IMAGE EVALUATION TEST TARGET (MT-S) C< A. 1.0 I.I 1.25 11 1.8 LA. ill 1.6 C*^^„ oV ^ ■* XK''*? y Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4S03 . (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Un des symboles suivants apparaftra sur la dernidre image de cheque microfiche, selon le cas: le symbols — ^ signlfie "A SUIVRE ", le symbols V signlfie "FIN". sire Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely Included In one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc.. peuvent dtre fllmis A des taux de reduction diffdrents. Lorsque le document est trop grand pour Atre reprodult en un seul cllchA. II est fllm6 d partir de Tangle supArleur gauche, de gauche d drolte, et de haut en bas. en prenant le nombre d'Images nAcessaire. Les diagrammes suivants illustrent la mAthode. by errata led to ent une pelure. Fa9on A 1 2 3 32X 1 2 3 4 5 6 A CONTRIBUTION TO THE PSYCHOLOGY OF TIME Mi '■■ i Si' i BY M. A. SHAW, B.A., AND F. S. WRINCH, tf^.A. I- i>'l i >'f f ^ i ' 1 i i: # * i I I. Hist II. The III. Exp IV. We V. Rep '^.- .«,. Aristotle, De Sensu et Sensilt, cap. 7, p. 4^9. 'Aristotle, De Coelo, c. 9, sec. 8-10. '('! 1 ! \ ^ !i' hi I I , tj ■■ • ■ I ' After Aristotle down to the close of the Middle Ages, the problem was scarcely considered. In modern philosophy, from Descartes to Kant, every philosopher grappled with the question to some extent, but all were governed by their respective pre- suppositions, and explained time, like all else, as either wholly intellectual or wholly material. Kant's solution of the problem is, in reality, to make t'me one of the categories (in the Aristotelian sense of the word) or ways in which the mind looks at its content, these categories being contributed by the mind. " With regard to phenomena, we cannot think time away from them," he says, just as we cannot think "quality" and "quan- tity" away from them. In other words, in that unified or determined assemblage of phenomena which he calls object or fact of exper'ance, there are two factors, the subjective and the objective, each of which is indispensable. In the subjective factor is included the temporal relation of phenomena. Since Kant, it may be said, speaking generally, there are three schools of interpretation of the time problem ; one may be characterized as the idealistic, another the materialistic, and the third is composed of those who make of time a special sensation. The first school adheres to the Kantian presentation, not merely as set forth in his chapter on Time, but as gathered from his whole philosophy. The second school is an off shoot of one which has existed from the beginning of philosophical inquiry. Its adherents would try to show that time has an exclusively sensational basis. The third, as stated above, treats the idea of time as a special sensation. Each of these schools has its representatives in modern psychology. Dr. Mach, of the University of Prague, may be mentioned as an adherent of the last. Among those belonging to the second is Dr. Hugo Munsterberg, while as a representative of the first school the distinguished Professor Wilhelm Wundt, of Leipzig, may be taken. These three psychological theories will now be more fully stated, in the order in which the names of their representa- tives have been given, and a comparison will be made of their relative merits. In the presentation of the first theory, we follow the exposi- tion of Dr. Mach in his " Beitrage zur Analyse der Empfindungen." The contention of this school is that "time is a special state of consciousness." Mach says : " The existence of a special specific 'Ma If i 7 [107] time sensation appears to me to be beyond doubt."* He draws his conclusion from such tacts as these. In the first place, the content of time may be chanj^ed without chan{»ing the time itself* In contiguous bars of music the rhythm may be exactly the same, but the tone entirely different. The recognition of time intervals as constant, though their content be continually chang- ing, is not a product of the reason, he says, hut is rather an immediate sensation. He illustrates this pot Ion further from the striking of a clock ; the separating of the strokes as first, second, third, fourth, and so on, by which their position as before and after is given, is not, he believes, a thought which accom- panies the sensation of hearing, but is rather an immediate " time sensation." To explain the time sensation a little more definitely, Mach notes that it is always present in every conscious state, that it is of necessity organically connected with every conscious state. When the attention is severely strained, time appears to pass slowly ; when the exertion is lighter, it passes more quickly. If we are so interested that the exertion of attention is scarcely felt, then the hours pass rapidly away. Where attention is wholly wanting, as in dreamless sleep, time passes quite unconsciously, and the only connection between the two waking periods is an intellectual tie. Besides this influence of attention on the passing of time, a very strict concentration of the attention on some expected event may actually change the time order. The blood may appear to the overstrained attention befot > the surgeon's lancet has actually pierced the skin. These considerations, Mach thinks, indicate such an organic connection between the time sensation and attention, and such an obedience of the former to the latter, that he concludes that " time is the work of attention." Before examining the validity of the grounds on which the above theory is based, we will state the position of those who maintain that the presentation of time is attached to certain special states of consciousness, characterized also by other content. Since both views are affected more or less by the same errors, they may be better discussed together. In the presentation of the second theory, the exposition of Miinsterberg in his " Beitrage zur experimentellen Psychologic" will be followed. He begins with an attack on W^undt's position, that in estimating the relative length of smaller intervals, e.g. 'Mach, Beitrage zur Analyse der Emffindungen, p. 104. [lOH] 8 Si' m )ii' ;* ' 'I V, ■J ' -'I i it -I vi ■' i 1 , 1 t - 1 ! i ^, ■*;» from 0.5 to 3 seconds, the actual time-lengths themselves are compared directly, and not through the medium of their content. MUnsterberg holdri that these small intervals without content do not normally occur, but that in all time presentations the judg- ment of the interval depends on muscular tension, that is, on tension of the different organs occasioned by muscular conduc- tion, or by the memory of such. These are the only data at our disposal for the immediate feeling of time. Whence come these feelings of muscular tension ? Goldscheider says that they have their seat principally in the joints, in the thin sensitive layer which covers the ball of the bone and the socket in which it works. Mtinsterberg replies that there are no joints in the eyeball, the tongue, the lips, etc., yet that the feeling of tension is quite as noticeable in these as in the leg or arm, and further, that the feeling may change after the teeth are closed and no further movement takes place in the joint of the maxillary bone. The feeling of tension arises, then, not from the local sign in the joints, but from the muscles; in the muscles lies the whole source of the feelings of tension. In stating the subjective experience on which, according to this theory, an interval is estimated, he says ; " If there are given to me impressions of sight ; for example, if a point of brightness should appear upon a dark ground irregularly at intervals of from one to three seconds and vanish again, I feel at ever appearance of the stimulus the muscles of the ej'e exert themselves to direct the line of vision to the luminous spot ; all the muscles contract to fix the spot firmly, and the accommodation muscle exerts itself to secure a clear impression. In short, the whole organ of vision, as soon as the stimulation begins, comes into a state of exertion, by which the stimulus gains in distinctness, and its perception rises above the other content of presentations."