Objects of various forms and colours would pass across the field ; other objects would increase and decrease in size ; still others would undergo changes of form and shading. We 383 384 THE NEW PSYCHOLOGY. might even by long experience and by the develop- ment of "monocular science" come to quite a " know- ledge," connecting these phenomena together. We would then refer to the world, thus constructed, as the " real " world,, and would consider our particular monocular world as merely our way of seeing the reality. In any case we must distinguish between the actual monocular world as we see it and the " real" world as constructed by inferences. The monocular world is a purely mental affair. By dissections, experiments, &c., we are led to conclude that the monocular world corresponds to processes in the retina, in the optic nerve and in the brain ; the term "retinal field" is sometimes employed to mean monocu- lar world, but not quite justifiably. With the physiology of the retina, the psychologist has nothing whatever to do. As far as we are concerned, we may have no retina and no eye ; we experience a complex of phenomena which we call our visual field. At the outset we may suppose the whole affair to be a pure hallucination. Indeed, a purely monocular person, such as the one we pictured above, would distinguish between "appear- ance " and " reality," whereas a distinction between " hallucination " and " appearance " would be something inconceivable. Possessing other senses and other means of inference, we mark off, as hallucinations of vision, those experiences that are not confirmed ; but this dis- tinction has nothing to do with the distinction between retinal and cerebral processes except as a deduction and not as a direct psychological fact. In spite of the careful explanations of scientific in- vestigators, this error of treating our monocular field as a retinal field occurs persistently. The general mind has become saturated with the error, and even among scientific men the problem still reappears : why do MONOCULAR SPACE. 385 we see things upright whereas they are bottom up on the retina ? The confused condition of thought can be best cleared up by noting a few observations by Helmholtz. " In the following exposition I prefer to substitute the two surfaces lying outside of our eyes in place of the retina and the retinal picture, because they are correcter expressions of our actual consciousness, and also because by directly placing all points in the two spherical fields we avoid the ambiguity of expression which has so often led to the error, that we know anything of our retina, of its size and extent, when we say that we judge the position of objects according to the point of the retina involved. It is more- over for all constructions on spherical surfaces completely indif- ferent, how large we make the radius. . . . We can also take the radius as negative, i.e., we can place the spherical surfaces . . . where the retina and retinal pictures are. We can call such a spherical sur- face lying in the region of the real retina an ideal retina on which an ideal retinal picture lies. We must not suppose, however, that such a schematic retina corresponds to the real one in its dimensions, otherwise than as a very rough approximation. The real retina has an ellipsoidal form, and the retinal picture on it is in any case much distorted by assymmetries of the refracting apparatus. ... In the normal consciousness of the seeing person the retina does not exist at all. "When two bright points are present in the field of vision for the eye in a fixed position, two different optical fibres are stimulated by their light, and two sensations arise which must differ from each other by peculiar local signs because we are able to distinguish them in sensation. To which point of the retina these local signs belong, we know at the start just as little as where the optical fibres lie that carry them, and to what parts of the brain the stimulation is conducted. We can obtain information on the point only by scientific investigations ; in regard to the part concerningthe optical nerve and the brain, we have not got beyond the first introductory steps. Nevertheless, we know through daily experience how we must extend the arm in order to touch the one or the other bright object, or to conceal it from our eye. We can thus learn the direction of an object in the field of vision directly by such move- ments, and we learn directly to connect special local signs of sensa- tion with the point in the field of vision where the object belongs. This is also the reason why we see objects upright in spite of their reversed retinal pictures. In fact, in the localisation of objects, 26 386 THE NEW PSYCHOLOGY. the retinal pictures do not enter into the consideration ; they are only the means of concentrating the light-rays of eacL point of the field of vision in a nerve fibre. We have just as much right to wonder why the letters of a printed book are not reversed from right to left, because the metal letters from which it is printed are reversed." J In fact, by the "retinal field" most writers really mean the "visual field" (which is not reversed, but upright, p. 417). The fields of vision, monocular and binocular, are indeed purely mental affairs. They may be represented as spherical surfaces in relation to a solid, real world, as with Helmholtz and others, or they may be treated as groups of sensations having dimensions of different definiteness, as will be done in the following chapters. There are two important landmarks in monocular space, the point of sharpest vision and the point of regard. The point of sharpest vision is that place in the monocular field at which we can distinguish forms most accurately ; it generally goes under the name of " point of direct vision." It is found by examining the visual field in regard to its distinctness, or sharpness, of vision. The sharpness of vision can be tested by attempting to read type of various sizes. When the visual field is kept at rest, only a few words of the type in this page can be read, the rest is blurred. With very small type, or by moving the page away from the eye (whereby the test is made finer), this region of clear vision becomes reduced to a very small area, practically a point. This is the point of sharpest vision, or the point of direct vision. Observations with stars, dots, and lines lying close 1 Helmholtz, " Physiol. Optik," 2 Aufl., 680. MONOCULAR SPACE. 387 together, show that they must be separated by a dis- tance of 60" to 90" in order to be distinguished at this point. The point of regard is the point at which we are looking. If at the present moment I am looking at this dot ( ), that is my point of regard. The two funda- mental points in the field of vision are generally, but not necessarily, the same. Without changing the posi- tion of the point of sharpest vision, we can look at, or pay attention to, various other parts of the monocular field ; the point of sharpest vision remains stationary, while the point of regard moves. Thus, while looking steadily at the dot, I can attend to the word above it, below it, &c. It is this ability to separate the point of regard from the point of sharpest vision that renders possible the investigation of the whole extent of the monocular field. When objects are moved outward from the point of sharpest vision, but are followed by the point of regard, they finally disappear ; if moved inward from a place where they are invisible, they suddenly become visible. The "field of vision," therefore, does not extend in- definitely in all directions from the point of sharpest vision, but is a definitely bounded region. The point of sharpest vision is considered the " centre " of this region. The boundary of the field of vision is generally determined by means of a perimeter. A white surface of a definite area, and a constant illumination, is moved out of and into the field of vision, along various radii from the centre, the distance of its point of appearance or disappearance being registered. In doing this we have used the point of regard separately from the point of sharpest vision ; we were 38.8 THE NEW PSYCHOLOGY. looking at, or paying attention to, something to one side of the centre. Perimetry is thus a psychological affair ; it consists in drawing the boundary lines of our field of vision. Let us proceed to make a map of this field. In the first place, we put a dot on a piece of paper to represent the point of sharpest vision j then we draw Fig. 97. FIELD OF VISION. radii toward the edge on which to record our peri- metry measurements. Having the central point and the radii, let us examine the field carefully by moving an object in various directions. Beyond certain limits objects lose or change their colours ; beyond further limits they are not seen at all. A characteristic map is shown in Fig. 97 ; green objects lose their colour beyond G, red MONOCULAR SPACE. 389 beyond R, and blue beyond B, while all objects dis- appear beyond W. Hitherto we have spoken of a point of sharpest vision, a field of vision, and a point of regard. I wish now to call attention to the fact that there is also a <( field of regard." When I fix my regard on an object, whether at the point of distinct vision or not, I am dimly conscious of the objects around it ; these objects may be said to be in the field of regard. Let the point of sharpest vision and the point of regard be fixed on the letter X in the following diagram : a h b X g A f d All the letters of the A group are indistinctly seen and are dimly present in consciousness. Now, with the point of sharpest vision still at X, fix the point of regard on A ; the letters of the A group are still just as indistinctly seen, but A is the most prominent character in con- sciousness, the other letters are less prominent, and X is the least prominent. All the letters can be said to be in the field of regard around the letter A. I might have said " focus of attention " instead of point of regard, and " field of attention " instead of field of regard ; moreover, instead of speaking of the movement of the point of regard, I might have used the expression " fixing the attention." As expressions of ordinary language these would have done very well, but as scientific terms they are hardly definite enough. The facts are as stated. There is a field of variously 390 THE NEW PSYCHOLOGY. coloured and variously formed objects, with one point at which they are most distinct, and with another point at which they are most prominent. These two points .generally coincide, but often do not. 1 The measure of the distinctness at any spot is the just noticeable difference in space when that spot is made the most prominent. The measure of prominence or degree of regard might be found in the change in this just noticeable difference due to more or less prominence. In neurasthenic, hysterical, and other persons the perimeter often gives results that show a strongly contracted field of more or lest permanence of form. Measurements on children also show a field somewhat contracted. 3 This has generally been stated as a con- traction of the field of vision ; the eye is supposed to be blind outside the contracted field. I venture the suggestion that such a person is not blind to objects outside the field, but sees them in the same way as we do those parts of the visual field to which we do not attend. In other words, the perimeter measurements give the limits of the field of regard and not of the field of vision. These persons cannot direct their attention so far to one side. Perimeter measurements demand a separation of the point of regard from the point of distinct vision ; this requires an effort which in children w r ould be not quite so successful, and in hysterical persons would be far less successful. When an object suddenly enters the field of vision, it arouses 1 In young children the connection between the two points has to be established by trial and practice. The attempt at connection can be seen when a bright object is shown to one side of the child's point of sharpest vision. He will try to move his eye so that this point is brought to cover what has attracted his "attention," or rather his point of regard. - Luckey, Comparative Obsen'ations on the Indirect Colour Range of Children, &c. t "Am. Jour. Psych.," 1895, vi. 489. MONOCULAR SPACE. 391 regard, and by the fact of association of the two points the eye tends to turn toward it. With a limited field of regard, or field of attention, objects within the field of vision, but far from the centre, would not attract regard and would apparently produce no effect. Some experiments of mine seem to support this view. 1 Cards, each containing a picture in the middle and a letter in the corner, were shown to the observer for such brief intervals that only the picture could be seen. After a set of four or five such cards the letters alone were shown. 2 The person was to tell which of the pictures first came into his mind on seeing a letter. One of the series used was this : i. peacock (F) ; 2. shield (A) ; 3. cat (I) ; 4. flag (: :) ; 5. negro (C). A specimen result would be : I. I, cat ; 2. : :, flag ; 3. A, shield ; 4. C, negro ; 5. F, . Although the letters had not been seen before, yet in four cases out of five when they were seen they suggested the appropriate picture. As proof of the fact of such unconscious seeing and associating of objects, I give the results of my experi- ments in the following table. Five persons were experimented upon. The first column gives the person ; the second, the number of cards shown ; the third, the percentage of correct associations made ; the fourth, the percentage to be expected from chance ; and the fifth, the fraction showing the relation of fact to chance. TABLE. I. 15 0.27 0.20 n. 4 8 0-39 0.2T in. 45 O.2O O.2O IV. 25 0.36 0.20 V. 39 0.50 0.20 1 Scripture, Ucber den associative* Verlauf der Vorstclliingcti, Philos. Studien," 1891, vii. 136. 2 The method of experimenting was described on p. 205. 39 2 THE NEW PSYCHOLOGY. The number of experiments is not large, but it is sufficient to establish the fact. My explanation would be that, although the letters were not "seen" in the sense of "noticed," yet they were seen in the sense of being present in the field of vision ; the field of regard was not large enough to include them, and there was no time for moving it. There is one portion of the field of vision in which we see nothing ; this is the " blind spot." Holding this book about seven inches from the eye, close the left eye and look fixedly at the cross. + A O B The circle will disappear, although A and B are still seen. The shape of this blind surface may be readily deter- mined. With the eye looking fixedly at a point on white paper placed in a definite position, the inked point of a bright pen is brought to a position where it disappears in the blind spot ; it is then carefully moved outward, and its position when first seen is readily marked. This is done on all sides until the marks are sufficiently close for the outline to bu drawn. Although we have proven ourselves to be blind at. this spot, nevertheless it does not appear as a black hole in everything we look at. How is this hole filled ? What do we see with the blind spot ? When the circle is made to disappear, the space between A and B remains entirely white. No matter what may be the colour of the circle or of the field in which it is placed, whenever the circle is made to disappear, the colour of the field is spread over the place occupied by the blind spot. When the field does not consist of a single colour MONOCULAR SPACE. 393 but of two or three colours the blind spot is filled by the two colours with the dividing lines running directly between them. If a more complicated figure is used there is confusion and perplexity ; the spot is not filled out with anything definite, but is apparently occupied by an indefinite something of no particular form or colour. It is not like the space behind our backs, where we see nothing, for even in the most puzzling cases, the blind spot simulates any strong change in general illumination or colour of the surrounding field. Even on a printed page the blind spot simulates the clotted appearance that would be produced by letters. 1 We might now proceed to investigate, at each point in the field as compared with the centre, the sharpness of vision, or the sensitiveness to weak lights, or the changes in colours, &c. Let us, however, take up the following problem : how does our monocular space compare with standard space in regard to distances ? In regard to the physical world we are accustomed to believe that a yard is always a yard. In the psycho- logical world this is not true ; a horizontal yard is quite different from a vertical or any other yard. Let us put the question in a scientific form : a given distance laid off to one side of the point of sharpest vision is assumed as a measure, how does this distance change for other parts of the visual field ? Place a point on a sheet of paper held squarely in front of the eye ; measure off a distance of one inch outward i.e., towards the temporal side. Now, keeping the point of sharpest vision steadily at the original point, mark off equal distances above, below, and inward. These are equal distances in the monocular field. Applying the standard measure to these distances, we 1 A collection of blind spot cards is to be found in Bradley " Pseudoptics," Springfield, 1894. 394 THE NEW PSYCHOLOGY. find that they do not measure exactly an inch. Since we see the same measure moved from one to the other, and since our knowledge of it as obtained in various ways is sufficient proof that it remains a constant quantity, we are forced to believe that equal spaces in our monocular field are not equal spaces in our standard space. But why not say that equal spaces in the visual field are not physically equal ? This is just the point to be avoided. I see certain distances in my visual space to be equal ; experience by vision, by touch, &c., and inferences drawn from it, lead me to assume the particular inch measure as an unvarying standard. It might change its length as I turned it ; in fact, one could be very readily constructed to do so. If every material and every process used for such measures did change in this way, I should not know the difference and should still assume the measure as the standard in spite of its change. If this change happened to agree with that in my visual field, the latter would readily be assumed as a standard space. Suppose that we proceed to lay out, at various points, distances equal to the starting distance ; in this way we could construct a map of the monocular field referred to itself as a standard. The result would differ from the general standard. Vertical distances would be smaller in the monocular field than in the standard ; ver- tical distances above the centre would be shorter than those below ; horizontal distances would be pretty nearly equal ; finally, vertical and horizontal directions would not coincide exactly with the standard vertical and horizontal. A familiar example of the fact that upward distances are shorter than downward ones is found in the letter S and the figure 8, in which the upper half is apparently MONOCULAR SPACE. 395 equal to the lower, until they are turned bottom up, and g. But something still more curious is to come. The distances in the monocular field depend upon the way they are filled. If instead of distances marked by points we draw lines, the difference between hori- zontal and vertical becomes less and our map is changed. Not only this ; the apparent equality depends on how adjacent parts of the field are filled. If the two dis- tances are used as lines for the sides of a square, the difference is still less ; if they are used as points in the circumference of a circle, the difference disappears entirely. Again, the filling of the space, the directions of adjacent lines, &c., influence the results. Thus the map changes continually. We have just been speaking of comparing distances. In order to illustrate the methods employed in accurate psychological comparisons of distance I will describe an investigation by Merkel 1 into what is called "measure- ment by the eye." The investigation takes one of the particular cases I have mentioned ; it is, however, not confined to the determination of the lengths compared, but inquires into the psychological factors coming into play. The person experimented upon was seated looking clown on a black horizontal line drawn on white card- board (Fig. 98). The line was cut in the middle by a fine piece of steel ; two other pieces of steel cut off portions on each side. The observer thus saw an indefinitely long line with three fine cross lines, of which the middle one was at the point of sharpest 1 Merkel, Die Mcihodc dcr mitilcrcn Fehler, experimental begrfin- dctdnrch Vcrsuche aits dem Gcbiete dcs Rauwmasses, III., "Philos. Studien," 1893, ix. 400. 396 THE NEW PSYCHOLOGY. vision. Without any movement of the eye he was to compare the two pieces of line cut off by the cross pieces. The outer pieces were movable by means of micrometer screws turned by the wheels at the ends of the apparatus. These wheels were so arranged that the lengths of the lines were indicated in thousandths of a millimetre. By this means a line of a definite length is pre- sented at one side of the middle and a line equally or Fig. 98. COMPARING DISTANCES BY THE EYE. unequally long was to be marked off. Several problems now arise. The first problem is to find the just imperceptible difference between the standard line N and the varied line. Starting from a line B which is visibly too short to be equal to the standard, we gradually increase it till at MU it appears equal to N. The amount by which it falls short of real equality, d = N M',, is the just im- perceptible difference towards smallness, or, let me call MONOCULAR SPACE. 