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 %\: 
 
 t\ o<r S i/Or-l f 1 i(
 
 
 Vol II. No. 2. 
 
 REPRINTED FROM 
 THE 
 
 March. 1895. 
 
 Psychological Review 
 
 EDITED BY 
 J. MARK BALDWIN J. McKEEN CATTELI. 
 
 Princeton University ''^^ Columbia College 
 
 WITH THE CO-OPERATION OF 
 
 ALFRED BINET, tcoLE des Haute.s-£tudes, Paris; JOHN DEWEY, University op 
 
 Chicago; H. H. DONALDSON, University ok Chicago; G. S. FULLERTON, 
 
 University OF Pennsylvania; WILLIAM JAMES, Harvard University; 
 
 JOSEPH JASTROW, University of Wisconsin ; G. T. LADD, Yale 
 
 University; HUGO MUNSTERBEKG, Harvard University; 
 
 M. ALLEN STARR, College ok Physicians and Surgeons, 
 
 New York; CARL STUMPF, University, Berlin; 
 
 and JAMES SULLY, University Colleck. 
 
 London. 
 
 CONTENTS. 
 
 The Knoiving of Things Together: William James 
 Contributions from the Psychological Laboratory of Columbia Col- 
 lege {II T) Experiments on Dermal Sensations: Harold 
 Griffing. The After-image Threshold: S. I. Franz 
 Normal Defect of VisionTnTfJte Fovea 
 
 Christine Ladd Franklin 
 
 105 
 
 130 
 
 137 
 
 149 
 
 173 
 175 
 
 Proceedings of the Third Annual Meeting of the American Psycho- 
 logical Association, Princeton, iSg/j. ..... 
 
 Discussion : T/ie Se?isatiora are not the Emotion : G, M. Stratton. A 
 Correction .• W. J. . 
 
 Psychological Literature : ........ 
 
 Philosophical Rernains of George Croom Robertson : J. S., 175. Wundt's 
 Lectures on Human and Animal Psychology: A. Kirschmann, 179. 
 Ladd's Primer of Psychology : G. S. F. , 180. Deussens Elements of 
 Metaphysics : A. T. Ormond, 181. Hyslofs Elements of Ethics: A. T. 
 Ormond, 184. Johnson's Universal Cyclopedia^ I.-V.: J. D. Evolution 
 and Biology [Osborn's From the Greeks to Darivin, IVilley's Amphioxus, 
 for don's Factors in Organic Evolution, Gould^s Dictiomiry of Biology^ 
 Collins' Epitome of the Synthetic Philosophy'): J. M. B., 189. Chi/d 
 Psychology: F. Tracy, 190. Neurology: H. H. D,, 194. Hearijig : 
 Y. Angell, 197. Attention and Memory : H. N. Gardiner, 199. Re- 
 action-Time: J. McK. C., 200. Judgment and Belief : G. M. Duncan, 
 209. Pathological [Ziehen's Psychiatric, Dumas' Mt'latuJwlie, Charcot's 
 Cliniques des maladies: William Noves, A.B., 209. Ne^w Books. 214. 
 Psychological Questioning, 215. Notes, 216. 
 
 published bi-monthly by 
 MACMILLAN AND CO., 
 
 66 FIFl'H AVENUE, NEW YORK; AND LONDON. 
 Single Numbers, 75 cents (3s.) Annual Subscription, $4.00 (i6s. 6d.) 
 
 Beilin, Mayer & MUller (M. 16.50), Paris, H. Welter (Fr. 21), 
 
 Markgrafen Str., 51. Rue Bonaparte, 59. 
 
 Copyright, 1895, by MAcitiLi.Ai( k Co. 
 
 Entered %i the Post-office at New York as decond-class Matter.
 
 3? 
 f ^5 a 
 
 f 
 
 CK 
 I 
 
 ^ CONTRIBUTIONS FROM THE PSYCHOLOGICAL 
 
 ^ LABORATORY OF COLUMBIA COLLEGE. (III.) 
 