* These feelings of tension and relaxation are the whole data for the time idea, and on their nature depends the estimation of intervals. The presentation of time is the synthesis, made up of the perception of the impressions which limit the parts of time together with the sensations of muscular exertion, which increase and decrease in intensity, and which we usually do not refer directly to the muscles. We believe, he says, that we refer our special state of consciousness directly to time, we believe that we perceive time ^MUnsterberg, Beitrage zur experimentellen Psychologic, Heft 2, p. 22. 9 [109] sensation directly, just as the man gropinp in darkness believes that he perceives space directly, whereas he only perceives directly the limitations of space, and infers the rest from these directly perceived data. In the case of time, what is immediately felt is the muscular exertion increasing and diminishing in intensity, and from that time is inferred. On the hypothesis that the estimation of intervals depends on the change in intensity of muscular sensation;-., Mvinsterberg accounts for the intelligent division of the continuous Po./ of time by a physical process which is continually changing, the act of respiration. In this process, the muscles of the organs involved are continuously employed in contracting and expanding, and make a regular alternation of strain and relaxation in muscular tension. Although there are factors which cause irregularities in this periodical division of time, such as the existence of certain central processes, leading us to make an inspiration at the moment we turn to an agreeable impression, and to exhale at the moment when an impression of the opposite nature is experienced, still when the attention is closely occupied inspira- tion and expiration follow regularly, and thus afford a continuous uniform standard of time. Before explaining the experimental work with which he supports his theory, Mvinsterberg notes that the discoveries of different seats of temporal sensitivity by other experimenters may not be all wrong; indeed, if the cause of their disagreement were known, it might be shown that they were all right. Their different results may be accounted for by the varying sensibility of the organs involved. In auditory impressions, an interval of 2 Wundt, Outlines of Psychology , p. 149. [116] 16 i; In the tinic idea the elements bear a fixed unchangeable relation to one another ; none can be changed without changing the whole. But in addition to this the elements bear a relation to the ideating subject, so that when any element is changed in relation to another it also changes its relation to the ideating subject. These two relations are always found connected in actual experience, but when we isolate them for the purpose of investigation, we find that from the relation of the elements to one another we get the so-called modes of time, v'\z., brie*", short, long, etc., and from their relation to the ideating subject ve get the temporal stages, past, present and future. If a ser.es a, b, c, d, etc., represent points in space, they may all be perceived at once; the fixation point may rest on any one of them, and the rest be grouped from that centre. If it be a *ime series, they may also be perceived at once, if they be points in the past, but the fixation point of time is always the present moment, and from this point the other points in time are always ar.anged. Since the present moment is always judged in relation to the totality of the past, then it follows that no two momentf, are identical, for the totality of the past with which one moment is related is in- creased by that moment and thereby altered before the next moment is related to it. Thus there is a characteristic belonging to every point in time, which distinguishes it as past in relation to the present moment, and makes this present the fixation point from which all the rest are arranged. The fact that the affective element in time is conditioned by the totality of previous experi- ence, and so made different, produces an ever-changing impres- sion of the present moment. This impression of the present moment .3 called the inner fixation point, and the never-ceasing change in no inner fixation point is called the continuous flow of time. This continuous change means that no moment of time is like any other moment, and that no moment can ever return. There is no such thing as time in which no change takes place, and since the fixation point is continually moving forward it follows that time is of a one-dimensional character. The above is in substance Wundt's theory of time ; it is the theory of modern experimental psychology. And let it be observed that although by abstraction and analysis the time idea has been reduced to its elements for the purpose of investigating its nature, still it is only by artificial analysis that it can be so ii 17 [117] separated into its elements. In nature the time idea does not appear so separated, but only as a property of all facts of con- sciousness. This theory avoids the errors which Mach falls into in making the time idea a special particular sensation, and also the errors of which Munsterberg is guilty in making the time idea ♦.he property of a special sense only, and in working out his theory ultimately from a materialistic standpoint. Wundt's theory, starting as it does from what we hold to be the only consistent standpoint, viz., immediate experience, will, we believe, account for all the phenomena of time. II. THEORY OF T'ME ESTIMATION. In all states, the percipient subject is conscious of a temporal relation ; no experience is without duration. Both sensations and the intervals between them occupy time ; each has a content, but the content of a sensation is more evident than that of an interval. The duration of sensations has not been experimentally investigated in regard to its temporal value for consciousness. Experiments on the estimation of time in intervals, by Kulpe, Meumann, and others, show that below an interval of a certain length the limiting stimuli exercise an important influence. Above this interval, where longer periods are involved, the content of the inte'-val, e.g. respiration, heart-beat, or some other organic function, enters as a factor influencing the judgment. The interval that lies between the short and long groups, which has been found to be the most accurately estimated inter- val, we believe to be the " unit of time," and the basis of all time estimation. Tt differs in length more or less in different individuals, but in all cases the constant error and mean variation are less as we approximate to it. Here, neither the limiting impression, which influences the judgment of shorter intervals, nor the organically functioned content, which influences the judgment of longer intervals, modifies the estimation to any marked degree. This remarkable fact in connection with the estimation of intervals, that a more or less definite interval is estimated most ac ^urately, and the further fact that as we depart f [118] 18 if: from it in either direction errors ariso in judgment, lead us to believe it to be the basis of the estiniation of intervals in all cases — a temporal unit. This theory of a unitary basis of esti- mation, moreover, is in accordance with that demand for single principles, which is fundamental in the human mind. With dual principles the mind is never satisfied, and it was for this reason, in part, that the theory of a three-fold basis of estimation advanced by Kiilpe was rejected. The theory of a temporal unit is therefore in harmony with the scientific demand for explanation by as few principles as are consistent with facts. That this theory has an experiuiontal basis, we shall now proceed to show in the three cases of the unitary interval, of intervals below, and of intervals above the temporal unit. 1. In the estimation of the jnitary interval, the interval itself is the basis of estimation, -if Kulpe, Meumann, and others have said. Here, also, its more cr less definite content (obtained by analysis) of feelings of expectation and relief, and of muscular sensation, is scarcely noticed. Some investigators would mske this content the basis of time estimation. Among these, Schumann, whose theory" will be examined later, may be men- tioned. The estimation of this interval, too, as would be naturally expected, is more accurate than that of any other. 