397 it, the lower just imperceptible difference. (In Fig. 99 the relation is represented on an exaggerated scale.) Starting with a line C evidently too long, we diminish it till at MO it appears equal to the standard N. This gives do = M ' N as the upper just imperceptible difference. The next problem is to find the just perceptibly different line. Starting with the two lines just alike, we decrease the variable line till it appears just AT Fig. 99. DIAGRAM TO ILLUSTRATE THE JUST IMPERCEPTIBLE AND THE JUST PERCEPTIBLE DIFFERENCES. smaller than the standard. We have M as the just per- ceptibly smaller line, and d = N M^ as the lower just perceptible difference. In a similar manner we obtain MO as the just perceptibly longer line, and d^ = M^ N as the upper just perceptible difference. It must be clearly understood that Fig. 99 expresses the judg- ment of the lines from a psychological point of view. The actual measurements may give entirely different results even negative quantities. . 398 THE NEW PSYCHOLOGY. Psychological interest does not end with the just perceptible and imperceptible differences ; it desires a calculation of the mean variation of the results obtained for each of these. The value given for d u , for example, will be the average of all the records for d' u in the whole series of experiments ; the average fluctuation of the single values around this average will be obtained as described on page 47. By making the apparatus sufficiently accurate these mean variations become purely psj^chological quantities indicating the insecurity of judgment. We thus have the four quantities F u ', FO, F'u, FO representing the fluctuations in the values of d u , d^ d u , d^. With these values we can determine several things. Let us take the results for a single stan- dard distance, say, I mm., for which Merkel obtains d u ^ 0.002 d t ' = 0.028 d", = 0.057 d ," = 0.026 FU = 0.007 FO = 0.007 F u = -9 FO = 0.006 The lower "least" perceptible difference is the average of d u and d'u, or d u = 0.028 ; the upper is similarly d = o.ooi. The minus sign of d indicates that the just imperceptibly larger line was really smaller than the standard, owing to the direction of the change from C downwards (Fig. 99) ; this gives a small minus differ- ence in the result. Let us ask what was the average least perceptible difference from the standard ; it was the average of all four, or d = 0.013. Let us ask what was the most accurate method for comparing lines. We see that the smallest error was with d u ; therefore the most accurate way was to begin with a line B (Fig. 99) and increase it till it appeared equal. The regularity of judgment was about the same in all four methods of comparison, the values of F being practically the same. MONOCULAR SPACE. 399 Suppose now the experiments to extend over the distances from i mm. to 50 mm. We can then trace the influence of the length of the line on the just perceptible and imperceptible differences and on the certainty of judgment. In Merkel's results the two differences generally increase with the length of the line ; in one form of judging, namely, M ', there is a steady increase as a negative quantity. The uncertainty of judgment steadily increases as a very constant frac- tion of N. Curiously enough, there is no simple pro- portionality for the values of d while there is a very close one for F. In conclusion, it is perhaps necessary to call attention to the fact that the just imperceptible difference, de- scribed on p. 397, is quite a different mental quantity from the just perceptible difference going toward the standard, described on p. 291 ; the former involves a positive judgment of equality between two things whereas the latter records simply the failure to detect a difference. Optical illusions of the various kinds have, as matters for curiosity, long been subjects for amusement and speculation. Lately they have attracted the ardour of the investigator. Here, as elsewhere, science was the resultant of curiosity mixed with patience. Suppose we investigate the effect of marking off the ends of a line by cross lines at different angles. The fact that such cross lines affect the apparent length of th6 main line has long been known, but a satisfactory explanation was first rendered possible by a systematic investigation. 1 1 Heymans, Quantitative Untersuchungen ubcr das " optische Paradoxon" ''Zt. f. Psychol. u. Physiol. d. Sinn.," 1895, ix. 221. I give the account somewhat in detail as a good example of a systematic search for facts and explanations. 400 THE NEW PSYCHOLOGY. a The apparatus is made of cardboard a rectangular piece, abed (Fig. 100), measuring 25 x 15 cm. ; there is placed a band a' b' c' d', and on this two pieces a" e" f" d" and g" b" c" h" ; they are pasted together in such a way that similar letters are over one another. When the piece iklm is pushed under the top pieces, b a' e' n' (L Fig. 100. PARTS OF THE LINE ILLUSION BOARD. the result looks like the complete diagram shown also in the figure. To enable measurements two millimetre scales are placed on the edges ; they are covered by paper flaps when an experiment is being made, and are uncovered, as shown in the figure, when the result is to be read. The apparatus shows a horizontal line divided into MONOCULAR SPACE. 4OI two parts by side lines meeting at an angle. The two halves are made apparently equal by pushing the card- board ik I m with the variable line under the piece to the left with the constant line. The problem to be investigated is the effect of the angle lines with various lengths and inclinations on the distances between them. For each length of angle line and each size of angle a new pair of drawings has to be made. Let the length of the angle line be made 20 mm. and the length of the constant line 75 mm., while experi- ments are made with various angles. The results of Heymans's experiments are shown in the table, which gives the angle made by the angle line with the hori- zontal and the average number of millimetres by which the variable line was made shorter than the other Angle 10 20 30 40 50 60 70 8c 90 Average illusion ... 18 17 17 15 14 n 8 3 o In this particular case there is a curious constant relation between the amount of the illusion and the cosine of the angle. The length of the angle lines also has an influence on the amount of the illusion. Let us take 75 mm. as the length of the constant horizontal line, and 30 as the con- stant angle, and repeat the measurements with different lengths of angle lines. Heymans's results were as follows : Length of) angle line} 2 ' 5 5 7 ' 5 IO I2 ' 5 l5 I7 '5 2O 3 4Q 43-3 50 60 o Average ) illusion } 3 * I0 I2 J 3 T 4 16 16 17 15 13 12 IT 10 With increasing length of angle line the illusion in- creases to a maximum and then decreases. This holds true for all angles, but the maximum changes its place 2; 402 THE NEW PSYCHOLOGY. with a change in the angle. The results of experiments similar to those just stated, but with various angles, show that the maximum effect for an angle of 10 is obtained with 27.5 mm. for the angle line, for 30 with 30 mm., for 50 with about 40 mm., and for 70 with from 50 to 80 mm. What influence has the size upon the illusion ? Up to this point the constant horizontal has been made 75 mm. long. Now let us take different lengths for this line. By proportionately increasing the angle lines Fig. 101. ILLUSION FIGURES WITH ANGLE LINES LACKING. also the whole figure is simply enlarged or diminished, the angle being kept constant. The results obtained by Hey mans are as follows : Length of constant line... 25 50 75 100 150 Average illusion 6 12 18 22 31 The increase in illusion is almost proportional to the size of the figure, but it drops off slightly for large figures. But the figure has three pairs of angle lines ; what would happen if some of them are omitted ? The following constants were assumed : horizontal line MONOCULAR SPACE. 403 75 mm., angle line 20 mm., angle 10 ; and four figures were used (Fig. 101). The results gave 12 mm., 12 mm., 5 mm., and 9 mm. as the average amounts of illusion for the four figures respectively beginning with the upper one. It thus appears that it is quite indifferent whether the three a*igle lines are all on one side or the middle one on the opposite side to the end ones. Also that the angle lines that are turned outward are more influential than those turned inward ; and finally that the omission of angle lines decreases the illusion. The difference between the results for the two lower figures in Fig. 101 suggests a further investigation into the relative influences of inward to outward angles in determining the maximum point of illusion. Two sets of experiments were made ; in the first, the constant line had inward angles ^ ^ and the variable line had none ; in the second, the constant line had none and the variable had outward ones ^> <^. The constant line was 75 mm., the angle 30, and the angle lines 15, 30, 45, or 60 mm. The results were as follows : Constant line. Variable line. Angle lines. Average illusion. I 30 5 mm. 6 45 7 " 60 7 > < I5 8 ,, 30 ii M 45 9 " 60 7 It is seen that when a line without angles is compared with one with inward angles < >, the illusion shows no tendency to decrease even with an angle line 404. THE NEW PSYCHOLOGY. of 60 mm., whereas when a line with outward angles <^ is compared with a line without angles a tendency to decrease is noticed even with angle lines of 45 mm. We may therefore conclude that in a complete figure the appearance of a maximum point of illusion, with the following decrease, is to all effects exclusively produced by the outward angles > < . Suppose we inquire into the grounds for the illusion. It has been stated that the reason why we over-estimate or under-estimate the lengths of the lines is that we pay attention to the areas included between the angle lines. Thus the total area included in an inward figure Fig. 102. ILLUSION FIGURE WITH INCREASED AREAS. is less than that in an outward figure and we really judge the whole area rather than the line in the middle. There are various deductions to be made from such a hypothesis which disagree with the experiments reported. But the matter can be made the subject of direct experiment. If we pay attention to the areas, the addition of lines as in Fig. 102 ought to increase the illusion as the included area is greater. Using as constants, standard line, 75 mm., angle line 10 mm., angle 30, the results give as the average illusion : regular figures, 12 mm., Fig. 102, 10 mm. That is, the result is just the opposite from what would be expected if the hypothesis were true. MONOCULAR SPACE. 405 Let us try again. If the area or additional imagi- nary lines are influential in the illusion, the result would be greater if the area were made more prominent by actual lines. Three figures (Fig. 103) were used, with Fig. 103. ILLUSION FIGURES WITH AREA LINES. constants as before; the results were 401111., n mm., and 12 mm. respectively as the amount of illusion. Thus the additional lines were of very small influence and the essential part is evidently not in the area, but in the angle lines. Fig. 104. ILLUSION FIGURES WITH FILLED AREAS. Let us fill the entire area with lines as in Fig. 104. We get the results (constants as before except angle line 20 mm.) : 6 mm. and 8 mm. for the illusion, while the original figure gave 14 mm. 406 THE NEW PSYCHOLOGY. Again, let the area be filled entirely with black or with white whereby the hypothesis would require a like result for both figures. The result gave (constants as before except angle line 10 mm.), 9 mm. and 13 mm. respec- tively. The hypothesis evidently falls completely. Another hypothesis asserts that the illusion is due to the over- estimation of acute angles. According to such a hypothesis the illusion would reach a maximum at 30, and would increase steadily w y ith the length of the angle line ; this is refuted by the experiments. More- over, a direct experimental refutation can be made. Take the two Figs. 105 where there are no acute angles at all. The results gave 8 mm. and 10 mm. Fig. 105. ILLUSION FIGURES WITH NO ACUTE ANGLES. Still another hypothesis explains the illusion by in- voluntary, forced movements of the point of regard. In his experiments Heymans was accustomed to place the constant line to the left of the figure. Happening to turn the figure around, he noticed that the illusion which had previously decreased owing to practice, reappeared with fuller force than ever. He also noticed a surpris- ingly irresistible impulse to follow the angle lines, especially the middle ones. Such impulses are un- doubtedly present ; how could they bring about the illusion ? The fact of a most favourable size for the angle and the angle lines seems to indicate that two forces are at work, one to assist the illusion, the other to suppress it. UNIVERSITY MONOCULAR SM^gJU*!^ 407 These we can find in a contrast between movements. As the eye starts to follow the horizontal line, it gets an impulse to movement at the angle also. If the angle opens in the direction of the eye-movement the horizontal component of this side-movement will agree with the intended movement ; if the angle opens in the opposite direction, the horizontal component will be opposed to it. The actual horizontal movement afterwards executed will appear in the former .case smaller and in the latter larger by contrast. This effect would be a factor favouring the illusion and depending on the angle. But this applies only to the angle lines at the beginning ; the other pair of angle lines gradually comes into vision as the eye proceeds. The effect of the end lines is opposed to that of the starting lines. Since the angles are equal and opposed, we should expect no illusion. It is readily noticed, however, that the first angle has its full effect, Avhile the second begins its work only at the end ; the first angle consequently determines the presence of an illusion. Now, as the angle lines in- crease in length, the illusion, as due to the first angle, should increase. It does, until the lines reach a certain length, after which the amount of illusion diminishes. This point is explained by the fact that with short angle lines the first angle can be seen more nearly alone, whereas with longer lines the second angle pushes itself into notice and diminishes the illusion. There must consequently be a maximum point where the influence of the first angle, as increasing with length, begins to increase less rapidly than that of the second angle. The matter depends on the distinctness with which the two are noticed. With inward angles both are from the beginning about as distinct as they ever will be, and the gain of the first over the second will remain about constant. 408 THE NEW PSYCHOLOGY. In conclusion, a test for this theory is planned. By lengthening the horizontal line, the second angle is moved further away from the first ; consequently the length of the angle line must increase much more before the second angle gains over the first, and the maximum appears later. Experiments were made with horizontals of 50 mm., 75 mm., and 100 mm., and an angle of 30. The results gave a maximum for the 50 mm. line at 20 mm. of angle line, for the 75 mm. line at 40 mm. of angle line and for 100 mm. at 60 mm, of angle line. The results are such as demanded by the theory. The whole field of the " optical illusions " opens up before us. A general view of the subject can be found in Helmholtz's " Physiologische Optik." Unfortunately, very few researches have been made T ; our know- ledge still remains largely general, and experimental psychology has little to contribute. Up to this point we have treated our monocular field as a flat space ; is it anything more ? When objects are moving around in our visual field, we notice that one frequently hides another. For example, some one passes a red sheet of paper sidewise toward a blue one ; if you know nothing concerning the relative sizes and can keep out deductions from other objects, e.g.j by looking through your hand bent like a tube, you cannot tell which will hide the other till it actually happens. We might say that one object pushes the other out of existence. So it docs, as far as our 1 Kundt, "Ann. der Phys. und Chem.," 1863, cxx. 118. Aubcrt, " Physiologie d. Netzhaut," 266, Breslau, 1865. Knox, On the Quant. Determination of an Optical Illusion, "Am. Jour. Psych.," 1894, vi. 413. Thierry, Ueber geowetrisch-optische Tiltischiingcii, " Phil. vStud.," 1895, xi. 307, 603, xii. 67. Burmestcr, Beitmg zur cxpcrimcn- tcllcn Bestimniunggcotiictrisch-optiscJier TanscJiungcn, "Zt. f. Pyschol. u. Physiol. d. Sinn.," 1896, xii. 355 (full references). MONOCULAR SPACE. 409 monocular field is concerned ; the hidden object is simply not there. By feeling around with our hands we can grasp the two objects at once ; they both really exist, yet only one of them is present in our monocular field. Any one who has read the romance of " Flatland " will remember the story of A Square who lived in the world of two dimensions where there was nothing but length and depth. A Sphere coming into Flatland out of the third dimension appeared as a circle of varying size. When the Sphere rose, as we would say, he simply disappeared out of existence. Our monocular field is also a flatland. Things appear and disappear, increase and decrease in size. The end of a receding railway-car seems to shrink up, and, if we -had no knowledge by inference, we could not say that it " receded," but merely that it grew smaller. If we put our hand before an object, it is simply gone ; it has disappeared out of flatland. Our flatland, however, differs from Square's Flatland by consisting of length and breadth, not length and depth. To Square his country appeared as a lineland, but was flatland because he could walk about in it and because he learned to make inferences from shading, perspective, &c. To us the monocular field appears primarily as a flatland laid out like a map before us. This view of the world as a flatland is characteristic with persons who have lost one eye while retaining the other. On page 243, experiments were described that were made on a young man who had lost one eye. This subject reported that a few months after the removal of the eyeball, the wounds healed and his left eye became serviceable. At first he had great trouble in seeing objects near him. He could not fix his eye 1 A Square, " Flatland," Boston, 1891. THE NEW PSYCHOLOGY. for the near objects. He could not estimate the distance from one object to another behind it. In looking from the third story of a building in which he was working, the sidewalk seemed to be level with the street. I have said that our flatland has no depth. This is not exactly true j from various experiences we actually manufacture the ghost of a third dimension. The subject just referred to relates that after a few months he learned to determine depths almost as accurately as before. What was it that gave him a third dimension ? Let us illustrate by an experiment. Into a rod of the form shown in Fig. 106, several pins are driven so that their heads are almost, but not Fig. I06. ACCOMMODATION BOARD. quite, in a line. The small screen hides the bases of the pins and nothing but a group of heads is seen by the eye, looking in the direction of the arrow. One of these heads will appear sharply denned ; the rest will appear misty, or blurred. At will we can make any other one of the heads appear sharp, whereby the previously sharp one becomes blurred. We cannot, however, tell how far off the pins are. If we attempt by sight to place the finger on one of them, it falls quite in the wrong place. Of course, as the finger does or does not cover the view of the pin, we know at once which is the nearer. We likewise know from the com- parative sizes of the pins that some of them are further away than others, that none of them are 50 feet away, MONOCULAR SPACE. 411 &c. Finally, for near objects the sensations involved in accommodation of the eye give us some idea of their distance away. In this way we have some idea of depth, just as the one-eyed person has. This idea of depth is not a feeling of space like the length and breadth of monocular space or the depth of binocular space. With only one eye open we can distinctly feel the sensations involved in accommodating from a distant wall to a finger held at arm's length, yet, as far as any vision of depth goes, the finger appears to be on the wall. The statement that the monocular field lacks the third dimension does not mean that all things are localised in a definite plane ; our flatland is a land of definite length and breadth, but of an utterly indefinite depth. 1 1 Hillebrand, Das Verhftlfniss von Accommodation u. Konvergcnz zur Tiefenlocalisation, "Zt. Psych. Phys. Sinn.," 1894, vii. 97. Arrer, Ueber die Bedeutung der Convergenz- und Accommodations- bewegungen fiir die Tiefenwahrnchmung, "Phil. Stud.," 1896, xiii. 116, 222 (full references to previous work, particularly to the opposed views of Bering and Wundt). CHAPTER XXIX. MONOCULAR SPACE AND BODILY SPACE. IN the monocular field we find two sets of lines constantly recurring, those that have the same direction as the horizon and those that have the same direction as the trees, the course of freely falling bodies, &c. We may call these directions horizontal and vertical ; the terms refer to ocular space, and need not necessarily stand in any relation to the horizontal and vertical of bodily space (p. 363). We have thus the foundation for a system of orientation in the ocular field, namely, the vertical and horizontal lines always present. The point of sharpest vision can be made to traverse these or other lines. This movement of the point of sharpest vision lies in a space of practically two dimensions (the third dimension, representing the feeling of accommodation, being indefinite and negligible, p. 41 1). This form of the statement involves no hypothesis concerning the action of the eye muscles and does not go beyond the bare facts. Regarding the cardinal directions in the monocular field as the axes, we can express the movements of the point of sharpest vision in the usual way by use of co-ordinates. Suppose the eye to be looking at a surface so large that no objective boundaries are present, the visible 412 MONOCULAR SPACE AND BODILY SPACE. 