 Experiments on Dermal Sensation.s.' 
 
 ijv iiaroiij griffing. 
 
 The Relation between the Intensity of the Stiutulus and its 
 Estimated Intensity. 
 
 \T\vo stimuli differing greatly in intensity were success- 
 ively applied to the hand of the observer, and he was re- 
 quired to judge how much greater one was than the other. 
 The pressure was given by weights placed in the pan of a 
 balance, and was transmitted to the hand by a wooden rod 
 attached to the pan. The stimuli were 2, 10, 50, 250, 1250, 
 and 1800 grams. The area of stimulation was that of a cir- 
 cle 4 mm. in diameter. The experiments made on four 
 observers showed that on the average 10 g. was considered 
 about twice as heavy as 2 g, ; 50 g. twice as heavy as 10 g. ; 
 250 g. three times as heavy as 50 g. ; 1250 g. five times as 
 heavy as 250 g. ; and 1800 g. three times as heavy as 1250 g. 
 It thus appears that for low and moderate intensities the 
 estimate of intensity increases much more slowly than the 
 objective intensity; but as the stimulus approaches the 
 pain threshold, the reverse appears to be the case. Indi- 
 viduals differ, however, in their underestimation of low 
 intensities, and also, but to a greater degree, in their over- 
 estimation of hiirh intensities. 
 
 The Discrimination of Weights of Different Intensities. 
 
 Cylindrical boxes filled with shot served as stimuli. The 
 method used was that of right and wrong cases; that is, the 
 stimuli were placed successively upon the hand, and the ob- 
 
 * A full account and discussion of these experiments will be found in the writer's 
 dissertation, On Sensations from Pressure and Impaet. Supplement Monograph 
 (No. i) to this Review. 
 
 12 J 'i 
 
 i-^S
 
 126 HAROLD GKIFFING. 
 
 "V 
 
 sexver was asked to decide which was heavier. The accu- 
 racyvof discrimination is measured by the probable error, or 
 that increment which the observer perceives correctly 75% 
 of the time.' Thus the greater the probable error the less 
 the accuracy of discrimination. The stimuli varied from 
 100 to 320d\g., no more than four intensities being used for 
 any one observer. The results of 9040 experiments made 
 on 5 observers showed that the probable error for pressure 
 stimuli tends to increase in proportion to the intensity of 
 the stimulus within the approximate limits 300-3000 g. For 
 low intensities the probable error increases much more 
 slowly than the stimulus. For 5-7 g. the probable error 
 for a good observer was \ of the stimulus. For high inten- 
 sities also there seems, to be a similar tendency, but it is not 
 so marked. As illustra.tive of our results, we give the prob- 
 able errors in grams for McW. : for 100 g., 19; for 500 g., 
 36; for 1500 g., 112; for 3200 g., 193. The average value 
 of the probable error for all stimuli (100 g. and above) and 
 all observers was approxirnately i of the stimulus. That 
 is we can, on the average, judge correctly whether one 
 stimulus is heavier or lighter than another 75^^ of the time 
 when the stimuli are in the ratiip 9: 10. 
 
 In these experiments the constant error, or tendency to 
 overestimate the second stimulus, was found to be for some 
 persons very great, running as high as \ of the stimulus. 
 The constant error is more variable than the probable error; 
 the expression 'constant error' is thus quite misleading. 
 The constant error seems to be greater for observers having 
 a large probable error. A great constant error for pressure 
 is not necessarily accompanied by a similar overestimation 
 for lifted weights. 
 
 The degree of confidence was studied by having the ob- 
 servers say a, b, c and d, according as they were certain, 
 quite confident, less confident, or doubtfuL Individuals 
 differ greatly in their confidence, the percentage of wrong 
 judgments of which observers were confident varying from 
 2% to 33%. The probability of correctness when confident 
 
 ' This quantity has been considered to be equivalent to the least not3,ceable differ- 
 ence. It is doubtful, however, if such a relation can be justified.
 