2. In the estimation of intervals below the temporal unit, the experiments of Kiilpe and Meumann revealed a tendency to reproduce these intervals longer. Such was also the case in our own experiments.^ This eiror in estimation seems to be due to the tendency of the temporal unit to complete itself, it being the individual basis of estimation. It will then be made up of both the empty interval and the limiting stimuli; and the judgment will be affected more or less by the nature of these, but the over- estimation becomes less dUc less as the interval approaches the length of the unit of time. This tendency to complete itself, on the part of the unit, is confi.-med by results of other investiga- tions. In experiments on the time relations of poetical metre, a tendency to complete the foot, where the metre was irregular, was noticed.* In this connection, we may note that Leuba* * Kulpe, Outlines of Psychology, sec. 65, 3. ^Zeitschrift fiir Psychologic, Bd. xviii., p. i, »Cf. Tables HI., IV. and V., infra. *See ^^Experiments on the Time delations of Poetical Metres," hy lUziiK, Hunt and McKay, in this volume. ^Psychological Review, 1898, p. 483. of 19 [119] suggests, as an explanation of the quant' Mtive change in memory, that there is a typical representative for each class of experiences (conscious processes), which is a residuum left over from all the experiences we have had. Towards this middle type or unit all our memory images are drawn. As was said above, the nature of the limiting stimuli is a factor which enters into the estimation of intervals smaller than the unit, and has a bearing on the accuracy of their reproduction. It is found, for example, that intervals which are bounded by a fairly loud, sharp sensation are judged to be shorter than intervals bounded by a weak sensation,* while on the other hand they are judged to be shorter likewise than intervals whose end-signals are still stronger.* This difference is accounted for by the sub- jective strain of attention or expectation in the weak and also in the very strong sensations, which tends to lengthen the intervals. From these facts, Kiilpe* concludes that the limiting stimuli are the basis for the estimation of short intervals, whereas they are but a disturbing factor in the estimation. Schumann, in the same way, makes the feelings of strained expectation and surprise negotiate the estimation of the interval. Intervals shorter than the unit of time, however, cannot be estimated and reproduced individually, but only by being grouped into a series. This is confirmed by the fact that they are thrown into a subjective rhythm, which divides itself according to the temporal unit or multiples of it. Rhythmic reproduction of short intervals is established by the results of Meumann, Kiiipe, Miiller and others. We do not believe that such rhythmic grouping is confined to intervals limited by auditory impressions alone, as KUipe says.* Experiments were made by students -^nder the direction of Professor Kitschmann, in the laboratory of the University of Toronto during the session 1894-95, with the following recorded results.' Mr. Warren, under the heading Pendulum Experiments, writes: "In the first experiment, a striking rhythmic interval occurs, showing itself from the first and continuing with the same regularity during the reproduced time, the periodic return of under-estimation and over-estimation increasing during the iCf. Tables IV., V. and VI., infra. 'Wundt, Outlines of P:ycho'ogy, p. 151. 'KUipe, Outlints of Piychrlcgy, sec. 65, 3 (i). *Kulpe, Outlines of Psychology, fee. 65, 5, 2a, ^These results are unpublished, \j\x\. they are preserved in the Archives of the Psychological Department. y ■ ' [120] I"*'! progress of the experiments." Mr. Crawford's experiments show a noticeable, although not a constant, periodicity in visual impressions. Under the heading Points to be Noticed, he says : " In experiments with visual impressions (pendulum vibration), a periodicity is noticeable m some series of experiments, but not in all." Mr. F. W. Varley, in a very carefully prepared paper, summing up results of experiments with both visual and auditory stimuli, says: " On viewing the graphic representations of these experiments, it may be seen that they have been characterized by waves of attention. Periodically there has been a compara- tively great aberration, indicating a relaxation." In our own experiments with visual impressions, the intervals ranged from half a second to nine seconds, and the tendency to rhythmic accentuation was not noticeable. In nine series of experiments with auditory (metronome) impressions, there was a marked periodicity in some, while in others it was not apparent. From the above statements we do not think that the exclusion from rhythmic accentuation of all intervals except those bounded by auditory impressions is warranted. On the contrary, it seems to be a constant characteristic in the reproduction of all short intervals, and is due, in part at least, to the fact that such short intervals cannot be estimated individually, but are thrown into a subjective grouping. Thus the experimental facts in connection with the estimation of the class of short intervals supply a basis for the theory of a temporal unit. 3. In the estimation of intervals above the unit of time, observers find great, almost invincible difficulty in excluding the influence of the content. This content is generally some regu- larly recurring organic function, and upon it depends largely the accuracy of the judgment. The observer K. attempted to ex- clude the influence of content as far as possible. The results show that this attempt vitiated his judgment to a very marked extent. The explanation is not, however, that the content is the basis of judgment, but that the mind estimates intervals longer than the unit in terms of the unit itself, and that the unit or the multiple of it is here represented by some regularly recurring organic function. As in short intervals reproduced in groups the quality of the limiting sensation is a factor enterine into the estimation of the interval, so in long intervals the character of the content plays a part m the estimation. An interval which has a full and varied content is judged to be comparatively have. I i 21 [121] longer than one which is not so crowded, because of the strain required to keep the attention on the interval, when there are other things to distract it. If, however, the content becomes so interesting as to absorb the attention entirely, the time passes more quickly and is judged to be shorter. The part thus played by attention does not make it a basis of estimation, as Mach thinks, but only shows its influence as a single factor. We may now sum up our conclusions as follows : (i) A certain interval, which varies considerably in different individuals and which may vary in the same individual at different times, is the unit of time and the psychological basis of the estimation of intervals in all three classes. (2) In the first and third classes of intervals factors enter which influence the judgment, but they arc only modifying con- ditions, not the bases of our estimation. There are, in our opin- ion, not three different kinds of temporal judgment, but three applications of the one form of temporal judgment. (3) Although time must be considered as an elementary property of consciousness, incapable of further analysis, the unit of time, nevertheless, which seems to be the basis of the estimation of intervals, is of the nature of a psychic compound. It contains, as may be seen by analysis, both subjective and objective factors. Of these two factors, the objective seems to have, at least genetically, the predominating influence. It may be some organic function, or multiple of such, which has accustomed us to the duration which is our unit more than to any other, or the duration of some objective impression or interval to which we have been always accustomed may have played the funda- mental part in its formation. Before proceeding to give any account of our experimental work in the laboratory of the University of Toronto, it may be well to consider briefly two recent articles on this subject of time judgment by F. Schumann.