413 surface being limited by the limits of monocular field. Let the surface be marked off with the axes X and Y. We will start with O at the point of sharpest vision (Fig. 107). Suppose this point to move through the distance O I. The monocular field changes to a new position with I as its focus. We Fig. 107. MONOCULAR FIELD WITH POINT OF SHARPEST VISION AT O. can distinguish two kinds of ... \ results. In one kind the limits \ of the field remain nearly as before for all moderate Y changes of the focus ; the nose, eyebrows, &c., are seen as fixed in relation to X, Y. (Fig. 108). This we call Fig. 108. RESULT OF CHANGING * movement of the eye. In POINT OF SHARPEST VISION TO the other case the limits of I BY EYE-MOVEMENT. the field move in regard to X, Y ; there are at the same time sensations from the / neck, and we say that the head is moved (Fig. 109). Of course, the two can be com- bined in any way. Let us denote the eye movement, of the monocular field, by H, whereby we F : & I0 9- RESULT OF CHANGING * POINT OF SHARPEST VISION mean the sum of. all our TO i BY HEAD-MOVEMENT. 4H THE NEW PSYCHOLOGY. experiences when the point of sharpest vision has been moved from O to I with the limits of the field practically unchanged. The quantity H is what we know as the voluntary movement of the eye. Physiologically this corresponds to a movement of the eye-ball by the eye- Fig. IIO. APPARENT CHANGE IN THE SYSTEM OF ORIENTATION AS THE EYE IS MOVED. muscles ; mentally it is composed of sensations from the muscles, &c., and of the visible changes in the field. "Movement of the eye" is psychologically the factor H. In geometry the system of co-ordinates is considered as fixed, regardless of the movements of a point within it. Is this the case in monocular vision ? MONOCULAR SPACE AND BODILY SPACE. 415 By looking steadily at a coloured cross in the point of sharpest vision we can force its image, in its comple- mentary colour, to move as the point moves. We can thus carry a portion of the monocular field from one place to another. To perform the experiment a double cross of coloured paper is placed in the middle of a large board with cross lines at right angles. This board, suspended at its centre, is placed so that the X axis is horizontal. The point of sharpest vision is held on the cross for a few minutes and is then moved outward successively in various directions. The result is indicated in Fig. no. The general law for the dependence of the system of orientation on the position of the point of fixation can be thus stated : if the original system be regarded as a fixed plane, the system after movement will appear on this plane as the projection of a system in a plane rotated with respect to the first around an axis per- pendicular to the direction of the movement. 1 It is noticed that a given movement of the point of fixation produces a constant change in the system of orientation. If we move from the point A to the point B, and back again, we find the system at A to be as we left it. Likewise, if we move from A to B and then from B to C, we find the system at C to be the same as we should have found it by moving from A to C. The relations of the systems of orientation are therefore constant which, in the midst of a change of system for every movement, would seem to be a gain in simplicity. In stating the law of dependence of orientation in movement I spoke of the original system " regarded as 1 This law is roughly true ; for rapid or extreme movements and under special conditions there are deviations from it ; particulars are to be found in Helmholtz, " Physiologische Optik," 27 and following. 416 THE NEW PSYCHOLOGY, a plane." In the illustrative experiments it was a plane, and the double cross actually appeared to be distorted. In our ordinary experience we do not see such distor- tions. We can move the cross around over the sky without any noticeable distortion. When we move the point of sharpest vision from one point to another over the scene before us, we do not see a continual expansion and contraction of the objects in view. Indeed, the view seems to remain practically constant in shape and arrangement, both with movement and without. The conclusion is evident : we do not see the monocular field as a plane. To determine the actual form of the monocular surface we can ask : What form would give an un- changing system of orientation ? The answer would be : The inner surface of a sphere. In fact, we do regard the upper half of the monocular field, when out of doors, as a spherical vault, namely, the sky. Like- wise, to persons on a mountain or in a balloon, the earth appears as the inside of a bowl. The form of the sphere may not be perfect. Owing to various influences the sky is flattened till the edges are much further away than the centre. The third dimension still remains very indefinite under all circumstances, yet there is a hollowness about all our monocular views, indoors and out, although the form may not be spherical. By moving an object around in our monocular globe we can find its centre with considerable defmiteness. Not far from this centre we find a fixed object, the point of the nose. We also find a human body not far away. A few tests soon convince us that this visible human body is to some extent connected to the felt human body with its touch sensations, &c. We naturally' suspect that there may be some connection between bodily space and monocular space. MONOCULAR. SPACE AND BODILY SPACE. 417 There is an actual relation between the two spaces. We can tell without sight the position of the body, i.e., of the trunk (p. 364), as vertical, horizontal, or inclined. We can also without sight move our hand in a vertical, horizontal, or inclined direction. If, now, we open the eye, we can see that the ocular vertical coincides with the bodily vertical, e.g., a drop of water runs lengthwise down the trunk, or the hand moves in the path of a falling ball, and that the ocular horizontal coincides with the bodily horizontal, e.g., we see the moving hand to coincide with the horizon. We thus have the beginnings of a system of orientation for the ocular-corporeal space. Moreover, we know bodily the meanings of front, back, sidewise, &c. A tap on the chest is located bodily as lt front." With the eye we can see the instrument strike the blow. We can thus see the directions known bodily as front, sidewise, and (par- tially) back. At the same time we see that the monocular field lies in front of and (referred to the trunk) somewhat upward from the body. In the next place, we can move the point of sharpest vision with or without moving the centre of the monocular sphere. When we do move the centre, we experience certain sensations from sinews, joints, and skin, which in bodily space indicate to us movements of the head in relation to the trunk. Thus, although the monocular field is changed by every movement of the head, we always know its relation to the funda- mental bodily space. The fixity of the monocular field in relation to the )ody is not always maintained. Let us suppose ourselves on a rotation board (Fig. :i). Our monocular field is, say, a ceiling with gas-fixtures, 28 418 THE NEW PSYCHOLOGY. &c. The board is started in rotation. The ceiling apparently remains fixed in position, and we feel our body moving. The original system of orientation of bodily space remains constant, and our body appears by its changing sensations to change its position in regard to it. The monocular field actually rotates but this visible rotation is corrected by reference through the bodily sensations to the original position. Suppose, now, these bodily sensations to fail. The Fig. III. ROTATION FOAKD. ceiling then appears to rotate. Such rotation (or Bother movement) of all or part of the monocular field in reference to bodily space, with bodily sensations of movement absent, is considered to be "objective" movement when confirmed by our other means of determining it and " illusion " of movement when not so confirmed. The experiment has been varied by Warren. 1 The * Warren, Sensations of Rotation, "Psych. Rev.," 1895, ii. 273. MONOCULAR SPACE AND BODILY SPACE. 419 room was darkened. The subject lay on the rotation board with head slightly raised and eyes screened to permit of only a small area being seen towards the feet. This area was covered by a screen at the feet ; a square hole was made through the screen. Two strips of white paper were hung on the opposite walls of the room. When the strips were not visible the subject felt the usual sensations from being rotated, with the usual result (p. 367) that a steady rotation was finally felt as rest. The strips were now made visible in a faint light. The subject's -internal sense of rotation prevailed and the strips seemed to flit by or move according to judgments from this sense. With a stronger light the visual sen- sations prevailed. The slightest movement of the body was detected. With the eyes closed there was a sensation of reversed movement when the rotation was stopped ; this was now checked by the sight of the strips. When a mirror was inserted in the screen so that the strip behind the head was seen and was therefore apparently moved in the opposite direction to the movement of the head, the subject thought himself to be moving sidewise (not rotating) in the direction in which the head was going. CHAPTER XXX. BINOCULAR SPACE. MOST of us possess two monocular fields, the left- hand one and the right-hand one. These two fields are alike in general outlines but differ in particulars. Looking through the window with the right eye closed, we see the window bars crossing the scene over the way ; looking with the left eye closed we see the scene practically as before, but the bars cross it in different places. Closer examination shows us that the two fields, although in the main alike, differ everywhere as to par- ticulars of size and arrangement. This becomes very apparent when the eyes are opened and closed in rapid succession. What happens when both eyes are open ? Our two flat monocular fields differ from each other ; when both are combined into one binocular field the general out- lines are as before, but the field receives an entirely new character, that of depth or relief. By combining two slightly different fields from flatland, the result becomes a model in spaceland. The laws that govern this com- bination form the problems of binocular vision. We will suppose two monocular fields to be present with their points of sharpest vision. We will disregard the unusual cases where the scene for one eye is different from that for the other ; and will suppose the two mon- 420 BINOCULAR SPACE. 421 ocular fields around the points of sharpest vision to be alike, say, a door. Although we see a door with each single eye, we see only one door with both eyes. This is the fundamental fact of binocular vision ; namely, the union of two monocular views into one binocular view. There is no question of why to be asked any more than there is why red and yellow make orange. It is a matter of fact in either case, and psychology is concerned with determining the laws that govern such combinations. While we are looking at the door, the sunlight sud- denly shines on the floor. When a new object appears, it generally becomes the point of regard, and the point of sharpest vision of each eye at once moves from its previous position to the new point of regard. Again, the table, the chairs, &c., successively attract the point of sharpest vision. The passage from one object to the other is accompanied by particular sensations of sight and muscular movement known as " movements of the eye." Such sensations from a single eye did not give us what we now notice : a distinct, definite, irresistible feeling of depth. The varying movements of the two points thus build up the whole field of binocular depth with a system of distances from zero to infinity in all visible directions. We thus at any moment definitely locate any object we look at in binocular space. When the two points of sharpest vision are the same, the single point is called the " point of fixation." What is the relation of the other points of the binocular field to the point of fixation ? Let us start with two monocular fields. Fig. 112 shows a pair of views taken by a stereoscopic camera. The stereoscopic camera contains two lenses a few inches apart on the front board of the camera box. A 422 THE NEW PSYCHOLOGY. partition in the box divides it into two distinct compart- ments. When we compare the two views on the ground glass of the stereoscopic camera, we find them to differ practically in the same way as the view differs for us when we look at it with one eye successively in the two places occupied by the lenses. It is this principle that enables us to photographically record the two monocular scenes just as they would appear to us if we did not combine them into one. The tw r o views of Fig. 112, thus repre- sent the two monocular fields of a person looking at the L. R. Fig. 112. TWO MONOCULAR VIEWS FOR THE LEFT AND RIGHT EYES RESPECTIVELY. scene presented to the camera. The point of sharpest vision is at the window of the house in the distance, as indicated by the black dot. It will be observed that in reference to this point the other parts of the picture are differently situated in the two views. Disregarding, now, the manner in which these views were obtained, we will consider them as what we actually see with the left and right eyes singly. What happens when the two are combined ? The most effective method of producing monocular fields experimentally and then combining them binocu- I'.I \OCULAR SPACE. 423 larly is that of stereoscopic projection. Of several forms of this method I have found the application of polarised light to be the best. 1 Light is said to be polarised when its vibrations occur in only one plane. This condition is accomplished in several ways. One of them is to place a bundle of parallel glass plates at an angle of 55 in the path of the beam ; part of the light is deflected sidewise, being polarised in one direction, and part passes onward through the plates, being polarised at right angles to the other. Let such a bundle of plates, called a polariser, be placed in front of the lens of a projection lantern. The light reflected sidewise is destroyed by the blackened surface of the casing, and the picture will be thrown forward on the screen in. light polarised in one particular direction. To the eye this picture does not differ from that in ordinary light, although the light is polarised in one plane, say vertically. The term " vertically polarised " indicates the readjustment of the light around a vertical axis, but does not imply that the vibrations occur vertically rather than horizontally, this fact remaining still undetermined. Let us now place another polariser, turned at right angles to the first, in front of another lantern. The picture thrown -by it on the screen will be in hori- zontally polarised light. To the eye, pictures in this light do not differ from those in vertically polarised or in tmpolarised light. 2 1 Weinhold (" Physikalische Demonslrationen," 341, Leipzig, 1881) suggested the use of polarisers, analysers, and a bronzed screen for stereoscopic projection, but added that no one would attempt to carry out the idea in earnest. The method has been made success- ful by John Anderton, of Birmingham, England, whose apparatus I have described here. 2 In order not to destroy the polarisation of the light a silvered screen is used. 424 THE NEW PSYCHOLOGY, We place the two polarisers in front of the lenses of a biunial lantern (Fig. 113), and throw two pictures at the same time. If the two pictures are alike, one single picture appears as usual. Now place the view Fig. 112 L Fig. 113. THE LANTERN STEREOSCOPE. in one lantern, and Fig. 112 R in the other; the result is a confused mixture of both views (Fig. 114). When the two points of sharpest vision, indicated by dots, are made to coincide, no other points will do so ; the branches, for example, are quite some distance apart. BINOCULAR SPACE. 425 The two views thus physically mixed on the screen are now to be received into the eyes separately. For this purpose we use the pair of analysers (Fig. 115). They are composed of bundles of parallel glass plates, having the same effect as those of the polarisers. One of the analysers allows only the vertically polarised light, the other only the horizontally polarised light, to pass through it. We thus see with the left eye the picture of the left field only, and with the right eye the picture of the right field only. The result is remark- Fig. 114. MIXTURE OF THE TWO MONOCULAR VIEWS OF FIG. 112. able. We clo not see two different flat pictures as they really are. We also do not see a confused picture as it appears on the screen. What we do see is a single picture with all the points coinciding perfectly, but with an entirely new property to it which we experi- ence in no other way. This property is "binocular relief." The picture is no longer on the flat screen, but is a picture in relief of exactly the same kind (excepting the colouring) as the objects we see in the world around us. 1 1 Another method of stereoscopic projection throws the two views in different colours and employs eyeglasses of corresponding colours. It can be conveniently used in place of the polariser 426 THE NEW PSYCHOLOGY. The uniqueness In illustrating the process of binocular vision I use this method of building up solid pictures by means of flat pictures on the screen, because it makes evident to the observer that binocular relief is not necessarily a property of objects themselves, but that it consists in a binocular combination of pictures that differ according to certain laws. . binocular relief can also be brought out by looking at the objects in front of us with one eye and with two eyes alternately. Although we may be perfectly acquainted by sight and touch with the chair and the table before us, there is always a marked and specific change in the character of the picture when we change from monocular to binocular vision. No amount of monocular and tactual education can produce binocular relief ; the person with one eye must always remain as ignorant of this experience as the colour-blind person of full colour vision. To illustrate the laws governing binocular relief, let us take a pair of views (Fig. 116). The points o sharpest vision F, F are made to coincide. The points A, B, C, D also coincide. The point G in the left field method whenever good lanterns are at hand ; it does not require a special screen, and the total cost is a trifle. I have described various technical points in regard to this method in the " Scientific American," 1895, Ixxiii. 327. To the account there given I would add the recommendation of the use of sheet gelatine instead of glass when lime-light is employed. *. 115. EYEGLASS FOR THE LANTERN STEREOSCOPE. BINOCULAR SPACE. 42; Fig. Il6. BINOCULAR FIGURES TO ILLUSTRATE CROSSED AND UNCROSSED DISPARITY. 428 THE NEW PSYCHOLOGY. is to the right of F, while in the right field it is to the left. This condition is called "crossed disparity." With other points like E the point of the left field is to the left of that of the right field ; this is the condi- tion of " uncrossed disparity." When we look at this pair of views on the screen, the point G is seen to be further in front than F, and the point E to be further behind ; in general we can say that crossed disparity places a point nearer, and uncrossed disparity places it further away. In the foregoing experiments the point of fixation has remained fixed on the screen. The binocular depth was thus constant at the distance of the screen, and the binocular relief was a transformation of a flat surface into a solid figure at that depth. We thus have two qualities of binocular space in addition to those derived from monocular space ; these are (i) depth, which corresponds to differences in movement of the point of fixation ; and (2) relief, which corresponds to the union of disparate points of the monocular fields. The law governing the amount of binocular relief can be expressed in the following way. In order to avoid negative signs we will suppose ourselves to be look- ing at a distant point, e.g. r the stars or the horizon, whereby the point of fixation is at a practically infinite distance, and whereby also there is no disparity except crossed disparity. If a stereoscopic picture of such a scene be taken and the two views be laid together so that the distant points coincide, all objects in the left- hand picture will appear further to the right than in the right-hand picture. The amount of this disparity is called the stereoscopic parallax. As the point of fixation is changed from infinity, the distant points become double in steadily increasing uncrossed disparity ; while the previously double points BINOCULAR SPACE. 429 steadily diminish in crossed disparity. The stereoscopic parallax for the infinitely distant points, which was formerly zero, becomes a steadily growing negative quantity, while the positive parallax of the nearer points decreases. What is the relation of stereoscopic parallax to binocular depth ? We will start with the point of fixation at infinity; the two monocular fields for this position we will name the fundamental monocular fields. We will suppose these fields to have systems of co-ordinates with the origins in the points of sharpest vision. For each point of one field there is (except where the field is lacking) a point of the other field with the same values for its co-ordinates ; such pairs of points are " identical points." All objects infinitely distant will occupy identical points. Nearer objects will not occupy identical points. The amount by which the actual points differ from identical ones is the amount of disparity. As the point of fixation is moved nearer, the identical positions in the two fields of vision will no longer be occupied by infinitely distant objects, but by nearer ones. For every change in the position of the point of fixation the identical positions will be occupied by different systems of objects. The sum of all the objective points occupying identical positions for a given position of the point of fixation is called the "horopter" for that position. The determination of the form of the horopter is a purely mathematical problem. 