 EXPERIMENTS ON DERMAL SENSATIONS. 127 
 
 \ 
 
 was fo'T^ most observers about .8 to .9. There appears to be 
 no relalrion between these quantities and the accuracy of dis- 
 crimination. The percentage of correct guesses varied from 
 52% Lo /^%^, the average being 59%. 
 
 'K 
 
 The Place ofyStimiilation. 
 
 The accuracy of discrimination for weights of 100 g. or 
 more is not for 'two observers appreciably different for the 
 pahii of the hand, the back of the hand, and the volar sur- 
 face ot the third phalanx of the index finger. For 5-7 g. it 
 was found at first to be much less for the back of the hand 
 and wrist than for the index finger of one observer, but 
 to increase greatly by practice. Stimuli of low intensity, 5 
 and I cog., when placed on the forearm, tended to be judged 
 lighter than when placed on the finger. This result was 
 obtained by placing a weight first on the finger and then on 
 the arm, increments being added until the weights seemed 
 equal. 
 
 The writer tested the sensitiveness to pain at different 
 parts of the body by the algome-ter.' It was found that the 
 sensitiveness is greatest where the skin is thin and not sepa- 
 rated from the bone by other tissues. Among the most sen- 
 sitive parts are the upper regions of the head, whereas the 
 palm of the hand, the thigh and the heel are among the least 
 sensitive parts. \ 
 
 Sensations from Impact. \ 
 
 The tactile threshold for pressure stimuli without move- 
 ment was found by observing the anguiar elevation of a 
 bristle which was attached at one end to a'^ wooden handle, 
 and at the other could transmit pressure to the skin. In 
 this way it was found that .4 g. is about as easilv perceived 
 when movement is thus excluded, as is .01 g.. when the 
 stimulus is placed carefully upon the hand. The difference 
 in the results is due to the sensorv effect of movetnent. 
 
 By dropping weights upon the hand, the heights were 
 found at which different weights caused pain. The weights 
 were 25. 100, 200 and 300 g. The area of stimulation was 
 
 ' An instrument by which pressure couiii be exerted up to 15 k.
 
 128 HAROLD GRIFFING. 
 
 \ 
 
 constant, a circle about i cm. in diameter. The results of 
 60 measurements showed that the product of the mass and 
 hei.^ht ^ain-thresholds is fairly constant. iVs the height 
 through ~\vhich a body falls is proportional to the square of 
 the velocity, the pain threshold and therefore the intensity 
 of pain, depend as much upon the square of the velocity as 
 upon the mass of a striking object. 
 
 By the method of right and wrong cases we studied the 
 accuracy of discrimination for impact stimuli. The results 
 of 800 experiments showed that a weight of 50 g., falling 
 through 17.5 cm., is judged about as well as 1000 g. without 
 movement. The average probable error for pressure only 
 was y^y of the stimulus for S. F,, and Jj for L. F. For im- 
 pact the corresponding values were -^-^ and y^. 
 
 In 900 experiments, carried on in the same way, the 
 weight was kept constant and the observer required to esti- 
 mate differences in the intensity of the blow due to differ- 
 ences in height and thetefore velocity. The results were 
 compared with those based upon the same number of experi- 
 ments on the same obseX'vers, in which the height was 
 constant and the weight variable. We found that, on the 
 whole, differences in weight are judged less accurately than 
 differences in velocity, but more accurately than differences 
 in the square of the velocity. But great individual varia- 
 tions occur. \ 
 
 Experiments were also made on the intensive effect of 
 the weight as compared to that of the velocity. A 100 g. 
 weight having fallen upon the hand from a height of 5 cm., 
 the height was found at which 25 g. would cause a sensation 
 of the same intensity. Here also observers differed greatly. 
 The average height for 5 observers was 38 cm., the maxi- 
 mum being. 58, the minimum 20 cm. Hence the mass has in 
 general greater intensive effect than the height or the square 
 of the velocity. Otherwise the average height found would 
 be about 20 cm. On the other hand, the mass has less effect 
 than the velocity or square root of the height. 
 