^ 1 le views there presented might be classed with the second of the time theories given above (p. 7) and passed without further comment, for they partake of the same general nature, being one-sided and materialistic in tendency. The views are, however, the most recent exposition of the school, and for that reason we consider them a little more fully. ^ Zeitschrift fur Psychologie, Bd. xvii., p. 106, and Bd. xviii, p. i. :i|f [122] 22 Schumann maintains that in the estimation of time intervals the judgment is mediate.' Whether it is mediate or immediate must be answered, he says, by experimental psychology, and not from theoretical principles, and he concludes from his experi- ments that the feelings of expectation and surprise mediate or negotiate the estimation of the interval. Without following the steps by which he reaches this conclusion, to be noted later, we shall first examine the basis from which he starts and his theory of judgment. The starting point for psychology, according to Schumann, must be " inner perception." " The latter term is used for the psrcept'-^n which arises on the occasion of a sense stimulation. In making this the basis of certain knowledge Schu- mann is unduly emphasizing the subjective, almost to the exclusion of the objective element of the immediately given fact of experience. The immediately given is the idea-object, as Wundt has shown, and not the idea, which must be the element of inner perception. The idea and the object are secondary products, the result of the analysis of the immediately given fact. Hence Schumann's "inner perception," which he assumes to be the immediately given, and therefore the basis of certainty, is not the immediately given, but an abstraction. However valuable the accuracy of his experimental investigation may be, the value of the conclusions he arrives at will be, if not vitiated, at least much impaired, on account of this erroneous basis of certain knowledge from which he starts. Schumann's state of confusion as to the nature of the immediately given is again apparent in his theory of the judgment of time intervals. In his conclusion^ that expectation and surprise mediate or negotiate the judgment of time intervals, he is using two complex temporal processes as the basis of his judgment. Hence, on his own showing, time estimation is not a judgment mediated by untem- poral processes, differing entirely in nature from time itself, but it is rather of the nature of an immediate comparative judgment. For those processes, which he says mediate the judgment, in so far as they play a part in that judgment, do it through their own time element, which in the act of judgment is compared with the respective time intervals under discussion. Schumann seems to leave out of consideration, in his theory of ^Zeitichrift fiir Psychologie,^d, xviii. '^Zeitschrift fiir Psychologie, Bd. xvii. ^Ztitsckriftfur Psychologie, Bd. xviii . 28 [123] judRment, the relativity of the whole content of consciousness. He maintains that there is no comparative activity in judgment, on such grounds as that the intensity of an impression advances a number of units before the judgment of increased intensity arises. But, if there be no comparison, to say that the intensity is in- creased means nothing. It must be increased in relation to some other intensity. Further, if there be no comparison \n judRment. then Schumann's theory that expectation and surprise mediate the judgment cannot be sustained, for in this process of media- tion there is comparison involved. Either Schumann must give up his theory of judgment being entirely passive, or else he cannot maintain his theory of time estimation. A clear compre- hension of experimental psychology, the standard to which Schumann appeals, should show that the most fundamental and primary judgment involves activity from one point of view, and passivity from another. For the more or less relatively isolated immediate experience may be viewed from one point as the active knowing, and from another as the passive known. These are not two different experiences, but two ways of looking at the one unitary experience. The most fundamental judgment, then, is both active and passive, and every other judgment must partake more or less of the same nature. Having shown what we believe to be the errors of Schumann's theory of judgment, and that too by an appeal to the same stan- dard which he himself applies, viz., the decision by experiment- al research, we shall now consider his theory of the estimation of small intervals. Schumann says: ^" Ich habe nun die Ansicht ausgesprochen und zu beweisen gesucht, dass diese Nebenein- driicke der Erwartungsspannung und der Ueberraschung die Schatzung der Intervalle vermitteln und zwar in der Weise dass ein Intervall, vor dessen Endsignal eine lebhaftere Erwartungs- spannung auftritt, langer erscheint als ein Intervall, bei welchem sich nur eine schwachere Erwartungsspannung geltend macht, und dass jedes durch Erwartungsspannung ausgefUllte Intervall fUr langer gehalten wird als ein Intervall dessen Endsignal un- erwartet kommt." We have stated in a previous part of this paper what place these feelings of strained expectation and sur- prise occupy in the estimation of intervals. That they are not the basis of our estimation seems evident from the following considerations : '^ Zeitschrift fiir Psychologie. Bd. xviii., p. 2, [124] 24 1. There is one fact in connection with the estimation of in- tervals which has been experimentally established almost beyond a doubt, viz., that there is a certain more or less definite inter- val which is most accurately estimated. It is admitted by in- vestigators that in the estimation of this interval these accom- panying impressions of expectation and surprise are less marked than at any other. Why is it then, if they negotiate the estima- tion of the interval, that where the sensible discrimination is most accurate we are least conscious of these feelings ? If they negotiated the estimation of intervals they should be most marked where that estimation is most accurate. That this is not the case has been experimentally established. Not only are they not marked where the estimation is most accurate, but according to Schumann^ himself, when the strain of attention is strongest, and surprise greatest, there the greatest errors in judgment are made. This error, he goes on to say, becomes less as the feelings of ex- pectation and surprise decrease. Hence we must look deeper than these for the basis of the estimation. 2. It is as clearly established as the fact of a most accurately estimated interval, that above and below this interval there is a gradually increasing error in judgment. This fact of the over- estimation of intervals shorter than the one we have called the unit of time, and the under-estimation of intervals longer than the unit, is not explained by Schumann's theory. If these negoti- ated the estimation of intervals, it would follow that wherever they are as little noticed as at the unit of time the estimation should be just as accurate. But that this accuracy does not occur has been established by experiment ; for, both above and below the unit of time, after the strain consequent upon the change of normal time has passed away, when the attention has adjusted itself and the end-signal enters just when it is expected, there is ever found an error in judgment which increases as we depart in either direction from the most accurately estimated interval. Hence we conclude that the feelings of expectation and surprise do not mediate the estimation of the intervals, either when these feelings are most marked, or when they are at the mean of alternation. We do not deny their presence, but they are only factors in the estimation, not its basis. 