1 Some of the particular cases are as follows : With the point of fixation at infinity directly in front 1 The equations for the form of the horopter were stated by Helmholtz in 1862 ; the first published statements concerning its form in the simpler cases were made by Hering in 1863. 43 THE NEW PSYCHOLOGY. the horopter is a plane perpendicular to the line from the point of fixation to the face. Mathematically this plane is at an infinite distance ; practically, since the eye cannot distinguish minute differences, the horopter is a space covering all objects beyond a certain limit. With the point of fixation directly in front, but at a distance nearer than infinity, the horopter is a circle lying in a plane passing through the eye and the point of fixation and passing the point of fixation and the centres (for the lines of direction supposed to be drawn from objects to the eyes) of the two eyes, and also of a perpendicular line erected at the point of fixation. For all other positions of the point of fixation the horopter is the same as in this case, as long as the point is not raised or lowered from the horizontal plane extending outward from the eyes. When the point is on the floor directly in front the horopter line likewise lies on the floor. For other positions the horopter becomes more complicated. 1 The importance of the horopter lies in the fact that points lying in it are more readily united by the two eyes. The a fixation surface " is a curved surface whose points occupy, in the two monocular fields, positions which are identical horizontally, regardless of possible vertical disparity. Careful experiments 2 have estab- lished the law : the distance from the fixation sur- face of any point seen singly in binocular space depends only upon the amount of disparity between the points of the two fields. That is, the position of any point in regard to it is determined by the points 1 For the determinations see Hering, " Der Raumsinn und die Bewegungen des Auges," 377, in Hermann's " Handbuch dcr Physiologic," and Helmholtz, " Physiologische Optik," 2te Aufl., 860. 2 Hillebrand, Die Stabilittit tier Rtiiinni'cHc tinf tier Nctslitiiil, u Zt. f. Psychol. u. Physiol. d. Sinn.," 1893, v. I. BINOCULAR SPACE. 431 it occupies in the fundamental monocular fields, and is utterly independent of the position and form of the fixation surface. Up to this point we have attended only to the space elements in binocular vision ; it is interesting to inquire concerning the experimental study of points moving in three dimensions just as we studied their movement in two dimensions (Chap. VI.). Dvorak/ Sanford, 2 and Miinsterberg3 have developed the stereostroboscope for this purpose. "The principle of the stereoscope is to have the two eyes converging to one point, and yet see two different pictures. If these two pictures represent a solid object as it would be presented to the right and left eyes respectively, they are perceived as one solid object. The instrument shown in Fig. 117 con- sists of two discs united by a steel rod, which may be rotated rapidly. The distance between the discs may be varied, to give any desired degree of convergence. " The front disc is made of heavy black cardboard, having in it two concentric circles of radial slits. The inner and outer slits alternate at 30 from each other. The observer sits before this disc with the eyes on a level with the slits when they are horizontal, so that one circle of slits will pass before his right eye and the other circle before his left as the disc rotates. 1 Dvorak, Ueber Analoga der personlichcn Differenz zwischen beiden Augen und den Netzhautstellen desselben Atiges, "Sitzb. d. kgl. bohm. Ges. d. Wiss. in Prag," 1872, Jan.-Juni., 65. 2 Sanford, Notes on New Apparatus, "Am. Jour. Psych.," 1894, vi. 576. 3 Miinsterberg, A Stereoscope without Mirrors and without Prisms, "Psych. Rev.," 1894, i. 56. In choosing the Miinsterberg apparatus for description I was not guided by any questions of priority or completeness of invention, in regard to which I am not sufficiently informed to express an opinion. The following account was pre- pared for me by Mr. E. Lough, of Harvard. The block for Fig. 117 was obtained from the " Psychological Review." 43 2 THE NEW PSYCHOLOGY. "The back disc, which rotates with the front one, contains a series of twelve figures 30 apart, whose middle points are 16.5 cm. from the centre of the disc. These figures are stereoscopic pictures, so placed that the right eye looking through its slit sees only the right-hand view and the left eye only the other. Fig. 117. THE STEREOSTROBOSCOPE. "With each rotation of the disc six views are presented to each eye. When the rotation is so rapid that these images fuse into continuous impressions the condition of simultaneous stereoscopic vision is fully attained. If, BINOCULAR SPACE. 433 now, these figures vary slightly, after the manner of those used in the stroboscope (p. in), the effect of a solid moving object results." The apparatus thus applies, in the first place, Dvorak's principle 1 of binocular union, which is as follows : Two successive impressions reaching the eyes separately are perceived as simultaneous, provided the difference does not exceed a certain limit. When the two impressions are made to appear in the same place this limit is about ^ sec. The second principle 2 is : When the two impressions are such as would be required for relief vision, the relief is actually seen. Thus, instead of having the two monocular views pre- sented simultaneously, as in viewing real objects or the ordinary stereoscopic views, they may be presented successively. It is not difficult to see the great advan- tage of the method in some cases. In most persons the acts of accommodation and convergence are insolubly connected. With the points of sharpest vision of the two eyes at the horizon each eye is accommodated also for the horizon. As the points are brought to meet on a nearer object, the accommodation is likewise changed to suit. In the ordinary stereo- scope, however, the two pictures are placed beside each other, and, as the points of sharpest vision must be placed on the corresponding points of the pictures, they are practically in the same relation as if placed at the horizon. Thus the two views of Fig. 112, when placed in a stereoscope, require the points of sharpest vision to be about 50 mm. apart at a short distance from the face, which is the distance required when the points unite for a very distant object. The accommo- dation is thus adjusted for a distant object, and the near pictures appear blurred. With Dvorak's method, 1 Dvorak, as before, 70. 2 Ibid., 70. 29 434 THE NEW PSYCHOLOGY. as well as with the method of stereoscopic projec- tion previously described, the pictures occupy the same place, and the convergence and accommodation are adjusted to the actual distance of the object. The difference of method is well brought out by the case of one man who, on account of excessive myopia of one eye, had never been able to successfully see stereoscopic figures in the usual stereoscopes, but who saw them perfectly when shown in Miinsterberg's apparatus. The third principle involved is that of kinetoscopic, or stroboscopic, vision, which has been described in Chap. VI. The result is a movement of objects, not only on a plane surface, but also in depth. The successful development of the kinetoscopic method for showing moving pictures on the screen leads us to hope for its combination with some method of stereoscopic projection. With the stereoscopic method employing polarised or coloured light a double vitascope, accurately synchronised, would be required. Dvorak's method would require only one apparatus, with which the two views are presented alternately. This would involve the change of the polarisers or colours at each exposure, a problem which does not present insuperable difficulties. When this is accom- plished, the entire equipment for the presentation of a play as far as concerns the eye will consist of a " kinetostereoscope," a flat screen and the eyeglasses for the audience. The actors will come, go, advance, and retreat on an apparently real stage having true depth. The colouring of the pictures is to-day accom- plished without great difficulty. One thing alone is lacking : the words and music. This can be supplied by a phonograph synchronised with the pictures. This has actually been attempted for the kinetoscope, as BINOCULAR SPACE. 43 5 described on p. 116. The union of the three methods kinetoscopic, stereoscopic, and phonographic would not only make it possible to reproduce everywhere an opera or a play, but would also enable future genera- tions to see and hear, in practical reality, the actors, singers, and musicians of former ages. PART V. PAST AND PRESENT. CHAPTER XXXI. AN INEVITABLE EVENT. THE fundamental difference between the science of the Greeks and the science of to-day lies in the introduction of methods of careful observation, of statistical calcu- lations, of measurement, of experiment, and of mathe- matical deduction, in the place of superficial obser- vations as the basis of a fabric of speculation. For Aristotle a few observations of nature were sufficient for the most widely-reaching conclusions. For the other Greek philosophers even these few observations were not necessary ; pure thought was amply sufficient for the attainment of all knowledge worth having. The revival of learning brought about an adoption of the Greek methods of thought which was applied to the science of the Middle Ages. The blow delivered at this fabric by the heliocentric theory of Copernicus and the later astronomy followed by the development of the method of carefi observation by Galilei. The tremendous change tin brought about can be understood by comparing ttu methods of ascertaining astronomical knowledge previ 436 AN INEVITABLE EVENT. 437 lent in Galilei's time and those of to-day, as is illustrated by the following extract from Francesco Sizzi, a Floren- tine astronomer, who argues thus against Galilei's discovery of Jupiter's satellites : " There are seven windows in the head, two nostrils, two eyes, two ears, and a mouth ; so in the heavens there are two favourable stars, two unpropitious, two luminaries, and Mercury alone un- decided and indifferent. From which and many other similar phenomena of nature, such as the seven metals, &c., which it were tedious to enumerate, we gather that the number of planets is necessarily seven. " Moreover, the satellites are invisible to the naked eye, and therefore can have no influence on the earth, and therefore would be useless, and therefore do not exist. Besides, the Jews and other ancient nations, as well as modern Europeans, have adopted the division of the week into seven days, and have named them from the seven planets ; now if we increase the number of the planets this whole system falls to the ground." J Of course I do not mean to imply that Galilei was the first to make careful observations ; he was, however, the most prominent and powerful figure in this new method of acquiring knowledge. From astronomy the method has gradually worked its way into various departments of thought. The introduction of this method into the study of mind came through Hobbes, who was strongly influenced by the teachings of Copernicus, Kepler, Harvey, and Galilei. After Hobbes there arose a succession of brilliant English thinkers, such as Locke, Berkeley, Hume, Hamilton, and Mill, in whose hands the method received the furthest development to which it could possibly be brought as long as it was confined to the study of the person's own mind. It is greatly to the credit of English psychology that the victory of observation over speculation was won Lodge, " Pioneers of Science," 106, London, 1893. 438 THE NEW PSYCHOLOGY. there long before elsewhere. It was not until the beginning of the present century that it occurred in Germany. Then it happened as a revulsion from the widely spread speculative philosophy. The attack on the speculative method was successfully made by Herbart. In place of speculation the material of psychology was to be found by "internal observation, association with persons of various degrees of culture, the observations of the educator and the statesman, the expositions of travellers, historians, and moralists : finally, experiences with the insane, the sick, and with animals." Herbart was followed by a school of brilliant disciples who excelled in sharp observations and wide-reaching deductions. Thus both in England and Germany a scientific treatment of psychological questions was made possible by the victory of observation over speculation. We must turn again to Galilei for the development of still another method, that of experiment. The step taken by Galilei was a simple but mighty one. It is difficult for us of the present day to understand the state of mind at the time of Galilei. The works of Aristotle were considered as the final authorities for all matters of fact, and no one ever dreamed of looking for facts except by reading books. Aristotle had said, among other things, that bodies fell at rates depending on their weight. " Why he said so nobody knows. He cannot have tried. He was not above trying experiments, like his smaller disciples ; but probably it never occurred to him to doubt the fact. It seems so natural that a heavy body should fall quicker than a light one, and perhaps he thought of a stone and a feather and was satisfied. " Galilei, however, asserted that the weight did not matter a bit, that everything fell at the same rate (even a stone and a feather, but for the resistance of the air), and would reach the ground in the same time. AN INEVITABLE EVENT. 439 "And he was not content to be pooh-poohed and snubbed. He knew he was right, and he was determined to make every one see the facts as he saw them. So one morning before the assembled University, he ascended the famous leaning tower, taking with him a 100 Ib. shot and a I Ib. shot. He balanced them on the edge of the tower, and let them drop together. Together they fell, and together they struck the ground." x This was the tocsin which sounded the approach of future armies of experimentalists who were to enter in succession so many domains of human knowledge. The origin of a third scientific method, namely, that of measurement, is to be sought in antiquity. The ancient astronomers determined the intervals of a time for the heavenly bodies. " By the introduction of the astrolabe, Ptolemy and the later Alexandrian astromomers could determine the places of the heavenly bodies within about ten minutes of arc. Little progress then ensued for thirteen centuries, until Tycho Brahe made the first great step towards accuracy, not only by employing better instru- ments, but even more by ceasing to regard an instrument as correct. Tycho, in fact, determined the errors of his instruments and cor- rected his observations. He also took notice of the effects of atmospheric refraction, and succeeded in attaining an accuracy often sixty times as great as that of Ptolemy. Yet Tycho and Hevelius often erred several minutes in the determination of a star's place, and it was a great achievement of Roemer and Flamsteed to reduce this error to seconds. Bradley, the modern Hipparchus, carried on the improvement, his errors in right ascension, according to Bessel, being under one second of time, and those of declination under four seconds of arc. In the present day the average error of a single observation is probably reduced to the half or quarter of what it was in Bradley's time ; and further extreme accuracy is attained by the multiplication of observations and their skilful combination according to the theory of error." 2 These errors of observation arise from surrounding conditions, from the apparatus, and from the observer 1 Lodge, " Pioneers of Science," go. 2 Jevons, "Principles of Science," 271, London, 1887. 440 THE NEW PSYCHOLOGY. himself. It is part of the trade of a scientist that he must make a special study of these sources of error with a view to eliminating or controlling them. Thus on every hand there were men on the watch for their own peculiarities ; what was more natural than that it should sometimes occur to them to study these peculiarities for themselves? This occasionally happened for special purposes, for amusement, &c. A large mass of miscel- laneous pyschological material (chiefly in optics) had accumulated in this way, the particular value of it lying in the fact that it consisted of measurements. It was inevitable that at some time the man would come forward to develop a system of mental measurements. Turning from measurements, we find still another method that has inevitably appeared in psychology, namely, scientific statistics. This method is, in its mathematical form, the gift of a series of men like Poisson, Bernoulli, and Laplace. Its application to human beings was accomplished by Quetelet. Fechner pointed out the median as an advantageous mean in statistical work, and left behind him an as yet unpub- lished but nearly completed work on the methods of statistics. Galton has used statistics for the anthropo- logical treatment of mental qualities. In psychological research it has been used by Ebbinghaus and others. The possibility of the successful use of psychological measurements and statistics combined has been proven by researches in the Yale Laboratory. 1 The final method to be considered is that of mathe- matical analysis. The great mathematicians have repeatedly run across psychological problems and solved them as far as possible without the basis of experimental 1 See the explanation Hi Scripture, Untcrsuchungcn ilbcr die geistige Entwickeluiig der Schnlkinde^ " Zt. f. Psychol. und Physiol. d. Sinn.," 1895, x. i6i ; AN INEVITABLE EVENT. 44! data. The law of relativity (p. 267) was first enunciated by Daniel Bernoulli in respect to the psychical value of physical possessions. Physical possessions have a value or a meaning to us only as the means of producing sensations in us. In this respect the gain of a guinea is a very different matter for a rich person and a poor one ; to the poor man it will bring several days of happiness, while the rich one will not notice it. Generalising the statement, we can say that the value of any physical possession is relative to the amount we already have. Upon such considerations as these, Bernoulli developed formulas equivalent to the differential and logarithmic ones we have spoken of when considering Fechner's law (p. 271). Further developments were made by Laplace and Poisson, and the results were accepted by the later writers on the subject. To make the law a general psychological one, nothing more was needed than to bring it into relation with measurements of mind. It was inevitable that methods of measure- ment would be found, and the union of well-established facts with the methods of analysis would inevitably produce for the first time a perfected science of mind. This survey of the methods that have been introduced into scientific research in general leads us to the conclu- sion that sooner or later the world would demand an investigation of the phenomena of mind according to such methods, The particular way of applying them on a large scale required the development of a fuller science of psychology than could be obtained by obser- vation alone, and, with the forces of civilisation and science behind the demand, the new psychology was an inevitable event. CHAPTER XXXII. SOURCES OF THE NEW SCIENCE. PSYCHOLOGY, as already explained, has been largely the product of other sciences. In most cases the first impulse to .the investigation of psychological phenomena was given by the discovery of sources of error in the other sciences which were due to the scientist himself. In astronomy Tycho Brah6 did not accept his instru- ments as correct, but determined their errors ; it was not, however, until centuries later that a suspicion arose concerning the possibility of errors in the observer. Astronomers have to record the time of the passage of heavenly bodies across parallel lines in the telescope. When the star is about to make its transit the astrono- mer begins counting the beats of the clock. As the star approaches and passes the line he fixes in mind its place at the last beat before crossing and its place at the first beat after. The position of the line in respect to these two places gives the fraction of a second at which the transit occurred. In 1795 the British Astronomer Royal found that his assistant, working with another telescope at the same time, was making his records too late by half a second, Later on, this amounted to o.8 s . This difference was large enough to seriously disturb the calculations, and as the astronomer did not suspect that he himself might 442 SOURCES OF THE NEW SCIENCE. 443 be wrong, the blame was laid on the assistant. 1 In 1820 Bessel 2 systematically compared his observations with those of another observer for the same star. They found a difference of half a second. Later he made similar experiments with Argelander and Struve with the result of always finding a personal difference. Bessel sought for the cause of this " personal equa- tion " by varying the conditions. He first made use of the sudden disappearance or reappearance of a star instead of steady motion. The personal difference was much decreased. This seemed to indicate that the trouble lay in comparing the steady progress of the star with the sudden beat of the clock. The next step was to change the beats, with the result that for Bessel the observations were made later with the clock beating half seconds than with one beating seconds whereas Argelander and Struve showed no particular change. One other point was investigated, namely, the effect of the apparent rate of the star ; within wide limits the personal equation was not changed. About 1838 the personal equation began to receive regular notice in astronomical observations, as appears from the publications of Airy 3 and Gerling* of that year. It was natural to wish for a comparison of the astro- nomer's record with the real time of transit. At the suggestion of Gauss an artificial transit was arranged by Gerling, the object observed being a slow pendulum. This is probably the first measurement of a reaction time. In 1854 Prazmowski 5 suggested an apparatus carrying a luminous point for a star, and closing an elec- 1 'Greenwich Astronomical Observations," 1795, iii. 319, 339. 