 The Area of Stimulation. v; 
 
 In the experiments on Weber's law two areas were used, 
 8 sq. cm. and .12 sq. cm. approximately. It was found that
 
 EXPERIMENTS ON DERMAL SENSATIONS. 1 29 
 
 on the whole\his difference of area did not affect the accu- 
 racy of discrinjjnation for \vci<^hts. Individual variations, 
 however, were Very marked. 
 
 If stimuli of the same weight, but different areas, be 
 placed successively upon the hand, the stimulus applied on 
 the smaller area will be overestimated. By applying the 
 method of right andwrong cases we measured this overesti- 
 mation. The result^ of 400 experiments on one observer 
 gave an overestimation of \ of the stimulus at 200 g. Ex- 
 periments bv a different application of the method of right 
 and wrong cases on 5 observers gave about the same result, 
 except that one observe*; showed a tendency to underesti- 
 mate, rather than overestimate, the stimulus applied to the 
 smaller area. By a third method, however, we found a 
 decided overestimation for 0nly 2 out of 5 observers. From 
 these experiments on 10 observers, we conclude that this 
 tendency is by no means univ'ersal. 
 
 The effect of alterations iii the intensity of pressure on 
 the accuracy of discrimination pf areas was investigated b}' 
 the method of right and wrong cases, differences in area 
 being judged instead of differences in intensity. The stand- 
 ard areas used were i and 8 sq; cm. and the intensities 
 200 and 800 grams. The results oi 1900 experiments on 3 
 observers showed that the accuracy of discrimination for 
 areas was, on the average, about \ greater for 200 g. than 
 for 800 g. \ 
 
 By placing thin circular cards upoi^ the hand and apply- 
 ing pressure upon these, we studied the effect of variations 
 in the area on the so-called tactile threshold. The areas 
 were approximately i mm., 10 mm. and 90 mm. The aver- 
 ages of the corresponding threshold values, based upon 60 
 experiments, were for F., .2 g., .9 g. and 1.9 g. ; and for the 
 writer, .5 g., 1.4 g. and 1.6 g. Thus the smaller the area 
 the greater the probability that stimuli of low intensity will 
 be perceived. 
 
 In a similar manner the relation of the pain threshold 
 to the area of stimulation was investigated. The average 
 values of the pain threshold, based upon 80 experiments on 
 two observers, were: for 10 mm., i.4kilog. ; for 30 mm..
 
 I 30 SHEPHERD IVOR V FRANZ. 
 
 2.8 kilog. ; for 90 mm., 4.4 kilog. ; and for 270 mm., 6.6 
 kilog. Thus the pain threshold increases with the area; 
 but, Hke the tactile threshold, much more slowly than in 
 direct proportion. / 
 
 The Time of Stimulation. / 
 
 The sensory effect of pressure stimuli of low intensity 
 was found to depend upon the rate at which the pressure 
 was increased. The instrument used was that referred to in 
 the experiments already described on the tactile threshold. 
 By this pressure was exerted upon the palm of the observer's 
 hand up to .4 g., at different rates of increase. These rates 
 were approximately .05 g., .3 g. and 2 g. per second. The 
 corresponding percentages of times the stimulus was per- 
 ceived in 300 experiments on 2 observers were 6;,^, 32^, and 
 82%. Thus the greater the rate of increase the greater the 
 probabilit}' of perception. 
 
 The time in which dermal stimuli of different intensities 
 cause pain was found in the following manner. Different 
 weights were placed in a balance pan so as to press upon 
 the palm of the hand, and the time was noted which elapsed 
 before the appearance of pain. The pressure was commu- 
 nicated from the pan to the hand by a wooden rod fastened 
 to the pan. The diameter of the base was 1.5 mm. The 
 averages in seconds, based upon 80 experiments on 2 ob- 
 servers, are as follows: for 100 g., 230 sec. ; for 200 g., 35 
 sec. ; for 300 g., 10 sec. ; for 500 g., 4.5 sec. It is evident, 
 therefore, that the time as well as the area and intensity of 
 stimulation determine the sensory effect. There is, how- 
 ever, an intensive limit, below which pressure stimuli never 
 become painful. This is probably from 25 to 50 g. for the 
 area used. 
 