3. In addition to the above reasons for rejecting the theory that makes time estimation depend on feelings of strained expec- ^Zeihchrifl fur Psychologic, Bd. xviii., p. 2. lil • 1 1 J k 26 [125] tation and surprise, there is another, and nc ^ one of the least im- portant. It has been mentioned above in connection with the criticism of Schumann's theory of judgment. Wherever a feeling of strained expectation is experienced a complicated process takes place, which has temporal relations and can itself be estimated. This feeling of strained expectation is one of the affective accom- paniments of any content of consciousness which is being actively apperceived. It is exceedingly complicated and may be accom- panied with excitement, pleasure, pain and the like, and its temporal relations may be of longer or shorter duration. Yet we are asked to take as the negotiator of temporal estimation a com- plicated affective process which is itself as temporal as that which we are estimating ! m III. EXPERIMENTS ON THE EFFECT OF A LAPSE OF TIME BETWEEN THE NORMAL AND COMPARATIVE INTERVALS. The purpose of the experiments now to be described was to investigate the effect of a lapse of time between the normal and the recording of the comparative interval upon the accuracy of the reproduction. The work on these experiments was done at regular times of the day and week, so as to secure as far as pos- sible uniform conditions in the subject, and the experiments were continued over a period of four months. Everything was removed that might create any counter-interest, or in any way disturb the subject whilst making the judgments, so that, as far as objective conditions were concerned, there was nothing to hinder the subject from giving his undivided attention to the work. The apparatus used was a Charles Verdin kymograph (Paris, 1892), with a number of fixtures designed by Professor Kirsch- mann, for the purpose of securing visual and auditory stimulation, and to insure accurate recording of the judgments of the subject. Visual stimulation was used exclusively in these experiments, and the method by which the light-flash was communicated to the observer may be seen by referring to the half-tone cut of the kymograph (Fig. i.) The flame of an incandescent lamp was reflected from a small mirror (C in Fig. 2) at the end of the drum [126] 26 of the kymograph, through holes cut at equal distances in a band- shaped ring which was fitted on to the end of the drum. As the drum revolved the reflected light was seen through a telescope by the observer, who sat about fifteen feet away. The light appeared ill successive flashes as the holes passed the mirror. The length of the interval was varied by changing the number of open holes. The field of vision of the observer for the flash of light was en- tirely obstructed except for what appeared through a graduated aperture in the screen A (see Fig. i.), in front of the'revolving band. The lamp B was enclosed, so as to throw not much light out into the room, which was darkened during the experiments ; the light flashes would therefore be sharp. The comparative in- tervals were registered on the carboned paper which covered the drum of the kymograph, by means of a rigid steel wire, one end of which the observer held between his fingers, and the other end, passing round a pulley, was connected with the pointer C in contact with the paper. At the pull of the observer the pointer slid along steel rods, thus making a curve in the otherwise regular line, and by this means the estimation of the subject was record- ed. A weight (D, Fig. i) connected with the pointer brought it back to its place as soon as the strain on the wire was released, after each reaction. The use of simple mechanical transmission might at first glance seem primitive, but, in accord with the request of the director of the laboratories, we wished to avoid all complications arising from the use of electricity. The current and silently accepted view that electricity, since it travels so swiftly, requires also but an exceedingly short time to accomplish work, i.e., to overcome resistance, is utterly fallacious. Wherever electricity has to accomplish a mechanical labour, be it in the form of chemical or electro-magnetical action, or simply the discharge of a spark, it requires time ; and this time is not independent of the duration of previous conditions.^ In the case where longer periods have to be recorded, and where efficient controlling apparatus can be applied, as in Wundt's chronograph, the errors mentioned do not amount to much ; but wherever short and varying intervals have to be recorded, the errors produced by electric marking will materially impair if not wholly invalidate the results. ^Kiilpe and Kirschmann, Ein neuer Apparat zur Conlrolle zeitmesstnder Instru- menu. (Phil. Stud., Bd. viii., p. 145.) thi 27 [127] In order to control the speed of the revolution of the drum, and to serve as a basis of measurement of the normal and the recorded intervals, the vibrations of a Konig tuning-fork were excited by an electric current from a storage battery, and trans- ferred to the carboned paper on the drum by a Deprez signal (D, Fig. 2). The steel point of the Deprez signal, which was used to record the vibrations of the tuning-fork, was mounted on the same rods, but just behind the pomter which the observer used to record his judgments. The lines made by the two points thus follow each other side by side round the drum, except where the straight track of the pointer is interrupted by the curve marking the reaction. The Deprez signal and the pointer passed gradually from one end of the revolving drum to the other, by means of a screw connection (E, Fig. i) worked by the assistant. The experiments of this investigation, the results of which are given in the tables below, were made by S. on intervals of half a second, three-quarters of a second, and a second and a half. In order to avoid the errors of reaction time involved in experiments where a single normal and comparative interval are used, a successive series of intervals was used in both cases. The observer was allowed before each series of judgments to see the objective stimulation for half a minute, and in order to assist in getting the rhythm of the successive stimuli, where necessary, some movement of the hand or foot was used. When the half minute had elapsed the objective stimulus was turned out, and the observer began immediately to record the series of compara- tive intervals, continuing until stopped by the assistant. The same series was exactly repeated twice again for each interval tested, with only this change, that half a minute and one minute respectively were allowed to elapse between the cessation of the objective stimuli and the beginning of the recording of the com- pared intervals. During this lapse of time the physical move- ment referred to above was discontinued. With the intervals of half a second and one and a half seconds three groups of the series were made, but only two with the three quarters of a second interval. In the first table below is given a summary of the ex- periments. Only the first twelve trials in each case are counted, making in all thirty-six trials at the " immediate," half minute, and one minute pauses with the half-second and second and a half intervals respectively: and twenty-four trials at the same three pauses with the three-quarters of a second interval. The M-\ [128] 28 second table is a summary of all the trials made. The normal, average, constant error, and mean variation are given in terms of one-hundredth of a secoi.d. The first table is given with an equal number of trials in each group of the series, lest the experiment should be vitiated by having an unequal number of trials at the various lengths of pause. Ji^l! Ill iii rmal, ms of equal ment it the ^mmmmnTffm' Fic. I. iMC. J. Jill m vimi I I'lc-,. 1 't Ji J. >:' ill IS 29 [129] a S _0 •s t« « ■g S!c* ssr^ ^ti'^^ ■c S3'r= S35 3?§3 >■ — 71 — (NriM rH > s —■tit K ?i M -r -^ 55 S a U u H CC Tl — i~ or: 83gS 838 1 3«.? ^S? Q 1- 31 r: If: ?t se c: X ^ 1^* ^ irSij; r: ©-<■ = d"^?* 5>j ,-1 CI t-^ P^ F- Tl •- Tl 4^ 1 1 1 1 1 1 1 1 1 4-» 1 1 t 1 1 1 0) 1 1 1 ! 