2 ' Astronom. Beobacht. d. Sternwarte zu Konigsberg," VIII. iii., XI. v., XVIII. iii. 3 ' Greenwich Astron. Observations," 1838, xiii. 4 'Astron. Nachrichten," 1838, xv. 249. s ' Comptes rendus," 1854, xxxviii. 748. OF THE UNIVERSITY (tt _~ -- 444 THE NEW PSYCHOLOGY. trie circuit at the instant it passed the line ; a comparison of the true time with the astronomer's record would give the real amount of his personal equation. From this time onward various forms of apparatus were invented and numerous investigations were carried out. The astronomers found that in such observations some- times the star was seen to pass the line too soon, some- times too late ; and that it depended upon every variation in the method of observing and in the mental condition of the observer. 1 Let us turn for a moment to another science. The new physiology, begun by the pupils of Johannes Muller, in which the phenomena of life were to be explained by physical and chemical processes, had undergone a remarkable development. Du Bois-Reymond had taught how to apply the experimental methods and apparatus of physics to the study of physiological pro- cesses. Soon after this, Helmholtz measured the velocity of nervous transmission (1850), an experiment that Johannes Muller had considered hopeless. This involved the construction of the myograph and the application of Pouillet's method of measuring small intervals of time. The nerves, however, are only the peripheral portions of the nervous system ; the desire lay near to measure the time occupied by the brain processes. Such measurements have been down to the present day impossible by direct physiological methods. It was, however, a sufficiently settled fact that the brain pro- cesses are closely accompanied by mental processes. This consideration led to the employment of similar methods on living human beings. The stimulus was 1 The history of the personal equation given above is summarised from Sanford, Personal Equation, "Am. Jour. Psych.," 1888, ii. 3, 271, 403. SOURCES OF THE NEW SCIENCE. 445 applied to the skin, to the eye or to the ear and the time acquired for the subject to respond by a muscular move- ment was measured. Since the subject could tell what he experienced under different variations of the experi- ment it was found possible to measure the time of sensation, of action, &c. The physiological processes corresponding to these mental processes were to some extent known. It was soon discovered, however, that other mental processes, e.g., discrimination, association, &c., could be introduced in such a way as to be measured. In 1865 Bonders began to make a systematic attack on the problem of psychological time-measurements and was soon followed by Exner. Helmholtz had already directed the experiments of his pupil Exner in measuring the time of sensation (p. 93) ; in 1877 the work of Auerbach and v. Kries on mental time issued from his Berlin laboratory. The interest of the physiologist lies, however, mainly in the deductions to be drawn concerning brain action. Even from the simpler forms of reaction-time the amount of physiological knowledge to be obtained is small, and for the more complicated forms it is zero. It was natural, therefore, for physiologists to pursue the subject but little further. 1 Thus the two sciences of astronomy and physiology discovered and developed the methods of investigating mental times ; the further development was the task of psychology. The result has been sketched in outline in Part II. 1 For the historical account of experiments on reaction-time see Buccola, " La legge del tempo nei fenomeni del pensiero," Milano, 1883, and Ribot, "La psychologic allemande contemporaine," Paris, 1885 ; for a summary with literature, see Jastrow, " Time Relations of Mental Phenomena," New York, 1890. 446 THE NEW PSYCHOLOGY. Another source of the new psychology is to be found in the physiological study of the sense organs. The most obvious method for determining the functions of the nerves and end organs of the skin, the nose, the ear, or the eye, is to ask the living subject what he feels when various stimuli are applied. In this way there has arisen a large body of knowledge concerning the sensory functions of the nervous system. In this form, however, the problem is a purely psychological one. To inquire if the skin " feels " heat is from a physiological point of view an indirect question. Physiologically the nerves of the skin may respond to heat by some chemical pro- cess. That they do so respond may be inferred on the hypothesis of a correspondence between the occurrence of a sensation of heat and the action of the nerve. 1 The direct question is one of psychology ; it is asked by physiology for its own purposes, and the psychological data are collected as long as they are of use in this way. Physiology, however, is " physics and chemistry of the body," and as soon as psychological data cease to afford physical deductions the interest of the physiologist generally ceases. The study of the psychology of sensa- tion and action, however, has formed and still forms an important portion of physiology. Historically considered, the study of the sensations of the skin received its first great impulse from Ernst Heinrich Weber's monograph : "Tastsinn und Gemein- gefuhle." 2 This has been followed by the work of a host of investigators trained in the laboratories of Ludwig, Du Bois-Reymond, and their pupils.3 1 I am, of course, not speaking of purely objective physiological experiments on nerves. 2 Wagner's " Handworterbuch d. Physiologic," 1851,. iii. (2), 561 ; also separate. An account of Weber's life is to be found in Ludwig, " Rede zum Gedachtniss an Ernst Heinrich Weber," Leipzig, 1878. 3 For summaries and references, Funke und Hering, " Physio- SOURCES OF THE NEW SCIENCE. 447 The physiology of the eye likewise originated much of Jhe psychology of sight. Concerning the functions of the optical system physiology can scarcely be said to have gone beyond the dioptrics of the eye. Nearly all further knowledge consists of deductions from the mental experiences of the subject. For example, physiology knows almost nothing concerning the functions of the retina. Psychologically, however, the colour sensations and their combinations can be accu- rately measured. It is true that the investigations of colour vision have been and are mainly carried out by physiologists and physicists ; but the point of view has become primarily a purely psychological one. This is strikingly exemplified in the researches of Konig (p. 333) from which physiological deductions are practically ex- cluded. For the various other phenomena such as those of the optical illusions, of monocular and of binocular space we have at present no hope of anything beyond a psychological knowledge ; and the investigations of Hering, 1 Helmholtz, and others can be regarded as direct contributions to psychology. There is a third science whose influence is to-day the strongest of all. Physics is theoretically the co-ordinate science to psychology. Every direct experience has an objective, or physical, and a subjective, or psycho- logical, side. Again, the fundamental science of nature is physics, that of mind is psychology. Practically, logic der Hautempfindungen und der Gemeingefiihle ; " Hermann's " Handbuch der Physiologic," 1880, iii. (2), 287 ; and Beaunis, "Nou- veaux elements de physiologic humaine," ii., Paris, 1888. 1 Among the notable publications of Ewald Hering (formerly Professor of Physiology in Prag, now in Leipzig) special mention is due to Der Raumsinn und die Bewegtmgen des Atiges, in Hermann's "Handbuch der Physiologic," iii., Leipzig, 1879. A list of his works can be found in the bibliography appended to the last edition of Helmholtz's " Physiologische Optik." 448 THE NEW PSYCHOLOGY. however, psychology receives from the most powerful science of modern times an invaluable protection, and an uninterrupted series of scientific gifts. The photo- metry of Lambert led not only to the methods of modern technical photometry, but also to the measurement of our sensations of light. The law of relativity had been, before Fechner's time, established for light by Bouguer, Masson, Arago, Herschel, and Steinheil. The study of the errors of observation in physics and astronomy has led not only to the science of physical measure- ments, but als^o to that of psychological measurements. Newton, Young, and Maxwell, began not only the science of ether vibrations, but also the science of sensations of light. The laws of mechanics apply not only to inanimate objects, but also to the results of our own volitions. In fact, in every department of ex- perimental psychology progress has been and still is closely dependent on the achievements of physics and technology. Another powerful influence in forming the new psy- chology was " physiological psychology." Alkmaion (about 520 B.C.) seems to have been the first to care- fully consider the functions of the nervous system in regard to mental life. In modern times the earliest prominent figure appears to have been Varoli (d. 1575), who considered the cerebrum to be the organ of mind. Gall (d. 1828) \vent further in specialising the con- volutions for this purpose, and in investigating the systems of fibres. The doctrine of Flourens (1842), the discoveries of Broca (1863), the experiments of Fritsch and Hitzig (1870) and of Ferrier (1873), the extirpations by Munk and Goltz, the development studies by Flechsig and the clinical observations of Charcot, have led to a remarkable activity in the study of the functions of the brain. The ultimate aim is a SOURCES OF THE NEW SCIENCE. 449 thoroughly scientific knowledge of the action of the brain and of its connection with mental life in health and disease. The direct knowledge of mental life assumed in these researches is that common to every- body ; psychological science is generally disregarded or distrusted. In Germany the physiological data first received recognition in connection with psychology through the work of Lotze (" Medicinische Psychologic," 1852). The work has had its chief influence in introducing empirical methods of thought, and in thus preparing for experimental psychology. A similar movement was begun somewhat later in England. Dissatisfied with the condition of introspec- tive psychology, and stimulated by the achievements of brain physiology, various enterprising minds under- took the reconstruction of psychology on the basis of physiology. The vigorous work of men like Maudsley (" Physiology and Pathology of Mind," 1867, and later editions) brought about closer relations between academic psychology and the phenomena of pathology, of animal life, &c. The principle of this " physiology of mind " (denying the validity of introspection and hoping to determine mental facts by brain-dissections) was a false one, as has been explained in Chapter I. ; yet introspective psychology began to take a wider view, and in the works of Carpenter (" Mental Physi- ology," 1874) and most of the later psychologists we find an introspective account of mind preceded and ac- companied by accounts of the nervous system. Finally, the whole movement toward the introduction of "natural science methods" into psychology has been greatly favoured by the exponents of evolution, such as Spencer (" Principles of Psychology," 1855 ; 3rd edit., 1880). This tendency of physiological psychology has of 30 450 THE NEW PSYCHOLOGY. late developed in two directions. On the one hand, it has led directly to the establishment of experimental psychology, which in some places still goes by the older name, although its standpoint has become a purely psychological one. On the other hand, it has led to a psychological program which at the present day is far from successful fulfilment. The " future " psychology was to begin with first investigating the nervous system, and then deducing psychological laws therefrom. The brain was to be accurately mapped out into faculties, the paths of nervous currents were to be traced along various fibres, and the interaction of nervous molecules was to be known in every par- ticular ; it was even expected by some that various cells could be cut out with a memory or a volition snugly enclosed in each. In other words, there was to be no psychology except on the basis of a fully developed brain-physiology. Unfortunately very little has been ascertainable concerning the finer functions of the nervous system, and aside from a general knowledge that the cerebellum has to do with co-ordination of movements, the convolutions of Broca have to do with speech, and similar facts, nothing of even the remotest psychological bearing has been discovered concerning the functions of the brain. The roseate hopes of those who expected a new psychology out of a brain- physiology were totally disappointed. In the effort for something new, however, the psychologist supplied the data concerning the " molecular movements " in the brain by his own imagination ; the familiar facts of mind were retold in a metaphorical language of " nerve currents," " chemical transformation," &c., of which not one particle had a foundation in fact. 1 1 It is to be noted that these statements refer to investigations of and speculations on the brain for psychological purposes. For SOURCES OF THE NEW SCIENCE. 451 While this was going on, physics had through Helmholtz, 1 Mach, 2 and others gradually come to a clear understanding of the relation of its facts to the immediate facts of consciousness. Direct experience as present in our sensations was accepted as supplying the facts of physics. For example, in measuring the length of a bar a visual sensation, the unit of measure- ment, was applied to another visual sensation, the bar. Indeed, as was clearly recognised, every direct measure- ment of physics was primarily a comparison between sensations in other words, a psychological measure- ment. From this combined measurement the physicist reduced as much as possible the psychological elements ; it was but a step for the psychologist to reduce the physiological purposes the case is utterly different. The develop- ment of brain anatomy and of the knowledge concerning the localisation of cerebral functions is among the greatest achieve- ments of modern times. (For a historical sketch and an account of the latest remarkable discovery see Flechsig, " Gehirn und Seele," Leipzig, 1896.) Moreover, the collection of facts and the develop- ment of theories of the nervous activities accompanying mental phenomena have given rise to the science of physiological psychology. (As a representative work see Exner, "Entvvurf zu einer physio- logischen Erklarung der psychischer Erscheinungen," I. Theil, Leipzig, 1894 ; for a convenient summary, see Ziehen, " Leitfaden der physiologischen Psychologic," 2nd ed., 1893, also translated.) With these sciences, however, the psychologist has very little to do. The study of brain function has contributed compara- tively little to our knowledge of mental life except in abnormal conditions ; the deductions of physiological psychology concerning nervous function are based upon the facts of experimental and observational psychology, and are still so unsettled as not to allow additional deductions backward. 1 Helmholtz, Ueber das Ziel und die Fortschritte der N aturwisscn- schcift, " Populare wiss. Vortrage," Braunschweig, 1871. Helmholt/, "Die Thatsachen in der Wahrnehmung," Leipzig, 1879. 2- Mach, "Die Mechanik in ihrer Entwickelung," Leipzig, 1883, 2nd ed., 1889 ; also translated into English, Chicago, 1895 (Mach's earlier monographs are mentioned in the preface). Mach, "Beitriige zur Analyse der Empfindungen," 141, Jena, 1886 (translated). 452 THE NEW PSYCHOLOGY. physical elements in order to have a psychological measurement. 1 This step made psychology for the first time a quantitative science in the full meaning of the term with all the previous achievements of physics for its use. There is still another science which we must consider, namely, the old psychology. By the " old psychology " I mean psychology before the introduction of experi- ment and measurement. In the previous chapter it was noticed that the victory of observation over speculation in mental science was mainly due to Hobbes and his successors. Thomas Hobbes (1588-1679), educated at Oxford and Paris, personally acquainted with Bacon, and deeply impressed with the importance of the Galileian and Baconian methods, was the founder of an observational as opposed to a speculative and dogmatic science of mind. After Hobbes the empirical method made little progress till the time of Locke (1632-1704). Educated at Oxford, and specially inclined to the natural sciences and medicine, Locke proposed to analyse the pheno- mena of the human mind directly on the basis of .the facts themselves, expressly excluding all ques- tions of metaphysics and of physiological psychology. 2 . l The psychological standpoint has been clearly stated by Wundt, Ueber die Messnngen psychischer Vorgiinge, "Philos, Studien," 1883, i. i ; Weitere Bemerknngen fiber psychische Messnngen, same, 463 ; Ueber die Eintheilung der Wissenschaflen, " Philos. Studien," 1 889, v. i ; Ueber die Definition der PsycJioIogie, " Philos. Studien," 1896, vii. i ; Ucber naivennnd kritischen Realismns, "Philos. Studien," 1896, xii. 307. I have taken the same view in The Problem of Psychology, "Mind," 1891, xvi. 305; Psychological Measurements, "Philos. Re- view," 1893, ii. 677. 2 Locke, " An Essay concerning the Human Understanding," bk. i. ch. i. sect. 2. SOURCES OF THE NEW SCIENCE. 453 Locke's introspective standpoint received strong em- phasis and thorough elaboration in the works of Berkeley (1685-1753). Somewhat later the empirical method, which Locke did not succeed in fully carrying through, was applied in a thoroughly consistent fashion by Hume (1711-1776). Thus at this early date the problem of psychology and its fundamental method were definitely understood and clearly expressed. The further development of psychology by Hamilton, Reid, Mill, and the later writers belongs to the history of " general " or " descriptive " psychology rather than to an account of that part of the larger science with which we are at present concerned. It is, however, not easy to draw the line between the new and the old ; some of the important works, written before the recog- nised introduction of laboratory methods but yet using the results of experimental work as far as obtainable, will be noticed in the following chapter. The method of direct observation of mental life is the only possible one, and until it had received a firm basis any science of psychology was impossible. As has been explained in Part I., all the other methods of psychology are only refinements of this method. The new psychology is thus merely a development on the basis of the old ; there is no difference in its material, no change in its point of view, and no degeneration in its aims. What the old tried to do, namely, to establish a science of mind, and what it did do, as far as its means allowed, the new psychology with vastly improved methods and facilities is striving to develop in finer detail. 1 1 For historical accounts, see also Kiilpe, " Grundriss der Psy- chologic," 24, Leipzig, 1893 ; Baldwin, Psychology Past and Present, " Psych. Rev.," 1894, i. 363. CHAPTER XXXIII. FECHNER, HELMHOLTZ, WUNDT. THE existence of experimental psychology as an inde- pendent science, begins with Fechner. 1 Gustav Theodor Fechner was born, 1801, in Gross- saerchen (Niederlausitz), Prussia. As a student of medicine at the University of Leipzig, he was a pupil of Ernst Heinrich Weber. His first scientific inspiration came from Oken's " Natural Philosophy." He was gradually led to more exact reasoning through the text- book of Biot, which turned him to the study of physics. He translated several French works and produced a number of original contributions. At the same time, under the name of Dr. Mises, he published a number of humorous and satirical essays. Chiefly on account of his scientific investigations, he was made professor of physics, Leipzig, 1834, but he was obliged to retire in 1840 on account of illness. His interest had long been vividly fixed on the relations of mind and body ; his training in physics made him desire some method of measuring sensation and some law of its connection with the physical processes in the nervous system. 2 Seeking to express 1 For the details of Fechner' s life, see Kuntze, " Gustav Theodor Fechner," Leipzig, 1892 ; for a brief account of his life and work, see Lasswitz, " G. Th. Fechner," Stuttgart, 1896. 2 Fechner gives the account himself in his "Elemente der Psycho- physik," last section. 454 FECHNER, HELMHOLTZ, WUNDT. 