 The After-Image Threshold. 
 
 by shepherd ivory fraxz. 
 
 Ever since Aristotle described in his De Somniis^ the 
 appearance of an after-image, the phenomena have attracted 
 
 ' This seems not to be generally known by German writers. Aubert and Helm- 
 holtz both credit Peiresc as being the first to mention after-images.
 
 THE AFrER.JMAGE THRESHOLD. 
 
 13« 
 
 
 ^ 
 
 attention. St. Augustine mentions them, and in modern 
 times such prominent men as Buffon, Goethe and Newton 
 have described their appearance. But very little was ac- 
 complished beyond the making of theories until this century, 
 when Plateau, Seguin, Fechner and others studied the color 
 changes. Up to the present time practically nothing has 
 been accomplished in the way of exact measurement. 
 
 The present paper gives the results of an attempt tf) 
 measure the smallest amount of light which will produce an 
 after-image. For this purpose three physical units had to be 
 considered — the intensity of the light, its area, and the time of 
 stimulation. The apparatus used was planned and formerly 
 used by Prof. Cattell, but was adapted by the writer. It is 
 represented in the accompanying cut. 
 
 Figure 1. 
 
 S is an upright iron screen pierced by a hole(H) through 
 which the light from the hooded lamp (L) may pass to the 
 observer on the other side of the screen. P is a seconds 
 pendulum. To this is attached a piece of sheet iron which 
 covers the hole when the pendulum is held up by the electro- 
 magnet (M). The key (K) which makes and breaks the cur- 
 rent to the magnet (M) is managed by the experimenter, and
 
 I 3 2 SHEPHERD I VOR Y ERA NZ. 
 
 the pendulum is held up or let swing at his pleasure. By 
 breaking and making the current the pendulum swings, per- 
 mits the light to be seen by the observer for exactly one 
 second, and is caught up again by the magnet. The lamp is 
 moved along the arm (A), increasing or decreasing the 
 intensity of the light. The opening (H) was covered with 
 ground glass, y^^ candle power was found a convenient 
 intensity, this being increased by moving the lamp nearer 
 the observer, and decreased by moving it away from the 
 observer. The lamp was used at the distances ^, ^, 1,2 
 and 4 meters, and so far as the intensity decreases inversely 
 as the square of the distance, the respective intensities would 
 be Z^, 2V' tItT' T¥ir ^'''^^ TeVir candle power. The absorbing 
 power of the ground glass was found to be 507^,) whence 
 the intensities were decreased by half — making the series — 
 ■h^ 3V' 200' -sio' n .^m;' c. p. In the experiments on inten- 
 sity, the time of exposure (one second) and the area (64 
 sq. mm.) were kept constant. For the experiments on area, 
 the lamp was placed at a distance of \ m., thus making the 
 intensity -^j; c. p., the time (one second) being the other 
 constant. The area was changed by using different pieces 
 of ground glass on which black paper blocked off all but the 
 small area required. The areas used were 64, 16, 4, i, i, ^-^ 
 sq. mm. When time was the changeable unit, the area (64 
 sq. mm.) and the intensity (^25. q p /) were the constants. The 
 series consisted of four times, ■^-^^', y^^j-, yV ^"^ ^ second. 
 The shorter times were obtained by means of drop screens, 
 made of pasteboard and weighted. As they did not fall in 
 grooves there was no appreciable friction, and hence the 
 real time practically corresponded with the theoretical time. 
 The screen was on the side of the apparatus near the 
 observer, and therefore is not shown in the cut. The time 
 one second was given by the pendulum. As will be noticed, 
 there was a common unit in the three series, /. e., when the 
 experiments were made with i sec, 64 sq. mm. and 2^ c. p. 
 The experiments were conducted in a dark room, and all 
 observations were made with the eyes open, so as not to 
 disturb the after-image. A cloth curtain was hung across 
 the room, shutting off from the observer everything but the
 