1 1 ai 1 1 1 I 1 1 1 1 1 B 1 1 1 c o u U a ^^^ OS — 0- S i-H I— t rH < M < »M H i4 ►^ m P3 i •s J^ tc 6 1= B ii ii CD _c cd ,c i. _f .2 ■2.5 _E .2 •S.S t c aSE SSE Iss aSE aSE a a a 1^- 5^- 1^^ s^- 1^- Ix- «i vi c^^^ *4 Se^ MMM 3SSS 3S5 rtit is M-t (*>i d d Z ;z; U5 lOifi 888 •a lOift Iff 888 g SkS IC ic IlO 1—1 t— 1 i-H gss iC iC »^ lo i6 »o I— 1 1-H -H ;z; z [130] 80 Results. (Taken from Table i.) (1) The interval of half a second approximates to what has been called above, the unit of time. The constant error and mean variation are less at this interval than at any of the others. Here also the effect of pause is less than with intervals above it. The mean variation is the same for " immediate " and " I min.", while the constant error is nearly the same for both. (2) With the intervals above the unit of time the mean varia- tion increases with the length of pause. Sensibility decreases with ■ itervals above the unit. (3) The constant error is practically the sa.me throughout for " I min." and " immediate." (4) After the lapse of half a minute the results are not regular; with the longest normal interval the constant error is less than for " immediate," but with the other normal intervals it is greater. The mean variation is always greater for " half min." than for " immediate." The results from Table 11. do not vary much from the above. IV. WEBER'S LAW AND TIME ESTIMATION. The limit of the sphere in which Weber's law holds accur- ately is still an open question. Sanford^ says that it holds " tolerably" for medium stimuli of several kinds, with very large and small stimuli only imperfectly, and with some it cannot be demonstrated. Kiilpe" says that with pressure, auditory, and strain sensation, also with light intensities, a constancy of sen- sible discrimination is experienced. The scanty investigation o^ the senses of temperature, taste, and smell has not yet reached a stage at which definite conclusions can be drawn. Wundt" says that the law has been shown to hold for the intensity of sensa- tions, and within certain limits for the comparison of extensive compounds, especially temporal ideas ; also to some extent for spacial ideas of sight and for motor ideas. On the other hand it 'Sanford, Experimental Psychology, Ch. viii., p. 334. JKuIpe, Outlines of Psychology, p. 126, 'Wundt, Outlines of Psychology, p. 2SS> nc tc cc of !|IH 81 [131] does not hold for spacial ideas of external touch, obviously on account of the complexity of the local signs, and it cannot be verified for sensational qualities. The above authorities do not differ much among themselves, but there is a great disparity in the direct testimony of thoLC who have investigated the validity of the law in reference to tim«: estimation ; and on this account our own series of experiments was undertaken. The great difference in the testimony of earlier investigators has probably arisen from their having failed to take into account correctly the many disturbing factors which may vitiate the results of experiments. One such factor is the general condition of the operator ; fatigue or nervousness may be the source of much divergence in the testimony of subjects at different times. The state of atten- tion also is a source of considerable variation ; a concentrated, well-governed attention will give more accurate judgment than a musing, listless or uncontrolled attention. This factor has been treated in detail above. The method of registering experiments has led to erroneous results, as noted in connection with the work of Mach and Munsterberg. A lack of appreciation of the true function of rhythm in time estimation has led many experiment- ers to regard it as a factor which detracts from the accuracy of the estimation of intervals, instead of as a condition which makes the estimation of certain very short intervals possible. The effect of aesthetic factors too has been often misinterpreted, as has also the part played by the content in the estimation of larger intervals. These factors, which are all involved in the estimation of time intervals, are mentioned to show the many sources from which confusion may arise in the treatment of the question. But if these, and perhaps others not noted, could be carefully eliminated from the experiments, there would probable be no such disparity in the testimony of investigators as to the validity of Weber's law in the estimation of time intervals. Ernst Mach, in a series of experiments which are neither fully nor definitely enough stated to sanction his conclusion, finds that Weber's law is not valid. His experiments were made from i860 to 1865, extending over a period of five years, during which the conditions were not very uniform, his rather primitive methods of stimulation and recording being changed from time to time. He professes to have tested intervals from .016 sec. upward, but he only gives figures for a few of the intervals. Taking such a [132] 32 lit' ill small interval as the lower limit, and testing the validity of the law from the whole range of intervals, from one so very short to a long one, he could scarcely have come to any other conclusion, since such small intervals, even if they could be individually estimated, could not be recorded with any degree of accuracy. Hence little importance can be attached to the results at which he arrived.* Karl Vierordt maintains that the law does not hold. He thinks that the fact of contrast between long and short intervals, making the former longer and the latter shorter, is sufficient to cause a discrepancy, and that this, together with some other factors, renders uniformity in time estimation impossible. Though Vierordt is right in maintaining that after a succession of short intervals a long one seems unduly long, still that fact is not suffi- cient to destroy the correctness and uniformity of time estimation. His experiments, moreover, were too limited in nu.noer to be very conclusive.* Volkmar Estel concludes with Mach and Vierordt that the law does not hold. He experimented on inter- vals ranging from 1.5 to 8 seconds, and his recording was done with the earlier form of Wundt's time-sense apparatus. His ex- periments were too scanty to be of real value ; some of the inter- vals received only three trials by each subject, and few were treated more thoroughly. In addition to this, his work is coloured by such a strong controversial spirit, arising from his dispute with Vierordt as to the effect of a pause between the normal and comparative intervals, that his results cannot be greatly relied on.» Fechner subjects Estel's work to a severe criticism, and exposes its weakness. He himself thinks that nothing is to be discovered which is irreconcilable with Weber's law.* Mehner comes to a conclusion midway between Estel and Fechner ; he finds that the law holds approximately above the interval of 7.1 seconds, where the sensibility is constant, but that below 7.1 seconds, where the sensibility is rhythmic, it does not hold. He maintains that in the results of Estel and others the disparity of results arises from lack of practice, strain of atten- ^ Untersuchen tiber den Zeitsinn ties Ohres, (Moleschott's Untersuchungen, 1866, p. 181.) *Der Zeitsinn. (Tubingen, i868). 'Neut Versuche titer den Zeitsinn. (Phil, Studien, Vol, ii., p. 37.) * t/ber die Frage des Webei'schen Gesetzes und Periodicit'dtsgesetzes im Gebiet des Zeitsinns. (Abhandl. d. mathtmat.-phys, Classe d. k^l. S] :hod ima- is of I the Iso a le by holes light ;s, in 3 pro- terval pegs. refer- vriting iction, jnding Fig. 2) ver, by vement rith the ine and jdiately mal and iterially s source oth the lediately intervals als were six thou- ecorded. 5 may be are sum- and long ;onscious- reactions 1 by from ■niograph. id it acted irise from diffused attention, and from the nervous confusion frequently involved in the first few reactions. The accompanying cut (Fig. 3) represents parts of three sample sheets taken from the drum of the kymograph, containing the tracings of a tuning-fork of one hundred vibrations to the second, by which the length of the interval was registered, and the tracings of the pointer which marked the limits of the estimated interval. We give next a sample sheet containing the readings in detail of the length of each estimation of the interval, together with their average and mean variation, the latter representing the average error. In the tables that follow appear only the summed results of the different series of estimations made by each subject in the experiments. Reading of Sheet ij, Observer K. Visual stimulation. Two holes open in the drum of the kymograph, through which the light stimulation flashed to the observer at each revolution of the drum. Three series of trials, a short stimulation each time, then twenty practice reactions with objective stimulation, followed by twenty reactions without objective stimulus, recorded on the carboneu paper on the drum. Normal interval 0.75 seconds. Series /. Series 11. Series ///. 68 - 8.jV 73 - 2^ 83 + «* 87 + io.i» 73 - 2 75 + 77 + 81 + l\k 68 - 6J 7.