455 the relation between mental and bodily processes, Fechner had thought of a law of direct proportionality ; for more complicated processes he had proposed the relation between lower and higher arithmetical series, or even geometrical ones. These were merely schematic relations j the unit of measurement was lacking until it Fig. Il8. GUSTAV THEODOR FECHXER. occurred to Fechner to use the relative increase of phy- sical energy (or , where R denotes the physical energy) as the measure of the increase in the corresponding psychological intensity. The fundamental formula followed at once as a deduction (p. 271). The confir- mation of this law appeared to be found in the ordinary 456 THE NEW PSYCHOLOGY. experience that the increase in sensations of light did not keep pace with the physical increase, a fact that was moreover true of all our sensations. Upon sending an account of his idea to the physicist, W. Weber, he received the reply that, though the idea was a good x>ne, it would not find acceptance until it was established by concrete examples. After long seeking, Fechner devised some special experiments in light. " With a half-covered sky it is generally easy to find a pair of neighbouring shades in the clouds which exhibit only the trace of a difference to the eye. . . . After I had found two such components of a just perceptible difference, I placed two grey glasses before the eyes. . . . One of these let through a little more than one-third of the light, and both together at the most one-seventh of it. ... It was natural to suppose that the difference which was before only just perceptible, would be lost by such a reduction or would at least become markedly less clear. This was not the case. The difference remained at least as clear as before." * The just perceptible difference, therefore, was a certain fraction of the stimulus regardless of the ab- solute intensity. This is what was demanded by Fechner's law. Thereafter Fechner undertook ex- periments with lifted weights (p. 268), which he carried on for many years ; whereupon he found that as he relates what he sought and had gained by hard labour was already present to a certain degree in the clear statements and experimental data of Ernst Heinrich Weber (p. 267). The investigations of Volkmann, the previous work of Masson, Steinheil's measurements of the stars these and other data were all gathered by Fechner in support of his law. Still later, Fechner developed his method of right and wrong cases (p. 268), wherefrom he was led to a consideration of-the^so- called method of average errors. To Fechner's mind, the law of the relation between the 1 Fechner, " Elements der Psychophysik," i. 141. FECIINER, HELMHOLTZ, WUNDT. 457 psychical and physical worlds and the unit of measure- ment were found. 1 The work of Fechner was followed by many discus- sions. The chief criticism to which it was subjected was that of G. E. M tiller, who, in his work "Zur Grundlegung der Psychophysik," Berlin, 1878, gave the subject a most thorough examination from every point of view. The position of this work in the history of psychology was stated by Fechner himself, who says that nothing had done more to render the founda- tion of psychophysics firmer. In the previous chapter we found that the name of Helmholtz occurred in connection with many of the sources of psychology. Hermann von Helmholtz was born in 1821 at Potsdam, Prussia. 2 He prepared himself for the pro- fession of army surgeon, and after passing through a practical course in the Charite Hospital, in Berlin, took up his duties in Potsdam. Happening to succeed in getting a microscope, he at once used it for scientific investigation, obtaining as a result the doctor's degree in 1842 by a valuable thesis on the ganglia of the inver- tebrates. In 1847 he published his essay " Ueber die Erhaltung der Kraft." This essay, the most important that had appeared for centuries in the history of the natural sciences, was his first one in physics. Freed from military service through the interposition of Alexander von Humboldt, he was appointed instructor in anatomy in the Berlin Art Academy (1848). He 1 The list of Fechner's works is to be found at the end of the first volume of the second edition of his " Elemente der Psychophysik," Leipzig, 1889; and also in Kuntze, "Gustav Theodor Fechner," Leipzig, 1892. 2 In the following account I have relied mainly on a tribute by Wiedemann, " Annalen der Physik und Chemie," 1895, liv. i. ; see also v. Bezold, " Hermann von Helmholtz," Leipzig, 1895. 45$ THE NEW PSYCHOLOGY. was then called (1849) to Konigsberg as professor of physiology and pathological anatomy, and to Bonn (1855) as professor of anatomy and physiology. In the meantime physiology had become an independent science through the work of Ernst Heinrich Weber, Ludwig, Du Bois-Reymond, Briicke, and himself. A Fig. 119. HERMANN VOX HELMHOLTZ. special chair for physiology alone was founded and given to him at Heidelberg (1858). Helmholtz's first great achievement in physiology was the measurement of the velocity of nervous impulses (p. 444), in 1850. He then turned to the investigation of the eye and the ear. For in- vestigating the eye it was first necessary to study FECHNER, HELMHOLTZ, WUNDT. 459 more accurately the anatomical and geometrical condi- tions of its movements and mechanical -changes. For this purpose he invented the ophthalmometer. This was first used for measuring the curvature of the cornea. In the course of his further investigations he invented the ophthalmoscope for directly viewing the interior of the eye. He then proceeded to the psych- ology and physiology of vision. The results of his optical work are to be found mainly in his " Physio- logische Optik," which appeared in sections during the years 1856-66. His psychological work led him to philosophical considerations and to mathematical developments concerning space, number, and measure- ment. Even while studying the eye he produced his " Lehre von den Tonempfindungen" (1862). By the establishment of the principle of the con- servation of energy, Helmholtz had become the fore- most physicist of Germany. In 1871 he was called to the Professorship of Physics in Berlin. From this time onward he stimulated many psychological in- vestigations, although he made none himself. Upon taking up the work (1884) of a second edition of the tl Physiologische Optik " he again applied his powers of analysis to psychological problems with the usual result. In 1888 he accepted the care of the Physikalisch-Technische Reichsanstalt, in which the chief work was the foundation of the methodology for measurements of the highest accuracy. He died in 1894. "When we view the scientific life of Helmholtz we are amazed at the extent and the fulness of his achievements. While many other prominent investigators select single themes, which they work out with the best of results, with Helmholtz all the undertakings of his life fit harmoniously together. From the investigation of the sense organs, in which definite physical and physiological data were opposed to arbitrary suppositions concerning the action of a vital 460 THE NEW PSYCHOLOGY. force, the same fundamental thought continues down to the ' Erhaltung der Kraft,' in which the changes of energy were limited by its constancy and indestructibility. Almost all his later achieve- ments are based on the same thought, and thus Helmholtz passes gradually, in correct scientific developments, from general me- chanical considerations to hypotheses concerning the structure and inner nature of matter, with which problem his life closes." ' Fig. 120. WILHELM \VUXUT. The third great figure in the history of experimental psychology is Wundt. Wilhelm Wundt was born at Neckerau in Baden in 1832. Having studied medicine at Tubingen, Berlin, and Heidelberg, his academical career began with a place as instructor in physiology at Heidelberg. In 1 Wiedemann, as before. FECHNER, HELMHOLTZ, WUNDT. 461 1862 he published his " Beitrage zurTheorie der Sinnes- wahrnehmung," containing important investigations in the psychology of the senses. This was followed (1863) by " Vorlesungen iiber die Menschen und Tierseele" (second edition 1892, also translated). In 1864 he was made assistant professor of physiology ; in 1874 he was called to Zurich as professor of philosophy, and in 1875 to Leipzig. Several earlier works were connected with physics and physiology. In 1874 there appeared his great psychological work "Grundziige der physiologischen Psychologic" (fourth edition, 1893). In 1883 begins the first volume of his " Philosophiche Studien." His latest psychological book, " Grundriss der Psychologic," appeared in 1896 (also translated). The development of psychology led him to the study of philosophical problems in methodology, epistemology, and metaphysics ; this resulted in his " Logik," " Ethik," and " System der Philosophic." Aside from his position as a philosopher, with which we have here nothing to do, probably the most im- portant and far-reaching achievement of Wundt's life is the successful establishment of the first psychologi- cal laboratory. Upon his arrival at Liepzig (187=5) one room was given him for setting up his own apparatus and conducting his investigations. The first students to appear were two who entered in the winter of 1879-80 ; one of these was G. Stanley Hall. In 1886 the laboratory was recognised as an official university institute, and an assistant was appointed. The internal history of the laboratory is to be found in the series of monographs describing investigations made in it, which are contained in the twelve volumes of the " Philosophische Studien." Among the names to be found there are those of Kraepelin, Merkel, Cattell, 462 THE NEW PSYCHOLOGY. Lehmann, Kuelpe, Kirschmann, Martius, v. Tschisch, Witmer, Pace, Titchener, Marbe, Meumann, Kiesow, Jucld, Station, and others, who now have laboratories of their own or have made valuable contributions to science. CHAPTER XXXIV. THE PRESENT SITUATION. AT the present day the new psychology is a recognised member of the family of the sciences ; its condition, however, and the character of its progress are different in the various countries. Down to a few years ago, experimental psychology was almost exclusively a German science. I have already traced its course in the preceding chapters. 1 At the present day there are laboratories in connection with the professorship of philosophy in several of the larger universities, e.g., Berlin, Bonn, Gottingen, Wiirzburg, &c., and also one at Heidelberg in connection with the chair of psychiatiy. In the year 1890 a special periodical for psychology, the " Zeitschrift fur Psychologic und Physiologic der Sinnesorgane," was established by Ebbinghaus and Konig, with the co-operation of Aubert, Exner, Helm- holtz, Hering, v. Kries, Lipps, G. E. Mueller, Preyer, Stumpf, and Pelman, all of whom have contributed scientific material of the highest value. Germany's position in psychology at the present day has been made so plain in previous chapters of this book, that further explanation or comment on the character of 1 For an account of German psychology to 1885 see Ribot, " La psychologic allemande contemporaine," Paris 1885 (also translated). 463 464 THE NEW PSYCHOLOGY. the work would be superfluous ; I will add merely a few words concerning the prospects for the future. In spite of the fact that so many psychological in- vestigations still come from Germany, the number of laboratories is not large, and the equipment is often not extensive. The progress, however, though slow, is sure. The most significant sign lies in the fact that the Prussian Government aims to found laboratories wherever the appropriate persons are to be found. " To be sure, there is still somewhat of a lack of the appropriate ones. Among the great number of teachers of philosophy in the German universities there are still relatively few who devote themselves specially to experimental psychology." Turning to a consideration of the neighbouring country, France, let us place the pen in the hand of the best-known representative of the new psychology, A. Binet. 1 "The first work of experimental psychology which we possessed in France is the book of Taine on < Intelligence ' (1870). This book, which created an epoch among us, is above all a treatise on patho- logical psychology, built on observations taken from the alienists. It is a very systematic work ; many of its parts are now antiquated ; others, like the chapters on representations, are still of value. "A second important date, 1875, is that of the appearance of the ' Revue Philosophique,' founded and directed by Th. Ribot. Professor Ribot has contributed greatly to the development of psychology 1 Professor Binet was kind enough to prepare the account for this book. I venture to hope that it will be of special interest in view of the fact that very little is known to the outside world con- cerning the history of psychology in France. The term " experi- mental " has in French a slightly wider meaning than in English. THE PRESENT SITUATION. 465 in France : in the first place, by the ' Revue ' which he has generously opened to new ideas ; again by his works (' L'Heredite psychologique/ * Psychologic anglaise con- temporaine/ ' Psychologic allemande contemporaine/ ' Maladies de la memoire/ ' Maladies de la volonte/ ( Maladies de la personalite/ ( Psychologic de Pattention/ &c.), z in which he has condensed in a remarkable way a profound understanding of physiological psychology ; and, finally, by his instruction at the College de France. We thus consider him in general as our leader. " In 1878 Professor Charcot, the eminent physician of the Salpetriere, began to publish researches on hypnotism, a nervous condition still poorly defined, which the French psychologists have studied with predilection. At a later date Professor Charcot, on the occasion of clinical instruction concerning aphasia, presented an ingenious theory of language and thought (the theory of visual, auditory, and motor images) which has become classical, although it is probably incorrect in many fundamental points. The same is true for his theories of hypnotism, some of which have fallen to pieces a fact which does not hinder his investigations from having rendered great services to science. "After these three names the most important of all we must mention Charles Richet, professor of physiology in the faculty of medicine, who has made numerous studies on pain, somnambulism, telepathy, &c. (' L'Homme et 1'intelligence/ ' Psychologic generate/ &c.) ; Charles Fere, physician at the Bicetre hospital, whose name is connected with questions of heredity and of the relation between stimulation and movement (' Sensation et mouvement/ ' Pathologic des emotions/ 1 Le magnetisme animal ') ; Beaunis, who with Bernheim has aided in showing the role of suggestion in hypnotism 1 Nearly all of these have been translated into English. 31 466 THE NEW PSYCHOLOGY. ('Le somnambulisme provoque ') ; Pierre Janet, who, by his studies on hypnotism, has especially thrown light on the phenomena of dissociation of consciousness (' L'automatisme psych ologique '); and Bourdon, known for his conscientious studies on memory and association of ideas ( l L' expression des emotions et des tendances dans le langage '). We must mention also Sollier, Seglas, Dumas, Godfernaux who, from various points of view, have contributed to the psychology of alienism (I, of course, do not speak here of the alienists by profession) ; Jules Soury, who has devoted himself specially to biblio- graphical psychology and has published, in this sense, valuable works on the brain ; Jacques Passy, to whom we owe well-finished and precise researches on the psychology of odours ; and Perez, the observer of children. Of descriptive writers, of critics, and of theorists like Arreat, Egger, Liard, Paulhan, Souriau, Seailles, Tarde, Le Bon, and, above all, Fouillee, and of the philosophers, the names are too numerous for complete citation ; we must, however, mention the greatest of them, Renouvier, the celebrated neo-Kantian. a We see by these names that the principal efforts of French psychologists have been directed toward pathology ; the chief subjects of study have been the insane and the hysterical. Let us note, moreover, that the majority of the French psychologists are physicians and not psychological specialists ; from this it results that the development of the science has occurred outside of the laboratory, away from official guidance and disre- garded by the university. " It is only eight years ago that the board of superior instruction created a chair of experimental psychology at the College de France, and about the same time (1889) founded the psychological laboratory of the Hautes Etudes, whose head director has been Professor THE PRESENT SITUATION. 467 Beaunis. These are the two official institutions for psychology. They have not, at the present, the com- plete practical influence that one could have hoped for, because experimental psychology does not figure in any examination, and in France leads to nothing. More- over, we do not have in our laboratory, to the same degree as in Germany, students who undertake investiga- tions in order to obtain a diploma ; students come to us only when they have a veritable vocation for psychology, and these are always rare. Among my students and assistants I will mention MM. Philippe and Courtier, M. Milhaud, who has been associated with me in most of my investigations, and M. Victor Henri who has already become known through his studies on memory and on tactile sensibility. Con- nected with our laboratory is the * Annee Psych ologique,' founded two years ago, and edited by Professor Beaunis and myself. u Finally, to be complete, I will mention the ephemeral existence of the 'Societe de psychologic,' which was founded a dozen years ago under the auspices of Professor Charcot, and which has disap- peared at the present time, from causes that are still discussed ; I believe that its death arose from the fact that it allowed itself to be invaded by the spiritists and telepaths. " We must now attempt to outline in a few words the character of the contributions which French scientists have made to experimental psychology. In this respect it is necessary to state, without bitterness but frankly, that our work is completely unknown abroad. Thus we see chiefly German works cited ; ours are generally absent from the best-made bibliographies. Thus it comes about that the American students, who to-day form incontestably the majority of the students of psy- 468 THE NEW PSYCHOLOGY. chology and of the future psychologists, are educated in the German laboratories. "The investigations in experimental psychology in France fall into two categories which form to a certain degree two successive periods. " The first period is that of hysteria and hypnotism. There was a certain epoch, approximately from 1880 to 1890, during which there appeared in France a considerable number of works on the questions of hypnotism and of hysteria. The contributions came mainly from the school of the Salpetriere and also from a rival school, that of Nancy. In spite of the objec- tions made to these contributions, it is certain that they have taught us many things concerning suscepti- bility, the influence of excitations in relation to move- ments, hallucinations, and the phenomena of the division of consciousness. The danger of studies in hypnotism is that it has furnished an easy transition to the study of telepathy, clairvoyance, and other phenomena ejusdem farina, which have in France attracted a great number of mystics and amateurs of the semi-obscure. "The second of the two periods which I have indicated is signalised by a relaxation of the studies in hypnotism. The effort is turned by preference to other questions aphasia, arithmetical prodigies, memory, the superior intellectual functions, and also the organic and motor functions connected with intel- lectual states. I believe, as far as predictions go, that French psychology will long continue in this path, on which it entered about 1890. To this period belongs Bourdon, who has just established a small laboratory at Rennes (the second one in France). As is known, the contributions of this scientist are nearly all devoted to the phenomena of ideation among adults. The sche- THE PRESENT SITUATION. 469 clules of questions and the investigations of Ribot on memory and abstraction belong also to this period. Finally, I may say that most of the investigations of this period have come from the Paris laboratory, which presents a special equipment for the study of organic and motor reactions, and for all that relates to the graphic method." ' In Italy there is one psychological laboratory, at Rome, in connection with the Anthropological Insti- tute ; it is conducted by Professor Sergi, who has pub- lished several works on psychology. A great deal has, however, been done in physiological laboratories, psy- chiatrical clinics, and asylums. Mosso (Turin) has made researches on fatigue (see Chap. XVI.), on the emotions and their effects, &c. Lombroso (Turin) has performed psychological experiments on criminals. Tamburini (Modena) has founded an institute for psychological work as a propaedeutic to psychiatry. Morselli (Genoa) has made several psychological investigations. Tito Vignoli (Milan) has published valuable works on com- parative psychology, &c. Of the other European countries, Russia (Moscow, Dr. Tokarsky) and Switzerland (Geneva, Professor Flournoy) are the only ones that have laboratories with psychological specialists. In England one of the most prominent figures is Alexander Bain, for many years Professor in the University of Aberdeen, whose comprehensive work, 1 Professor A. Binet, director of the psychological laboratory of the Sorbonne (Hautes Etudes), has published numerous books and monographs ; among them are : " La psychologie du raisonne- ment," "Le magnetisme animale," 'Les alterations de la per- sonalite," " La vie psychiques des micro-organismes," " La psycho- logie des grands calculateurs et joueurs d'echecs," &c. (The historical part of the last work is based on my monograph, Arithmetical Prodigies, " Amer. Jour. Psych.," 1891, iv. I.) 47 THE NEW PSYCHOLOGY. "The Senses and the Intellect" (1855, four later editions), has had a marked influence on the develop- ment of psychology. The standpoint is that of intro- spection with full recognition of physiological and experimental data. The results of experimental work have been carefully used at the appropriate places in several works on psychology by James Sully, Professor in University College, London ("Outlines of Psycho- logy/' " Human Mind," &c.). Professor George Croom Robertson, the former editor of " Mind," deserves special mention for his friendly attitude toward the new science. The brilliant work of Francis Galton (" Inquiries into Human Faculty," " Hereditary Genius," &c.) has had a lasting influence on many departments of experimental work. The psychological data concern- ing the sexes have been treated by Havelock Ellis (" Man and Woman"). The English quarterly, "Mind" (G. F. Stout), occasionally contains experimental articles, as also do the "Journal of Mental Science" and "Brain." An anthropometrical laboratory with con- siderable psychological apparatus was established by Mr. Francis Galton at South Kensington many years ago, and maintained at his own cost. In 1895, having obtained as many facts as he could utilise, Mr. Galton closed the laboratory and presented the apparatus to the anatomical department of the museum at Oxford, where some work was initiated. At Cambridge Professor Ward first lectured on experimental psychology in 1882. Practical teaching began in 1893, and is carried on by Dr. W. H. R, Rivers, who has two rooms at his disposal in the Physiological Laboratory. Four courses are given in the year two in experimental psychology, and two in the physiology of the sense-organs and there is a fair amount of apparatus (most complete as regards the study of vision) with which work can be done in most THE PRESENT SITUATION. 