 THE AFTER-IMAGE THRESHOLD. I 33 
 
 small openinf^ in the screen. The (jbserver's eyes were 30 
 cm. from the openin<j^, his head bein^ steadied by a support. 
 Before an)' experiments were made a rest of ten minutes 
 was taken to allow the observer's eyes to become accustomed 
 to the darkness; between the disappearance of one after- 
 image and the next stiimiliis there was a rest of thirty 
 seconds. When the thirty seconds had elapsed a signal was 
 given, five seconds were allowed for preparation, and the 
 stimulus was produced. 
 
 Very few ditihculties presented themselves, and of these 
 the only one not overcome was the lack of a fixation point, 
 as any fixation point was apt to produce a disturbing after- 
 image. By practice, however, the observer learned to look 
 in a certain way for the stimulus, and in the case of the 
 writer not over five per cent, of the time were the eyes 
 consciously focussed after any part of the light was seen. 
 The kerosene lamp used was trimmed at the beginning of 
 the experiments. By photometric determinations always 
 made before a sitting and generally during and after the 
 sitting, it was found that the light varied very little or not 
 at all. 
 
 Four observers were tested, C, McW. and S. respec- 
 tively with time, area and intensity. All were advanced 
 students in psychology, and S. had had previous experience 
 with after-images. F., the writer, was the fourth observer, 
 the three series being made upon him. 
 
 The results of nearly 3,000 experiments are given in the 
 following tables. In the first line the percentage of times 
 an after-image was seen is given, and in the second line the 
 average variation of the sets of ten trials; 100 experiments 
 of each sort were made, excepting in those cases in which a 
 different number is given in parenthesis. 
 
 Some preliminary experiments on area made on the writer 
 bear out in general the results in the corresponding series. 
 These experiments were made with an intensity of ^'^ c. p., 
 so that they could not be combined with the others. The 
 other constant was an exposure of one second. The same 
 areas were used except that the y^^ sq. mm. was omitted. 
 Seventy experiments were made on each area. The results, 
 with the average variations, are shown in the accompanying 
 table.
 
 134 
 
 SHEPHERD IVORY FRANZ. 
 
 INTENSITY. 
 
 Intensity in 
 
 candle power. 
 
 
 
 2 5 
 
 1 
 50- 
 
 200 
 
 ¥ucr 
 
 32 
 
 ( Percentage, 
 S. ] 
 
 ( Variation, 
 
 lOO 
 (So) 
 
 94 
 
 7 
 
 1 
 
 48 
 
 25 (no) 
 
 17 
 
 20.8 (no) 
 
 2 
 
 3-6 
 
 i Per cent., 
 * ( Van, 
 
 lOO 
 
 96 
 
 5-4 
 
 44 
 
 19-5 ('30) 
 
 15-5 
 13.5(130) 
 
 I 
 1.8 
 
 AREA. 
 
 Area in 
 
 square mm. 
 
 64 
 
 16 
 
 4 
 
 I 
 
 1 
 
 1 
 
 16 
 
 ( Per cent., 
 
 100 
 
 90 
 
 72 
 
 52 
 
 27 
 
 20 
 
 McW. \ 
 
 
 
 
 
 
 
 (Var., 
 
 — (50) 
 
 7.5(80) 
 
 14.8 
 
 12.4 
 
 9.2 
 
 6 
 
 ( Per cent.. 
 
 100 
 
 96 
 
 88 
 
 57 
 
 31 
 
 8 
 
 F- 1 
 
 
 
 
 
 
 
 ( Var., 
 
 
 4.8 
 
 8.8 
 
 13 
 
 15-4 
 
 8 
 
 TIME. 
 
 Time in seconds. 
 
 I 
 
 1 
 10 
 
 100 
 
 1 
 
 1000 
 
 ( Per cent., 
 C. 
 