-> - 1 78 + 2 71 - 3 74 - 2 76 + 77 + 2 72 - 4 73 - 2 76 + 1 82 + 5 77 + 1 72 - 2 70 - 6 70 - 5 78 + 3 76 - 73 - 2 70 - 4 76 - 74 - 1 72 - 2 72 - 4 73 - 83 + 8 82 + 5 74 - 1 6') - 5 75 - 1 73 - 2 73 - 1 82 + 5 76 + 79 + 4 80 + 3 81 + 5 75 + 73 - 3 75 - 76 + 79 + 2 73 - 2 76 + 1 73 - 3 76 + 68 - 6 74 - 2 76 + 1 80 + 3 18)1351 18)3!'g 80 + 5 t » J. i'M iif * 20)1.527 20)76ii Average = 75,^ M.V. =2,Va 20)1496 20)70| Average = 76a\ M.V. = 3-ft'j Average = 7tJ M.V. =3,%^ [136] 86 ■■' ;y Table in contains the records of the estimations of observer K. In the first column the stimulus intensity is stated; in the second, the number of separate judgments that the subject made on the intervals; the third contains the length of the normal interval in terms of a thousandth of a second, the fourth, the length of the average estimation of that normal, also in terms of a thousandth of a second. The fifth column contains the con- stant errors for each series, the sixth, the mean variations, and the seventh, the relation of the mean variation to the normal in percentages. In order to show exactly the average deviation from a perfect equality in percentage of the mean variations, and hence the deviation from the absolute validity of the law, the mean variation of those percentages is worked out and placed in the last column in each of the divisions of the tables. The summary of results contained in these tables represents practic- ally the whole of the estimations made, and not a few of the best, or those which best suited the theory of the experimenter. Table iii is divided into three divisions. The first division represents results of experiments made during the academic year of 1897-98. These experiments were made for the double pur- pose of testing Weber's law, and also to examine the influence of a change of intensity in the limiting impressions which marked the beginning and close of the intervals. In them an auditory stimulus was used. The second division records experiments similar to the first set, except that no change in the intensity of the limiting impressions was made, and these experiments were made in the following academic year, 1898-99. The third division contains the estimations of intervals of much greater length, and in these the limiting impressions were made by visual stimulation, instead of auditory as in the former series. The records in the table are arranged with the interval increasing constantly from the top to the bottom of the column, so that in reading down the column of the constant error the point of maximal accuracy may be easily noted where the constant error is smallest and just where the plus error of the short interval changes into the minus error of the long interval. That point seems to be what is called above the unit of time, and by this arrangement its relative length for the different subjects may be easily seen. Table iv is a similar record of the estimations made by W. They were made in the same years and under circumstances similar to those which obtained in the case of K. 37 [137] Table v differs from the above two only in that the first division was more comprehensive in the case of S., so that the second division which contained a number of series of experi- ments on approximately the same intervals as division one, in the above tables, was omitted in his case. Table vi is a set of trials made by B. on the short intervals only, viz., from gga- to 2^^ cn II 120 120 60 60 (iO 60 60 (iO 60 60 o %\ 101 101 125 125 150 150 187 187 < 113 114 117 114 128 185 152 150 180 1(K) W + 20 + 21 + 16 + 18 + 8 + 10 H- 2 + 2 + 3 > 4.5 5.1 3.6 4.8 4.5 '1.5 5.1 7.9 5.2 5.8 > (4-1 O 0.82% i ■Tl Division 3. V V ■i > .of th •softh Vs. B-n 3-w ^ S W > ".^^ ;2; !5 < o ^ ^S a ftO 97 122 + 25 5.10 5.28 120 111 126 + 15 5.60 5.05 90 132 13!) + 6 4.96 3.75 0.81% 90 156 158 + 2 6.49 4.19 90 189 185 + 4.62 6.48 3.41 90 225 257 + 5.05 5.58 2.48 -1 m 1.1381 88 Division j. The following trials were made during the academic year 1896-97, on inter- vals of increasing length : the "- t > .0 Wi 'A , 'A < S' s-s S 60 503 491 -12 15 3.11 1 1 60 750 752 + 2 31 4.15 0.99% • 6.67% 40 1500 i;«i - 1.69 48 3.46 CO 2i»50 2802 - 1.48 183 6.21 ) 40 4000 5363 + 7.63 803 17.46 20 9050 10785 + 17.55 1905 21.016 J Note.— In the estimations of the two longest intervals, viz., 46ooW . High. 1-3 60 60 40 40 40 40 60 60 g O 101 101 125 125 150 150 187 187 j: a w 125 121 129 127 167 159 180 180 + 24 -^20 + 4 + 2 + 17 + 9 - 7 - 7 7.8 6. 6.1 6.5 5.4 5.9 7.5 10.9 7.2 5.5 4.8 5.2 3.6 3.9 4. 5.8 St In( 0.92% 0.72% * See below, p. 47 (/ ttq. Low High. IvOW High. I/OW High. Low High. fvOW High. 39 [139] )n inler- Diviiion 2. As in the previous table the above intervals were also investigated again in the next year, with results as follows : ^6oocr and Ac above, jns of the time ; and ite. These il rhythmi- ist column iriations of the mean ii ii >'- . c -a 0.92% 0.72% 1 u i. is -A > 33 1 II W > z >5 < u a s 1.50 98 1,31 + 33 8.;w 8.59 1 90 108 136 + 28 8.67 , 8.03 1 tto 128 149 + 21 7.93 6.19 ) 1.51% w 0.67%* 90 157 149 - 8 5.79 ' 3.69 180 197 ! IHl -1(5 ; 9.71 4.93 90 250 248 1 12.75 i 1 5.1 J 'In Division 2 the first two intervals, i.e., 96(r and 108(r, are regard> d as abi^ormal (sea belo»). On this accouut we have itiven the mean variation of the peicentages of the last four lulervals, in which the recording was satisfactory, as well as that of the whole six. Division j. The following trials ere made during the academic year of 1896-97 on longer in tervals : 1 u"«< ■" *« •5 > ^^ U "s bi >■ a' .0 rt 'A :? < a s 60 500 .512 f 12 .34 4.48 ^ 40 750 730 - 20 49 3.89 40 1490 1414 - 76 47 2.98 • 0.727% 40 30,30 2895 -135 142 4.47 40 4500 4454 - 46 102 2.28 20 9150 9325 + 675 376 4.02 -' Table V. — Observer S. Division /. Stimulus Intensity. Low High Low High Low High Low High IvOW High o Il • S-c 180 180 180 180 8(1 80 120 120 120 120 o SB bc.s U TO W 107 107 125 12) 1.50 150 187 187 214 214 > 141 + .34 140 + .33 1.52 + 27 1.50 + 25 167 + 17 176 + 26 188 + 1 186 -1 213 -1 '>i,> •> 5.2 4.3 4.2 .5.1 6.8 6. 7.7 9.6 6.3 6.7 > a' 4.8 4. .3.4 4.1 4.5 4. 4.1 5.1 2 5 2.8 it u ~ .0 ^ 0.62% r i [140] 40 Mii !. , ■■ i: Division 2. v u MM « > ij en •3 y s 3 •« 2^ t4 > o O («) 500 4!t7 - 3 f 6.4 (>() 740 728 - 17 ; ■ 5.2 40 1505 1251 - 254 74.4 4.9 1.5% 40 2020 8271 + ;551 238.8 8.1 20 45(X) 4444 - 56 .351.4 7.7 20 8870 7884 -986 633.4 7.5 J Table VI.— Observer B. u u •g f > J3 J3 1^" "3 §>2 ^ §3 i 2*« 5ia W > O ^.^S ^ ^ ^ i •-J ■*><» x> > ■^ O ••>* ^ .s ^ ^ ^ a ^ I o s_ § 1 (A 46 I» h- r^ X t- t^ t~ X !>• X lOl/SQPpOiCiOiftO IC O iC O O O 'C o c •-" ?i N Q Q ^ 1(5 « !iCQpi5'5CO''±P i iC ift iC uj »C »0 Q O lO l« 1(5 O O P O lO l« p iC 1— lN« id ci cc 00 M 00 r-i > II •3 ^ (4 U5 'I w -4-( o l-H 5 8 S, II V 2 «• -5 s ^ I III 47 Table VII.— Observer K. Group 1 :— No. of intervals = 3. No. of judgnienU on each = l.'J, Average leiiKth 37» 192 182 Mean variation 11.08 8.28 4.08 %of M. V ;m 4.:! 2.2 Total duration of group 762(r. Total M. V. 24.2t> = 3.2%. [147] 8 II > IS « a 8 I I a Group 2 :— No. of intervals = .'5. No. of judgtiienta on eacb = 14. Average length 402 18(» 1H<( Mean variation It!. 5.'! 5,71 7.55 % of M. V 4.2 3 4 Total duration of group 772(7. Total M. V. 29.79 = 3.8% Group 3 :— ."'Jo. of intervals = 5. No. of judgments on each = 17. Average 'ength 284 288 130 137 352 Mean variation 13.04 12.50 10.59 14.58 18,.37 %ofM, V 4.6 4.3 8.1 lO.tt 5.2 Total duration of group 11924 688 175 214 932 Mean variation.. ;i().53 32.24 Ki.94 23.47 20.2 15.1 17.09 2.85 12.04 74.S9 %ofM. V 5.5 G.8 7.3 3.9 4.7 5.7 2.5 1.6 5.6 8 Total duration of group 4660o-. Total M. V. 256.37^5.4%. Group 8 : — No. of intervals = 15. No. of judgments on each = 8. Average length 517 340 165 785 528 331 175 6-12 195 Mean variation 21.87 22.5 8.75 46.87 10 16.15 4.37 69.37 12.a3 %ofM. V 4.2 6.6 5.3 5.9 1.9 4.9 2.5 10.8 6.2 Average length 360 180 507 514 520 919 Mean variation 6.25 6.25 13.12 14.53 17.5 27.5 °/oOfM. V 3.1 6.2 2.5 2.8 3.3 5.5 Total duration of group 6()8.3o-. Total M. V. 332.31=4.9%. ,.5 Table IX — Observer B. Group 1 : — No. of intervals=;!. No. of judgments on each = 21. Average length 373 198 1 78 Mean variation 17.19 7.17 8.02 %of M. V 4.6 3.6 4.4 Total duration of group 751a. Total M. V. .32.39 = 4.3%. Group 2 : — No. of intervals = 3. No. of judgments on each = 22. Average length 330 187 170 Mean variation 20.08 7.72 9.54 %of M. V 6.1 4.1 5.6 Total duration of group 693cr. Total M. V. 37.35 = 5.4%. Group 3 : — No. of intervals=5. No. of judgments on each = 16. Average length 527 471 252 254 500 Mean variation 20.5118.12 9.61 8.98 32.18 %ofM. V 3.8 3.8 3.8 3.5 6.7 Total duration of group 2005ir. Total M. V. 89.41 = 4.5%. Group 4 : — No. of intervals = 7. No. of judgments on each = 12. Average length 393 214 203 433 408 369 453 Mean variation 25.41 26.18 31.04 29.16 29.58 22.91 33.12 %ofM. V 6.4 12.2 15.2 6.7 7.2 C.l 7.3 Total duration of group 247()(r. Total M. V. 197.42 = 7.9%. Group 6 :— No. of intervals=8. No. of judgments on each-- 15. Average length 400 290 530 224 198 228 557 588 Mean variation 22.76 19.33 43.33 9,86 12 11.82 39.77 32.13 %ofM. V 5.6 6.6 8.1 4.5 6 6.2 7.1 5.4 Total duration of group 261 6(T. Total M. V. 192.62 = 7.3%. If H-'' 1' i-iu 1 [150] 50 Group 6 :— No. of intervals=15. No. of judgments on each = 7. Average length 403 312 178 708 391 313 177 554 188 Mean variation 16.53 14.69 9.18 47.96 18.98 20.61 13.06 26.32 13.87 %ofM. V 4.1 4.7 5.1 0.7 4.8 6.3 7.3 4.7 7.3 Average length.... 