471 departments of experimental psychology. 1 At present there is no psychological laboratory in London, but funds are now being collected for the establishment of such a laboratory at University College, and the matter is in the hands of an organising committee, consisting of Mr. Galton, Dr. Rivers, Professors Carey Foster, Karl Pearson, Schafer, and Sully. The University of Toronto has had a laboratory for a number of years (Professor Baldwin, then Dr. Kirsch- mann). In the United States the new movement needed the endorsement of the older universities. This came from courses in physiological psychology by Professor James at Harvard and Professor Ladd at Yale. A decisive form was given to the movement by the publication of Ladd's "Elements of Physiological Psychology" (1887). This received immediate recognition ; for a long time it was the only accessible source of information concerning the new psychology, and its character profoundly influ- enced the development of American psychology. James had already begun to collect material for laboratory work, but the first officially recognised laboratory was founded (1883) at Johns Hopkins University (Baltimore) by G. Stanley Hall, a pupil of Wundt. In 1887 the publication of the " American Journal of Psychology " (G. Stanley Hall) was begun ; in 1888 the first pro- fessorship of experimental psychology was founded at Philadelphia (Cattell) ; in 1893 the " Psychological Review " (Cattell and Baldwin) was established ; and in the same year a third psychological publication, " Studies from the Yale Psychological Laboratory," was begun. In 1890 James published his " Principles of Psychology," which aroused general public interest ; 1 Mr. Galton and Dr. Rivers have kindly supplied the information regarding their laboratories. 472 THE NEW PSYCHOLOGY. and in 1895 Sanford published the first part of his instructions for making elementary experiments (" La- boratory Course in Experimental Psychology"). In response to a demand for a book adapted to the average unscientific reader, "Thinking, Feeling, Doing" appeared in 1895. The rapid development of experimental psychology in America has brought into existence more than twenty laboratories of all sizes and degrees of equipment, often quite elaborate. 1 During the last few years the smaller laboratories have multiplied so rapidly in the colleges and normal schools that it is impossible to give any account of them. With a few exceptions, every university or college of note has an equipment of some kind. There are some peculiar characteristics of American psychology that have arisen from its rapid development. The invention of new and more accurate apparatus has come to the foreground through the establishment of the machine-shop with a trained mechanic as a fundamental part of the laboratory. This has long been recognised as the most profitable course in the great European and American laboratories of physics and physiology ; in psychology it was first accomplished at Yale. Still another characteristic is the development of systematised courses of instruction on a large and carefully adjusted scale. This also is but the logical outcome of the conditions where the psycho- logical work is placed in competition with the other sciences as elective courses in the great colleges ; merely as a matter of self-preservation, psychology must gain the confidence of the students by offer- ing lecture courses and laboratory exercises equal 1 See Delabarre, Lcs Laboratories dc Psychologic en Amerique t " Annee Psychologique," 1894, i. 209. THE PRESENT SITUATION. 473 in attractiveness and value to those of physics and chemistry. The modest and simple equipment with which the German investigator patiently produces his research-work, is quite inadequate for instructing large bodies of American students. Passing to Asia, we find a large laboratory (Professor Motora) in the University of Tokio (Japan). Experi- mental instruction has just begun in the University of Pekin (China). In conclusion, the future of experimental psychology seems a modest but assured one. It is now clearly understood that its methods are those of patient scientific work. It has not found and cannot hope to find an utterly new method of investigation or a startling prin- ciple of mental life ; it cannot dissect the mind with a scalpel, nor has it discovered how to project thoughts along imaginary telegraph wires. Again, at the present day, it should not be expected to make discoveries of 'the interest and value of those repeatedly made by the other sciences with many well-trained men and more thoroughly equipped laboratories ; many years of laborious development must ensue before discoveries equal in importance to those of argon and the X-rays can even be hoped for. The present firm establish- ment of our science in the leading universities, how- ever, makes this development an assured one. APPENDICES. APPENDIX I. VALUES OF THE PROBABILITY INTEGRAL ^~J ^ <# FOR THE ARGUMENT 7. """ r 01234 56789 o.o O.I 0.2 0-3 0.4 o.oooo 0.0113 0.0226 0.0338 0.0451 1125 1236 1348 1459 1569 2227 2335 2443 2550 2657 3286 3389 3491 3593 3694 4284 4380 4475 4569 4662 0.0564 0.0676 0.0789 0.0901 0.1013 1680 1790 1900 2009 2118 2763 2869 2974 3079 3183 3794 3893 3992 4090 4187 4755 4847 4937 5027 5"7 o-5 0.6 0.7 0.8 0.9 0.5205 0.5292 0.5379 0.5465 0.5549 6039 6117 6194 6270 6346 6778 6847 6914 6981 7047 7421 7480 7538 7595 765i 7969 8019 8068 8116 8163 0.5633 0.5716 0.5798 0.5879 0.5959 6420 6494 6566 6638 6708 7112 7175 7238 7300 7361 7707 7761 7814 7867 7918 8209 8254 8299 8342 8385 I.O i.i 1.2 1-3 M 0.8427 0.8468 0.8508 0.8548 0.8586 8802 8835 8868 8900 8931 9103 9130 9155 9181 9205 9340 9361 9381 9400 9419 9523 9539 9554 9569 953 0.8624 0.8661 0.8698 0.8733 0.8768 8961 8991 9020 9048 9076 9229 9252 9275 9297 9319 9438 9456 9473 9490 9507 9597 96n 9624 9637 9649 1-5 1.6 3 1.9 0.9661 0.9673 0.9684 0.9695 0.9706 9763 9772 978o 9788 9796 9838 9844 9850 9856 9861 9891 9895 9899 9903 9907 9928 9931 9934 9937 9939 0.9716 0.9726 0.9736 0.9745 0.9755 9804 9811 9818 9825 9832 9867 9872 9877 9882 9886 9911 9915 9918 9922 9925 9942 9944 9947 9949 9951 2.O 2.1 2.2 2-3 2. 4 0-9953 0.9955 0.9957 0.9959 0.9961 9970 9972 9973 9974 9975 9981 9982 9983 9984 9985 9989 9989 9990 9990 9991 9993 9993 9994 9994 9994 0.9963 0.9964 0.9966 0.9967 0.9969 9976 9977 9979 9980 9980 9985 9986 9987 9987 9988 9991 9992 9992 9992 9993 9995 9995 9995 9995 9996 2. 0-9953 0.9970 0.9981 0.9989 0.9993 0.9996 0.9998 0.9999 0.9999 0.9999 This table, first published by Encke, is now to be found in nearly all works on probabilities or measurement. I have reproduced the compact form used in Merriman's "Textbook of Least Squares." More extended tables can be conveniently found in the following : (4 places), Kampfe, " Phil. Stud.," 1893, ix. 145 ; (5 places), Meyer, 475 APPENDICES. "Wahrscheinlichkeitsrechnung," Leipzig, 1879; (7 places), Wein- stein, "Physikalische Maassbestimmungen," i. Berlin, 1886 ; Czuber, "Theorie der Beobachtungsfehler," Leipzig, 1891 ; (n places), Bertrand, " Calcul des probabilites," Paris, 1889. APPENDIX II. SCHEMES FOR BERNOULLI'S THEOREM (PAGE 2l). The theorem may be thus stated : If two opposite events A and not-A occur according to the laws of chance, and if r and s are the times of occurrence required by those laws out of a total u t then, when n is large, the probability is that on a given occasion A will actually occur a number of times lying within r I, where /2rs = y *J -- ' v The theorem may also be stated as follows : If p and q are the probabilities of the two opposite events A and not-A, it can be expected with a probability of P = -^r- / c~ f dt + _: that the actual result for A will lie within p k, where Operations can be performed on thin paper laid over the page so that the scheme is visible. The quantities are as follows : n is the total number of cases ; r is the number of cases of one kind (positive cases) ; s is the number of the other kind (negative cases) ; p and q 5 are the probabilities of r and s, or p = , q = ; / is the limit assigned to variation in r or 5, and k the limit to variation in p or q. 2 indicates addition. Q indicates the result after subtracting the upper number from the lower one. 4> (y) indicates the first portion of the expression for P, and the last portion. APPENDICES. 477 SCHEME WITH R, S, L. log r log s log n log J logr = log s = log 2 = 0.30TO s = log 11 = (1 = - 2 log y = log log e = 0.6378 I S = = log log log e = log VTT = 0.2486 2-aa log-f - a = from table = P 4/8 APPENDICES. SCHEME WITH P, Q, K. P= log p q= log q n log n k= log log 2 = 0.3010 a = a = = log = log r 7 = 2 log y = log log = 0.6378 I S = = log log log ef = log VTT = 0.2486 **l = a= = log (y) = from table. -2= = P APPENDICES. 479 APPENDIX III. THE MEDIAN. * Suppose that you have measured the heights of a group of twenty- five men, what do you do with the results, which vary, more or less, from one another ? Let us take a case that occurs all over the country every year. Each graduating class of every college and school has the heights of its members measured. For the sake of comparison with preceding and succeeding classes, the individual heights are generally "averaged." Thus the "average" height of the class of '93 is said to have been, say, 66 inches, that of '94 67 inches, &c. But a great deal of dissatisfaction arises with this "average" height. The presence of a single very tall or very short man upsets the whole result. Let us take a class of ten men, of the heights of 65, 64, 65, 66, 66, 67, 65, 66, 76, 66 inches ; the average height is 66.6 inches. Now let us take another class, with the heights 65, 64, 65, 66, 66, 67, 65, 66, 66, 66. Every man except one has the same height as the corresponding man in the previous class, but there is no extraordinarily tall man there. The average is 65.6, or an inch less. than that of the other class. Now it is evident that the one very tall man ought not to out- weigh the influence of the other nine men. It is apparent that the average is a very unsatisfactory representative value in such a case. What is especially striking is that every man influences the result in direct proportion to his deviation from the average. For example, in the first class the man of 65 inches influences the average by the amount - } ' ~ = 0.16 of an inch, while the tall man influences it by 7 ~ Q - = 0.94 of an inch. This does not seem quite fair. This difficulty and unfairness can be removed by treating every man alike, by allowing all measurements to affect the result to the same degree. This is done by the use of the median instead of the average. The median was first considered as a representative value by Laplace, who treated some of its properties from a theoretical point of view. Fechner believed that it could be used for statistical purposes. For anthropometric measurements it has been made familiar by Francis Galton and by the investigations of the Anthropometric Committee of the British Association. Aside 480 APPENDICES. from a few isolated attempts, the median was never practi- cally used in purely psychological computation until I introduced it into my laboratory in 1893. During the year 1894 fully 100,000 measurements of the most varied kinds were adjusted on the basis of the median in place of or in addition to the average. On the strength of this experience I have published (" Studies from the Yale Psychological Laboratory," vol. ii.) an analytical and practical consideration of the median and its properties. What is the median ? It is the middle value in a set of numbers. Suppose the numbers to be arranged in order of size ; then, begin- ning at the smallest or at the largest, count them off until you come to the middle one. For example, the first class mentioned above would run 64, 65, 65, 65, 66, 66, 66, 66, 67, 76. The middle value for ten measurements would be between the fifth and the sixth. In this case, both are the same and the median is 66. How much influence does the tall, man have ? Merely that of one man ; as long as he is above 66 inches, it makes no difference how tall he is. In like manner every value influences the median merely as one value above or below. As tall men or short men are added, the median goes up or down according to the number of men added, not according to the number of inches added. For the second class we had 64, 65, 65, 65, 66, 66, 66, 66, 66, 67. The median is 66. The median for n values is that one which is the th in 2 order of size from either extreme. For five values it will be the the third, for thirty the I5jth, &c. It is not necessary to write the values in order of size ; they can generally be selected by the eye. For short sets of values the whole process can be done mentally. For example, suppose we have the following results of a set of experiments on reaction-time : 213, 215, 214, 210, 212, 214, 215, 210, 211. There are nine values, and the middle value is the 9 "T T th or fifth. The smallest is 210, the next smallest is 210, the next 211, &c. The fifth is 213. The largest is 215, the next 215, &c. The fifth is 213. Let us take, as another example, the set of values : 44, 51, 46, 50, 47, 49, 47, 45, 48, 50. The median will be the - th or 5^th value. The fifth from the smallest is 47 ; the fifth from the largest is 48 ; the 5jth will naturally lie between the two, and we take 47^ as the median. A third variety of examples arises by taking a set of results where several values fall on the same number as the median. Suppose APPENDICES. 481 \ve have 124, 123, 121, 123, 125, 124, 121, 120, 122, 123, 124, 123, 123, 122, 121, 125, 124, 121, 122. Result 120 121 122 123 124 125 Times of occurrence .143542 The -i- ^th or tenth value is 123. The expression M = 123, however, does not mean M = 123.000..., but 123.5 > M > 122.5, because we have been rounding off by errors of scale and errors of number all records to the unit-place instead of writing them to an indefinite number of decimals. Owing to the fact that five values fall upon 123, we know something about the first decimal place. We are entitled to suppose that all records of 123 have arisen from values evenly distributed between 122.5 and 123.5. Counting from the smallest end, we have eight values up to the limit of the region covered by the middle values ; counting from the larger end, we have six values down to the other limit of this region. The general formula is expressed as follows : Let r be the value on which the median falls, and let there be m such values. Let the number of values above r be a and below r be b. Then take c = a b and M = r + . 2 in This will give the decimal places for the median. In the last example b 8, a = 6, c = 2, m = 5, r = 123, and consequently M = 123 + ? = 122.8. 10 Although we know something about the first decimal place, we know nothing of any worth regarding the second decimal place unless m > 100. To make clearer the third kind of example, I subjoin a set of specimens that show how the changes in c affect the value M. ii 12 13 13 13 13 14 15 15 15 in = 4 a = 4 M = 13 + | = I3i 32 482 APPENDICES. 2. r = 13 * T3 I3 3 b = 2 w = 4 c = o M = 13 + 0= 13 10 ii 12 13 13 13 13 /; = 3 c = I = 13 3 13 = 4 9 10 ii 12 13 13 13 13 b = 4 w = 4 c = 4 M = 13 = I2j 6. 9 10 ii 12 13 14 15 15 15 b = 4 ?;z =r i a r= 4 c = o M = 13 The computation in the last two kinds of examples is so simple that it can be performed with great rapidity. Those of the other kind are almost as easy as soon as the computer becomes familiar with the median. Indeed, the economy of the median, in respect to time, is something that can be appreciated only by one who is obliged to compute many sets of results. Persons familiar with the science of measurement will realise the theoretical advantage of the value of middle probability (the median x m ) over the value of mean area (the average x^), for all unsym- metrical curves of error (Fig. 121). Xh is the value of maximum probability. When the curve is symmetrical, the median and the average are the same. Experience has shown that the median is often a better value than the average in many statistical and psychological measure- ments and in many other measurements where psychological factors come into play, e.g., in the so-called errors of observation of astronomical and physical measurements. Strangely enough, such phenomena as the fluctuating price of corn or the varying records of the barometer are better represented by the median than by the average. Of course, in cases where the results are APPENDICES. 483 reckoned by the number of units and not by the number of things, e.g., meat by the pound, debts by the dollar, &c., the average is the proper value. (From the "Scientific American Supplement," Fig. 121. RELATIONS OF MOST PROBABLE VALUE, MEDIAN AND AVERAGE, WITH AN UNSYMMETRICAL CURVE OF PROBABILITY. 1895, xl. 16,270 and the " Psychol. Rev.," 1895, ii. 376 ; the original and complete account is in " Studies from the Yale Psychological Laboratory," 1894, ii. I.) APPENDIX IV. LAMP BATTERIES. For battery purposes the Yale Laboratory uses lamp batteries of my devising. The principle on which these are constructed is shown in Fig. 122. The plug at the end of the lamp cord is inserted into an ordinary lamp socket supplied with the city Fig. 122. PRINCIPLE OF THE LAMP BATTERY. current. The large lamp, 32 c.p. or 50 c.p., allows I or \\ amperes of current to pass from the main line to the apparatus. To eliminate the spark arising from the high voltage of the city current, a small 6 c.p. 12-volt lamp is placed in parallel with the apparatus. Whenever the apparatus circuit is broken, the current 484 APPENDICES. passes through the small lamp. For larger currents more lamps are arranged in parallel, or larger lamps are used. An entire lampboard on this principle is shown in the frontispiece. Further details are to be found in vol. iv. of " Studies from the Yale Psychological Laboratory." APPENDIX V. ON THE MEASUREMENT OF IMAGINATION. Iii the course of the investigations on measuring hallucinations it occurred to me that it might be possible to measure the intensity of an imagination also. The experiment was successful. The method is not difficult and is icadily intelligible. In order to explain the method it will be sufficient to describe the first simple experiment made. The apparatus consists of a screen of fine tissue paper. The tissue paper is illuminated by daylight in front and by a gas flame at the back. When the gas flame is turned down, the eye looking through a telescope tube sees a plain white circle illuminated by daylight. The first experiment was made on a student accustomed to using the telescope. He was told to imagine hair lines on the white surface, like the hair lines seen in an astronomical telescope. This was successfully done. He was asked to describe them and com- pare their blackness. There is, he said, a horizontal line, which is the blackest of them, and three vertical lines of about equal black- ness. He was told that the field of view was to be made gradually lighter by turning on a flame behind, and he was to tell how the lines behaved. As the gas was slowly turned on, he described various changes in the lines. Finally he said he saw a slant line that he had not imagined before. It appeared just about as black as the horizontal line and blacker than any of the others. There- upon the experiment was ended. The slant line was a real line. This he did not and still to-day does not know. On the back of the tissue paper a slant line had been drawn, and as the gas was turned up, of course it showed through. Thus we had a direct, unsuspecting comparison of intensity between a real line and an imaginary one. The photometric determination of the intensity of the real line is not a difficult matter. A phantasimeter has been devised in which the graduation is done beforehand, but the simple arrangement just described serves to indicate the method of experiment. (From the " Scientific American," 1895, Ixxii. 85.) APPENDICES. 