 ( Var., 
 
 97 
 3-5(70) 
 
 95 
 
 7 
 
 75 
 17 
 
 12 ; 
 
 10.8 
 
 1 
 
 r Per cent., 
 (Var., 
 
 100 
 
 97 
 
 4.2 
 
 82.5 19 
 8.3(120) 7.4 
 
 1
 
 THE AFTER-IMAGE THRESHOLD. 
 
 135 
 
 AREA. 
 
 Area in sq. mm. 
 
 64 16 
 
 4 
 
 I 
 
 i 
 
 ( Per cent., 
 (Van, 
 
 96 
 5 
 
 89 
 10 
 
 67 
 14.7 
 
 1 
 1 
 
 41 1 19 
 10 1 9.9 
 
 The results of the first three tables are represented graph- 
 ically by the accompanying curves. 
 
 Figure 2. 
 
 20 - 
 
 zi. 
 
 16 
 
 10 
 
 4 
 
 The abscissa denotes respectively divisions of time, area 
 and intensity, the ordinate the percentage of times an after- 
 image appeared. The curves are not carried out to repre- 
 sent the greatest intensity, the greatest area and the greatest 
 time. Each curve is the average of the two observers in 
 that series, the close agreement of the observers making this 
 method permissible. The figures on the abscissa represent 
 the proportion of that stimulus to the greatest stimulus, 
 taking respectively time, area and intensity as the variables. 
 
 If we regard the threshold as that intensity, time or area, 
 which produces an after-image 75% of the number of 
 stimuli, we conclude 
 
 (i). That with an exposure of one second and an intensity 
 of -^^ c. p., the threshold is 4 sq. mm. 
 
 (2). That with the area 64 sq. mm. and the intensity ^ 
 c. p., the threshold is y^ second.
 
 F 
 136 SHEPHERD IVORY FRANZ. 
 
 i 
 
 (3). That with the area 64 sq. mm. and the time of ex- 
 posure one second, the threshold is y^g- candle 
 
 power (approximately), or between Jj and 7?,-,, c. p. 
 
 If we substitute in our definition 25^^, or 50%, or 90%, for 
 the 75'/^, we but change the figures to suit the case. 
 
 It is worth noting that of the 1,500 cases when after- 
 images Avere seen, but five were negative, a proof of the 
 theory that the negative after-image is due to exhaustion of 
 the eyes, the low intensities, the small areas and the short 
 times not being sufficient to tire or exhaust the eyes. These 
 five negative images were all seen toward the close of a 
 sitting, when the eyes had been used for forty or fifty experi- 
 ments, and all were with the greatest intensity, the longest 
 time and the largest area. 
 
 With the results obtained we are able to make a further 
 comparison — a correlation of our physical units in terms of 
 the production of after-images — a purely psychological prob- 
 lem. How much time equals how much intensity or area? 
 A glance at the curves and percentages shows that equal 
 increments in area, intensity and time do not give equal re- 
 sults. If we represent our constants by the letters c, c' and 
 c" respectively for intensity, time and area, and let i, t and a 
 represent respectively g^ c. p., ywou sec. and ^ sq. mm., 
 from the table of percentages we get the following approxi- 
 mate equations. — 
 
 i c = t c' = a c'' 
 (2 i c) == (1.7 t c') = (4 a c") 
 4 i c = 3.2 t c' = 16 a c" 
 8 i c = 10 t c' = 64 a c" 
 16 i c = 100 t c' = 256 a c" 
 
 The 8 i c and the 3.2 t c' represent yw^ c. p. and y§^ sec. 
 (approximately). These figures and the second equation in 
 brackets are supplied from the curves. The relations, then, 
 may be stated as follows: "Squaring the time equals 
 doubling the intensity or quadrupling the area," and vice 
 versa, " reducing the area to one-fourth equals halving the 
 intensity and taking the square root of the time." Whether 
 this be a chance relation or a general one throughout the 
 phenomena of after-images cannot be dogmatically stated 
 now. The writer has in view the further study of this problem. 
 
 124910
 
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