317 175 403 414 424 661 Mean variation ... . 18.16 8.5714.4923.4724.3947.22 7oM. V 5.7 4.9 3.6 5.6 5.8 7.1 Total duration of group 5825(r. Total M. V. 318.02=6.6%. To turn now to the results of the experiments. We have seen that in reproducing one uniform interval in a successive series, the average mean variation in the whole of K.'s judg- ments was about 4.1 per cent., and that there was not much deviation from this mean in intervals of different length (cf. Table iii.). In the present experiments, where instead of a series of reproductions of one interval of uniform length a series of groups of intervals of unequal length rhythmically arranged is reproduced, the average mean variation for all the groups and intervals is 4.2 per cent., which is only one-tenth per cent, greater than for the simple interval. Although there is some de- viation from this average in individual intervals, ftill in the averages for the whole groups the mean variation is very uniform. This is another illustration of a phenomenon noted by Pringle in experimental investigation of poetical metre, ^ where there was a distinct tendency to complete a defective line, so as to make a time unit for the respective lines in a stanza. The phenomenon in these experiments shows itself in the fact that although there is a deviation within a narrow limit among the individual intervals of the more complicated groups, there is very little deviation in the average mean variation of each complete group. The relation of the different lengths of intervals to one another throughout the judgments of the different groups is very constant, there being no distinct or regular falling off in the accuracy from the first reproduction of the group to the last. This is well illustrated in the detailed readings of the sheet on page 46, which is a fair average representative of the other sheets. There is if anything rather an increase in accuracy than a falling off; in the above sheet the last two reproductions of the group are a little more constant, and a little nearer the average, than the first two. We do not wish to infer from this that there is ^The records of his work are preserved in the archives of the Psychological Labor, atory, University of Toronto. I ! 61 [161] a constant increase in accuracy in the reproduction of the groups, but that within certain limits they are comparatively uniform. Referring again to the above sheet we find in the ten inter- vals four distinct types. The first is about 440cr in length, the second about 3200-, the third about I20t. and the fourth about 2400-. The last interval in the group, averaging 792o-, is pro- bably in part composed of the pause at the end of the line, and thus it does not represent a definite length of note used in the composition. In the above four typical lengths of intervals, there is not the definite relation of one, a half, a fourt nd an eight, as in written musical compositions. The shortest unorval, I200-, is about half of the next shortest, but it is not a third of the next, nor a fourth of the longest. The subject who made the judgments in the above sheet is neither a true musical artist, nor a mechanical musician who would be dominated by the measure written on the sheet of music before him, but one who thoroughly appreciates melody and rhythm. Our experiments do not justify any definite conclusion as to whether the relative lengths of intervals in musical rhythm, as represented in the interpretations of the true artist or of the aporeciative repro- ducer, are the same as are represented on the written sheet. Such a conclusion would need the support of a special set of investigations. But the indications from our own experiments are that the relative length of musical notes in the production of a true musician is not in the exact ratio of one to a half, a quarter, an eighth, and so on. A further point illustrated by the above sheet is the indifference of the length of the interval to the pitch of the tones composing the melody. The intervals recorded on this sheet are intended to represent twenty intervals from the " Boc- caccio March ;" the rhythm in the first ten is similar to that of the second ten, but the pitch of the tones is quite different. In the records the second group of ten is placed directly under the first, and in that order through all the judgments made ; there is no noticeable regular difference between the lengths of the intervals in the respective groups, notwithstanding the great difference of pitch. In the first two groups of the i .ole, containing three intervals each, a mechanical auditory stimulation was used to give the subject the rhythm, but thii; stimulation ceased before he began to record. In the physical stimulation one interval was equal in i;m^i [152] 52 NM' nil!.! I!: ):■ ' ■'I •: 1 1 (.■ ■;! i length to the sum of the other two, and it was repeated in a regular succession so that either short or long interval might come first. The judgments of K. in the first group come defi- nitely in the rhythm of the dactyl, i.e., the long interval comes first, retaining its relation as almost exactly equal to the sum of the other two, the second interval is lengthened at the expense of the third, being lOo- longer, and the third is the shortest. This is the normal relation of the intervals of the dactyl, the second interval being longer than the third, though the relative lengths be not quite those given above.* The second group does not fall quite so definitely into dactylic rhythm, since on the average the two shorter intervals are exactly equal, but in the individual judgments seven out of fourteen are in the dactylic rhythm and two have the two shorter intervals equal. So that with K. there is a marked tendency to throw groups of three intervals, one long and two short, into the rhythm of the dactylic poetic foot. The other Tables, viii. and ix., very generally confirm the tendencies noted in connection vvith Table vii., with the ex- ception of the last point, in reference to the dactylic form of the grouping of the thre^ intervals. In regard to the comparative accuracy of the successive reproduction of the single uniform interval and of the groups of unequal rhythmically arranged intervals, with K. there was an average difference of one-tenth per cent, in favour of the accuracy of the judgment of the single interval ; the average percentage of the mean variation for the latter was 4.1 per cent., and for the groups 4.2 per cent. For W. the average difference is three-tenths per cent., being in the one case 4.4 per cent,, and in the other 4.7 per cent. The differ- ence for observer B. is greater ; for the single interval his average was 4.8, and for the groups 5.8, But the work of B. was not so comprehensive as that of the other two subjects, either in the number of judgments made or in the scope of the intervals tested, so that his testimony is not so reliable as theirs. In the groups of three intervals, where one was equal in length to the sum of the other two, W.'s results differ from those of K. Instead of the dactylic rhythm, W. definitely relates them in the rhythm of the anapaestic foot. In the first group his •Cf. Hurtt and McKay, Experiments on tht Time Relations of Poetical Metres, infra. II S i 58 [1531 judgments are i8i