485 APPENDIX VI. COLOUR SIGHT TESTER (P. 58 AND CHAP. XXIV.). The usual tests for colour blindness fail to detect those who are colour weak, although these persons are really colour blind for objects at a distance. For examinations of railroad employes and sailors I have invented a convenient instrument which not only detects the colour blind with rapidity and accuracy, but also detects the colour weak. The use of different intensities of light for the purpose of a quantitative determination of colour blindness was, I believe, first made by Donders. In the form of a somewhat cumbersome lantern by Edridge-Green the test is now, I understand, officially adopted by the English Board of Trade. In general appearance the colour sight tester resembles an ophthal- moscope. On the side toward the person tested (Fig. 123) there are three windows of glass one-quarter inch in diameter, numbered I, 2, and 3 respectively. The opposite side of the tester (Fig. 124) con- sists of a movable disc carrying t\velve glasses of different colours. As this disc is turned by the finger of the operater the various colours appear behind the three windows. At each movement of the disc the subject calls off the colours seen at the windows. The windows, I, 2, and 3, are, however, fitted with grey glasses. No. i carries a very dark smoked glass ; all colours seen through it will be dark. No. 2 carries a piece of ground glass, showing all colours in full brightness. No. 3 carries a light smoked glass. There are thus thirty-six possible combinations of the colours. The twelve glasses are, however, mainly reds, greens, and greys. A suitable arrangement of the colours gives direct simultaneous comparisons of reds, greens, and greys of different shades. The well-known confusion by colour blind persons of dark greens with reds, greens with grey, &c., are exactly imitated, and the instrument gives a decisive test for colour blindness. Its peculiar advantage, however, lies in the fact that it presents reds, greens, and greys simultaneously in a large number of different shades of intensity. The light of a green lantern, as it appears to a colour weak person at different distances, is simulated by the red behind the different greys ; at the same time a white light is also changed. The colour- weak person to whom weak green is the same as grey (white at a distance) is utterly confused and thinks that the weakened green is grey (white) and the dark grey is green. The actual test is performed in the following manner : The tester is held towards a window, but not in the bright sunlight, at about 2$ feet from the person tested. The operator begins with any 486 APPENDICES. chance position of the glasses, and asks the person tested to tell the colours seen through the three glasses, Nos. i, 2, and 3. He answers, for example, " No. i is dark red ; No. 2 is grey ; No. 3 is gresn." The operator records from the back of the tester the Fig. T23. COLOUR SIGHT TESTER (FRONT). Fig. 124. COLOUR SIGHT TESTER (BACK). letters indicating what glasses were actually used. Suppose he finds that A, D, and G were opposite the glasses Nos. i, 2, and 3, he records A i, dark red ; D 2, grey ; G 3, green. The disc is then turned to some other position, the colours are again named, and the operator records the names used. For example, the result APPENDICES. 487 might be : "No. I is dark green ; No. 2 is white ; No. 3 is red ;'. and the record would read : G i, dark green ; J 2, white ; A 3, red- Still another record might give : J I, dark grey ; A 2 red ; D 3, medium grey. Similar records are made for all combinations. Of course, the person tested knows nothing concerning the records made. The blank thus filled out is forwarded to the chief inspector of the railway or marine service. A comparison with a table con- taining the true colours for each position determines whether the test has been passed or not. The records can be taken by any one, and, on the supposition that the record has been honestly obtained and that the instrument has not been tampered with after leaving the central office, the comparison is likewise mechanical. There is none of the skilful manipulation required in the wool test and none of the uncertainty attaching to its results. The only instruction given to the subject is, " Name the colours " ; the results render the decision with mechanical certainty. The three records just cited were all obtained from the red glass A, the grey glass D, the green glass G, and the white glass J, in combination with the dark grey No. I, the white No. 2, and the medium grey No. 3. Those familiar with colour blindness will notice that these combinations place side by side the colours most confused. More important still is the fact that red, green, and white are made to undergo changes that detect the colour weak. Another set of colours includes red, white, green, and blue-green, subject to all the combinations. For green I use the ordinary green glass common on most railways ; the blue-green is known to dealers as " signal green," and is frequent on the water. The third set of colours is an additional test. It includes orange-brown, green, blue, and violet. These colours are confused in many cases of colour-weakness and colour-blindness. APPENDIX VII. FORMULAS FOR ADJUSTING MEASUREMENTS. For those who may use this book in the laboratory I add a few formulas for the adjustment of measurements. Let the results of a set of u measurements of the same quantity under constant conditions be x^ x z , ..., x n . The average is n The individual variations (p. 47) or errors are v ! = #! - a, v t = * a - a, ..., v a x n a. The mean variation, or mean error, is 488 APPENDICES. where | z> | indicates that the sign of v is disregarded. For many purposes the following approximate formula (p. 47) can be used for calculating the mean variation (or average deviation) n A more reliable characteristic variation is the mean square error -V/" 1 +V 'n-i" The most frequently used characteristic variation is the probable error r = 0.674 m, *' approximately r = m. The characteristic variations for the average of n measure- ments are In stating the results of a set of measurements, the average, one of the characteristic variations d, tn, and r, and either the number n or the characteristic for the series, D, M, or R, should be given. When, as is usually the case, several separate sets of measurements have been made on the same quantity, on different occasions, they may be lumped together or may be computed separately and then adjusted by weights. If the number of measurements is small, the only safe method is to average together all the single measure- ments made on the same quantity, unless the characteristic variations of the different sets are really very different. If the number of measurements is large, or if the conditions of the measurements change greatly for different sets, then the following method may be employed. The weights of sets of measurements are inversely proportional to the square roots of their characteristic variations. Thus, for a set of measurements with the variations, D, M, or R, the weight will be For k sets of measurements with the separate averages a lt rt a , ..., fl k , and the weights p lt /> 2 , ..., fa the general average will be pi di + P 9 Cly + ... + pk flk Pi .+# + . +A These few formulas will enable the experimenter to state simple results ; for more complicated cases reference can be made to the works mentioned in Appendix I. APPENDICES. 489 APPENDIX VIII. FECHNER'S METHOD OF RIGHT AND WRONG CASES (P. 269). Two stimuli differing by a small quantity D are compared together with the judgment " greater," " equal," or " less " for one of them as referred to the other. It is evident that the larger the difference D the greater will be the number r of " right " cases and smaller will be the numbers g and / of "equal" and "wrong" cases out of the total number n. As D decreases the proportion - f will also decrease, while * and - will increase. When there is 11 n no difference (D = o), it is reasonable to suppose that - = ^ (" right " and " wrong" being purely arbitrary terms in this case). Moreover, it would seem justifiable to divide the g cases into two parts and use r' = r + and /' =/ + ^ instead of r and /. This equal apportionment of the g cases is not very well justified except for D = o, but can be retained for practical reasons. For D = o, r' f = ' = . As D takes increasing values r' will increase and /' will correspondingly decrease by some quantity f(D). Thus r' f = + f(D) and - . f(D)- Since the conditions are those common to scientific measurements, we can assume that the usual laws of probability are valid whereby hD = t where e = 2.71828 and h is the factor known as the measure of precision. When all errors of the apparatus and of manipulation are rendered negligible, h can be used as the measure of the subject's sensitiveness. A definite relation is thus established between the percentage of right cases, the actual difference and the sensitiveness. This relation is given in Fechner's table x : 1 Fechner, " Revision der Hauptpuncte der Psychophysik," 66, Leipzig, 1882. # 490 APPENDICES. r' r 1 r' r' r' n n 11 n n 0.51 0.0177 0.61 0.1975 0.71 0.3913 0.81 0.6208 0.91 0.9481 0.52 0.0355 0.62 0.2160 0.72 0.4121 0.82 0.6473 0.92 0.9936 0-53 0.0532 0.63 0.2347 0-73 0-4333 0.83 0.6747 0-93 1.0436 0-54 0.0710 0.64 0.2535 0.74 0-4549 0.84 0.7032 0.94 1.0994 0.55 0.0890 0.65 0.2725 0-75 0.4769 0.8^ 0.7329 0-95 1.1631 0.56 0.1068 0.66 0.2917 0.76 0.4994 0.86 0.7639 0.96 1.2379 0-57 0.1247 0.67 0.3111 0.77 0.5224 0.87 0.7965 0.97 1.3297 0.58 0.1428 0.68 0.3307 0.78 0.5460 0.88 0.8308 0.98 1.4522 0-59 0.1609 0.69 0.3506 0.79 0.5702 0.89 0.8673 0.99 1.6450 0.60 0.1791 0.70 0.3708 0.80 0-5951 0.90 0.9062 1. 00 00 Thus, if a difference of 2 grammes produces 62 % of r' cases, a difference of 4 grammes will for the same degree of sensitiveness produce 73 %. Again, if with a given difference D = 2 grammes there are 62 % of r' cases for one person and 79 % for another, their degrees of sensitiveness bear the relation of 0.2160 to 0.5702 or I to 2.64. Finally, if a difference D = 2 grammes produces on one occasion 62 % of r' cases and a difference of D' = 4 grammes produces on another occasion (under similar circumstances) 84 / of r' cases, the relation of the degrees of sensitiveness h and h' r' can be determined as follows : For - = 0.62, /*D = 0.2160 and // = 0.1080 ; likewise for - = 0.84, h'D' = 0.7032 and h' 0.1783. Consequently h : h' = 0.1080 : 0.1783 = I : 1.65. INDEX. Absolute time, 81 Acceleration, 301, 367 Accommodation, 243, 410 Action, time of, 121 ; rhythmic, 1 80 ; force of, 215 ; fatigue of, 228 Act of will, 122 Adjustment of measurements, 487 ^sthesiometer, 371 Esthetics, 306 Age, 322 ; see also School children Agreeableness, 302, 305 Aiken, 164 Air transmission, 99, 124 Airy, 443 Algometer, 303 Alkmaion, 448 Alphabet, legibility of, 103 ; for blind, 380 Alteration, error of, 3 Alternation of movements, 125 American laboratories, 471 Analysis, 440 Anderton, 423 Angle lines, 399 Anschiitz, 112 Arago, 448 Argelander, 443 Aristotle, 436 Arm-reaction, 146 Arrer, 411 Aschaffenburg, 203 Association-time, 162 ; in school exercises, 167 ; in telegraphy, 164 ; for ideas, 198 Astronomy, 436, 442 Attention, and reaction, 140, 147 ; field of, 389 Aubert, 284, 408 Auerbach, 445 Average, 28, 46, 487 Average error, sec Mean variation Bacon, i, 3 Bain, 469 Baldwin, 453, 471 Battery, 483 Beaunis, 189 Berger, 145, 146 Berkeley, 436, 453 Bernoulli, 440, 441 Bernoulli's theorem, 21, 476 Bertrand, 476 Bessel, 439, 443 v. Bezold, 457 Binet, 132, 187, 258, 464, 469 Binocular space, 420 ; depth, 421, 428 ; relief, 425, 428 Blecher, 263 Bliss, 127 Blix, 285 Blind, 251, 378 491 492 INDEX. Blind spot, 392 Blocks, fluctuating, 101 ; sugges- tion, 273 Blows, rapidity of, 132 Board, tilting, 362 ; rotation, 417 Bodily space, 362 Bolton, 177 Bouguer, 448 Boys, see Sex Bradley, 439 Braille, 380 Brain and mind, 13 Bright and dull, 19 Broca, 448 Briicke, 458 Bruns, 269, 296 Bryan, 129, 134 Buccola, 445 Burmester, 408 Calkins, 198 Cambridge, 470 Cannabis Indica, 136, 361 Capacity for energy, 210 Capsule, manometric, 99 Carpenter, 449 Cattell, 89, 103, 104, 107, 146, 165, 167, 224, 471 Certainty defined, 21 Change, just perceptible, 296 Charcot, 448, 465 Children, field of vision for, 390 ; see also School children China, 473 Chin key, 161 Choice, 161 Chronoscope, 155 Clifford, 62 Clock, 80, 83 Clock contact, 83 Cobra, 309 Cold spots, 71 Cold colour, 335 Colour, 330 ; most agreeable, 309 Colour blindness, 54, 352, 485 Colour discs, 350 Colour equation, 333 Colour pyramid, 345 Colour sight-tester, 485 Colour triangle, 332, 340, 343 Colour weakness, 485 Colour wheel, 93, 97 Comte, 9 Constant error, 186, 320 Conscious method, 293 Contact, pendulum, 83 Copernicus, 436 Courtier, 132 Crossed disparity, 428 Cross memory, 190 Cumberland, 255 Czuber, 476 Daedelum, 109 Degree of validity, 20 ; of cer- tainty, 21 Delbceuf, 359 Delabarre, 257, 472 Demeny, 119 Depth, 421, 428 Descriptive psychology, 8, 453 Dichromat, 335, 341, 353 Dieterici, 333 Direction, 357, 373 Direct vision, 386 Disagreeableness, 302, 305 Discrimination, 161 Dislike, see Disagreeableness Disparity, 428 Distance, 357 Distinct vision, see Sharpest vision Distraction, 127 Dolley, 146 Donaldson, 374 Donders, 445, 485 Double consciousness, 259 Dresslar, 128, 132 INDEX. 493 Drum, for recording, 85 ; with clock-work, 98 ; in simple form, 124 Du Bois-Reytnond, 444, 446, 458 Duhauron, 348 Dull, 19 Dvorak, 431 Dwelshauvers, 147 Dynamograph, 125 Dynamometer, 74, 124, 215, 225 Ebbinghaus, 59, 193, 44<\4 6 3 Edison, 112 Eight, inversion of, 394 Eijner, 174 Eisner, 374 Edridge-Green, 485 Electric colour wheel, 94 Electric fork, 85 Elementary colours, 334 Ellis, 219, 304, 470 Emotions, 312 Emphasis-rhythm, 177 Empirical method, 452 Encke, 475 Energy, 209 ; of voluntary action, 215 English psychology, 437, 469 Equal, denned, 31, 41 Equality, " real," 34 Equipment of laboratories, 472 Ergograph, 230 Error, in observation, 2 ; probable error, 25, 488 ; definition of, 41, 488 ; sources of, 69 ; of percep- tion and judgment, 226 ; con- stant error, 186, see also Con- stant error ; mean error, see Mean variation Esthesiometer, 371 Excitement, 128 Exner, 93, 445, 451 Experiment, 7, 53 ; among Greeks, 53, 438 ; qualitative and quanti- tative, 72 ; introduced into psy- chology, 438 ; in physiology, 444 Experimental aesthetics, 305 Eye, judgment of depth, 237 Faraday, 5, 253 Fatigue, 128, 228 Fechner, 190, 267, 272, 306, 440, 454, 479 Fechner's law, 271, 342, 441, 455 Feelings, 305 Fencing, 167 Fere, 223 Ferrier, 448 Field of vision, 386 ; of regard, 389 ; of attention, 389 ; contrac- tion of, 390 ; binocular, 420 Fischer, no Fixation, 421 Flamsteed, 439 Flatland, 409 Flechsig, 448, 451 Flournoy, 469 Flourens, 448 Fluctuation, of sensation, 97; of memories, 101 ;of imaginations, 101 ; of illusions, 102 ; of voli- tions, 124 ; of tapping, 126 Fluctuating blocks, 101 Focus of attention, 389 Foot reaction, 146 Fork, 85 Forms, most agreeable, 309 Formulas for Bernoulli's theorem, 476 ; for measurements, 487 Free association, 162 French psychology, 464 Fritsch, 448 Front, 417 Fullerton, 167, 224 Function, 76 ; probability func- tion, 21, 475 Fundamental colours, 338 494 INDEX. Fusion, 377 Future of experimental psycho- logy, 473 Gall, 448 Galilei, 436, 438 Galton, 207, 289,321, 322, 440,470, 479 Galton whistle, 321 Gauss, 443 Geissler tube, 138, 145, 150 General psychology, 453 Gerling, 443 German psychology, 463 Gibbs, 210 Gilbert, 19, 130, 173, 272, 319 Girls, see Sex Golden cut, 307 Goldscheider, 248, 261, 304 Goltz, 448 Graphic method, 85, 98, 124 ; see also Spark method Grassmann, 345 Greater, 31 Greek science, 436 Griffing, 283, 303, 304 Grip, see Dynamometer Gymnastic work, 149, 220 Hall, 296, 374, 471 Hallucination, 326, 384 Hamilton, 201, 437, 453 Hansen, 63, 259 Harvey, 437 Heat, 70 Heaviness, 261 Hegelmayer, 187 Heller, 379 Helmholtz, 56, 333, 342, 385, 4*5, 429, 430, 444, 447, 451, 457 Henri, 187, 376 Hensen, 320 Herbart, 438 Hering, 429, 430, 447 j Herschel, 448 Heymans, 399 Hillebrand, 411, 430 Hitzig, 448 Hobbes, 437, 452 Hocheisen, 251 Holmgren, 57 Horizontal, 412, 417 Horopter, 429 Hot spots, 71 Howe, 203 v. Humboldt, 457 Hume, 437, 453 Identical points, 429 Illusion, fluctuation of, 102 ; in time estimate, 174 ; of resist ance, 262 ; of weight, 272 ; op- tical, 395, 399 ; of movement, 418 Imagination, 101, 484 Inaccuracy, in memory, 186 ; in effort, 236 ; see Error and Con- stant error Independent variable, 76 Induction coil, see Inductorium and Spark Method Inductorium, 145, 170, 302, 326 Instantaneous sensations, 102 Intensity, and latent time, 92 ; and lag, 95 ; of fluctuation, 96 ; of shortest sensation, 103 ; influ- ence in reaction-time, 144, 145 ; in energy, 210 ; in limit of pitch, 322 ; of tones, 324 Interval, in reaction-time, 147 ; in time estimate, see Time esti- mate Introspection, 8, n Inversion of S and 8, 394 Investigation, 75, 77 Involuntary movements, 253 Isolated room, 136 INDEX. 495 James, 471 Japan, 473 Jastrow, 208, 257, 445 Javal, 107 Jeffries, 57 Jerusalem, 206 Jevons, 3, 439 Joints, tapping with, 129 Judd, 371 Judgment, 40, 41 Just imperceptible difference, 396, 399 Just noticeable, see Just percep- tible Just perceptible movement, 251 ; weight, 284 ; change, 296, 317 ; acceleration, 301 ; difference, 267, 315, 397 Kaempfe, 476 Kammler, 284 Kepler, 437 Key, reaction, 126 ; touch, 135 ; telegraph, 126 ; multiple, 138 ; pistol, 150 ; mouth, chin, 161 Kinesimeter, 374 Kinetograph, 114 Kinetoscope, 113 Kirschmann, 471 Kliinder, 319 Knox, 408 Konig, 333, 447, 463 Kohlschiitter, 327 Kraepelin, 174, 207 v. Kries, 445 Krohn, 377 Kulpe, 453 Kundt, 408 Kuntze, 454 Laboratories, in Germany, 463 ; in France, 466 ; in Italy, Russia, Switzerland, 469 ; in England, 470 ; in the United States, 471 ; in Asia, 473 Ladd, 471 Lag, of sensation, 95 ; of volition, 123 Lambert, 345, 448 Lambert's pyramid, 345 Lamp battery, 483 Lange, 99 Language association, 164 Lantern, see Projection Laplace, 359, 440, 441, 4^9 Lasswitz, 454 Latent time, of sensation, 90 ; of volition, 123 Law of , memory, 192 ; of asso- ciation, 199 ; of monocular orientation, 415 ; of relativity, 441 ; of Weber, see Weber's law Least noticeable, see Just percep- tible Least perceptible difference, 398 ; sec also Just perceptible differ- ence Least perceptible stimulus, see Threshold Legibility of letters and words, 103 Lehmann, 63, 259 Less, 31 Letters, see Legibility Lexis, 26 Lifting weights, 267 Liking, see Agreeableness Limited association, 163 Limit of pitch, 321, 324 Lines, memory for, 190 ; direction of, 373 Local signs, 385 Locke, 437, 452 Lodge, 437, 439 Loeb, 223 Loewy, 187 496 INDEX. Lombard, 232, 247 Lotze, 449 Lower limit, 324 Luckey, 390 Ludwig, 446, 458 Luft, 317 Lumiere, 119 Mach, 366, 451 Magnetic counter, 128 Manoinetric capsule, see Capsule Marbe, 96, 100 Marey, 112 Martius, 144, 183 Masson, 448 Maudsley, 449 Maximum rapidity of tapping, 126 Maxwell, 59, 93, 350, 448 Mean error, see Mean variation Mean variation, 47, 48, 126, 141, 142, 1 86, 320, 488 Mean square error, 488 Measurement, 7, 30 ; principles, 43 I physical and psychological, 48 ; and experiment, 24 ; by the eye, 395 ; introduced into psy- chology, 439 ; formulas, 487 Median, 46, 288, 479 Mediate association, 201 Megamicros, 359 Meitzen, 16 Memory, 9, 26, 59, 185 Memories, fluctuation of, 101 Mental physiology, 449 Merkel, 270, 395 Merriman, 476 Method of right and wrong cases, 52, 268, 487 ; of minimum changes, 52, 290, 372 ; of average errors, 52, sec also Mean varia- tion and Constant error ; of multiple stimuli, see Scale ; of middle gradation, 52, sec also | Scale Metre, 358 Meumann, 174 Meyer, 476 Michelson, 327 Middle gradation, 52, see also Scale Mill* 5, 453 Minimum changes, 52, 290, 372 Mises, 454 Mixing sensations, 95 Monninghoff, 327 Monochromat, 334, 341, 353 Monocular space, 383 ; and bodily space, 412 Moore, 121, 128, 237, 245 Mosso, 230 Motion, see Movement Motora, 296, 473 Mouth key, 161 Movement, rhythmic, 180 ; pas- sive, 248 ; active, 251 ; voluntary and involuntary, 253 ; bodily, 366, 375 ; eye, 413 Mtiller, G. E., 196, 250, 268, 272, 457 Muller, Johannes, 444 Miinsterberg, 203, 431 Multiple key, 138 Munk, 448 Music, 177, 221 Muscle reading, 255 Muscle sense, see Movement, Heaviness, and Resistance Nasal whispering, 259 Nervous transmission, 4/14 Nevers, 208 New Haven, see School children Newton, 448 New York alphabet, 380 Xoise, 313 Nonsens6 syllables, see Syllables Number, 354 INDEX. 497 Observation, I ; criticism on, 2 ; errors in, 3 ; improvement of, 7 ; defence of, n ; history of, 436 ; basis of psychological methods, 453 Ochorowicz, 63 Old psychology, 452 Olfactometer, 372 Optical illusions, 395, 399 Oshvald, 212 Overtones, 314 Oxford, 452, 470 Pain, 302 Paradox, 262 Parallax, 428 Paralysis, 229 Patrizi, 149 Pekin, 473 Pendulum contact, 83 Pendulum chronoscope, 155 Perimeter, 387 Personal equation, 443 Phaenakistoscope, 109 $ (y) curve, 21, 288, 475, 476 Phonograph, 114, 116, 434 Physics and psychology, 447 Physiological psychology, 9, 448 Physiological zero, see Psycho- logical zero Physiology, 444 Physiology of mind, 449 Piano-trilling, 132 Piesbergen, 327 Pistol key, 150 Piston recorder, 125 Pitch, 314 ; influence on reaction- time, 144 ; memory for, 191 ; upper limit, 321 ; lower limit, 324 Plato, 221 Planchette, 257 Poetical rhythm, 177 Poggendorf, 53 Point of paralysis, 229 ; of sharpest vision, 386 ; of regard, 387 ; of fixation, 422 Poisson, 440 Polariser, 423 Porter, 19 Position, sensations of, 250 Pouillett, /j/i/1 Prazmowski, 443 Precision, 25 Prejudice, 3 Pressure, 262, 283 Pressure spots, 285 Preyer, 301 Probable error, 25, 489 Probability, 21 Probability integral, 475 Projection, of reaction experi- ments, 162 ; of colours,. 348 ; stereoscopic, 423 Psychical research, 62 Psychological colour triangle, 343 Psychological zero, 71 Psychological colour triangle, 40 Ptolemy, 439 Quartiles, 289 Qualitative experiments, 72 Quantitative experiments, 72 Quantity, defined, 30 Quetelet, 440 Quickest noticeable stimulus, 103 Quiet room, 136 Reaction, 135 ; typical experiment, 135, 140 ; in series, 148 ; mean- ing of, 150, see also Reaction- time Reaction-key, 121 Reaction-time, influenced by re- tinal light, 140 ; typical record, 141 ; for tones, 144 ; for light, 145 ; for arm, foot, thigh, 146 ; and attention, 147 ; of runners, 498 INDEX. 149 ; psychology and physiology of, 150 ; for words, 162 ; first measurement, 443 ; in physio- logy, 444 Recording drum, 85 Reflection, 9 Regard, point of, 387 ; field of, 389 Reid, 453 Relativity, see Weber's law Relief, 425, 428 Repetition, 193 Residues, 70 Resistance, 261 Resistance paradox, 262 Resonator, 324 Retinal field, see Field of vision Rhythm, 177 Ribot, 10, 445, 463, 464 Richet, 67 Riemann, 344 Right and wrong cases, 268, 489 Rivers, 470 Robertson, 470 Roemer, 439 Room, isolated, 136 Rotation board, 417 Rotation, law of, 367 Runner's reaction, 149 Ruskin, 311 S, inversion of, 394 Sanford, 104, 105, 107, 431, 444, 472 Scales, establishment of, 36 ; of voluntary energy, 216 ; of pres- sure, 283 Schemes for Bernoulli's theorem, 476 School children, tapping, 129, 130 ; time estimates, 173 ; memory, 187 ; suggestion, 273 ; sensitive- ness for pitch, 319 Schumann, 183, 196, 250, 272 , Scherer, 379 Screen, 423 Seashore, 243, 274, 297, 326 Second, 81 ; divided into hun- dredths, 86 ; into thousandths, 88 Seebeck, 56 Sensation, defined, 39 ; how to measure, 39 ; time of, 89 ; fluc- tuation of, 97 ; instantaneous, 1 02 Sensitiveness, 41 Sex, in tapping, 129 Sharpest vision, point of, 386 Sharpness of vision, 386 Shortest noticeable stimulus, 103 Sidereal day, 81 2, 142