carried on in the Leipsic laboratory. The limits of a single article confine my notice to the briefest summary; I can, however, refer the reader who is interested in any special line of research to the detailed accounts in the Philosophische Studien. It may also be worth while to call attention to Ladd's Physiological Psychology, noticed in the last number of MIND, and to the fact that Wundt is about to publish a new and rewritten edition of his Physiologische Psychologie. We can classify the work done at Leipsic under four heads: (1) The Analysis and Measurement of Sensation; (2) The Duration of Mental Processes; (3) The Time-sense; (4) Attention, Memory and the Association of Ideas. Such a classification is, of course, merely a matter of convenience. Experiments made in different directions throw light one upon another and at their boundaries overlap, so that many of the researches put under one heading reach beyond its limits and into others. All science is, indeed, an organism no member of which can be thought of apart from the rest. As Aristotle has said, a hand cut off from the rest of the body is not even a hand.

1. The Analysis and Measurement of Sensation.

In physics force is usually measured by its effects, and in psychology we may some day be able to measure sensation by determining the movement accompanying a given sensation. But the cause is no less constant than the effect, and we may with scientific accuracy specify and measure a sensation by the physical stimulus causing the corresponding cerebral commotion. The relation subsisting between the sensation and the physical stimulus has, therefore, been the subject of much experiment and discussion. An especially large share of attention has been given to studying the way in which the intensity of the sensation varies with the intensity of the corresponding stimulus. It is impossible to give much account of this here; the reader must be referred to the books by Fechner, Müller, Delboeuf and others, and to the many papers which have been published in the Philosophische Studien and elsewhere.

1 Papers in the Philosophische Studien giving a description of research will be noticed below (being cited by vol. and pp. only). The following are those concerned only with theoretical discussion:

W. Wundt," Ueber die Methode der Minimaländerung," i. 556-572. W. Wundt," Ueber das Weber'sche Gesetz,” ii. 1-36.

G. Th. Fechner, "In Sachen des Zeitsinnes und der Methode der richtigen und falschen Fälle, gegen Estel und Lorenz," iii. 1-37.

Alfred Köhler, "Ueber die hauptsächlichsten Versuche einer mathe

Weber first called attention to the fact that, when weights are laid on the supported hand, each must be increased by about of its original weight before any change is noticed. Since then many experiments have been made on the several senses, and it has been found approximately to hold that the least noticeable change in the intensity of a sensation is occasioned by a change in the stimulus directly proportional to the amount of the stimulus. Thus if there are 100 candles in a room we can just notice the change in the illumination caused by taking away or adding one candle; if there are 1000 candles, 10 must be taken away or added before a change is noticed. This relation holds most nearly for moderate intensities of the stimulus, and for the more mechanical senses, as sound. Weber's generalisation admits of several interpretations. It has been looked upon as a purely physiological fact, it being argued that the sensation must increase more slowly than the stimulus, owing to the inertia of the sense-organ and more especially to irradiation in the brain. The view supported by Fechner is that we have to do with a psychophysical fact, which expresses an ultimate relation between physiological and mental change. Wundt points out that it may be given a psychological interpretation, and referred to the apperception of the sensation, thus being brought under "the law of relativity". Weber's generalisation is of considerable interest both to physiologists and psychologists; inferences have, however, been drawn from it which I do not consider justifiable. The generalisation may be expressed in the equation

4S

a = c S

in which c is a constant, S the stimulus, 48 the change in the stimulus which can just be noticed, and a the least noticeable change in sensation. This equation, however, need only be true if a different value be given to a for every value of S, and only holds approximately and for certain values of S. It evidently is not true when S is very small, for then there is no sensation whatever. Fechner in order to get his equation

E = e log S

in which E is the sensation and S the stimulus, the sensation

matischen Formulirung des psychophysischen Gesetzes von Weber," iii. 572-642.

G. Th. Fechner, "Ueber die psychischen Massprincipien und das Weber'sche Gesetz," iv. 161-230.

1 See J. Ward, MIND i. 452.

being thus measured in terms of the stimulus, must assume the least noticeable change in sensation to be an equal increase or decrease in the intensity of sensation, and must, further, introduce in a questionable way the "fact of the threshold".

We have, however, more especially to do with the experiments made in the Leipsic laboratory. Sound and light have been used to investigate the relation between stimulus and sensation. The loudness of sound has not been satisfactorily measured objectively; so it was found necessary at Leipsic to set up some standard of sound before its intensity could be brought into relation to the sensation. Tischer1 was the first to attempt to make such determinations; he found that the noise made by a falling ball was not proportional to the weight of the ball multiplied by the height from which it falls, but increases more slowly. Later experiments made by Starke 2 and by Merkel3 seem, however, to show that

in which i is the intensity of the sound, w and h respectively the weight of the ball and the height from which it falls, and c a constant depending on the material of the ball and sounding-board. The results of Starke's experiments, especially, correspond more exactly with the law than could have been foreseen, as there were several sources of variation; c, for example, was not always the same. The balls were at first lead and polyhedrons, and afterwards steel and ellipsoids, and the different points in the sounding-board had different elasticities, &c. 4 The experiments by Tischer, Lorenz,5 Starke, and Merkel, all show the validity of Weber's generalisation, and give more exact results for sound than have been obtained in connexion with the other senses. Whatever the loudness of a sound may be, it must be increased by about before a difference is noticed. It should, however, be stated that the value of Lorenz's research has, not without cause, been questioned by Fechner, and that experiments made by Merkel in another direction do not seem to

6

1 E. Tischer, "Bemerkungen über die Messung von Schallstärken mit Rücksicht auf psychophychische Versuche," i. 543-555.

2 P. Starke, "Die Messung von Schallstärken,” iii. 254-304.

3 J. Merkel, "Das psychophysische Grundgesetz in Bezug auf Schallstärken," iv. 117-160, 251-291.

4 Op. cit.

G. Lorenz, "Die Methode der richtigen und falschen Fälle in ihrer Anwendung auf Schallempfindungen," ii. 394-474, 655-657.

6 Op. cit.

7 Op. cit.

8

Op. cit.

9 See Cattell, MIND xi. 229.

be trustworthy. Researches on the loudness of sound are still being carried on at Leipsic; so we may hope for further light on the subject.

Ever since Helmholtz published, in 1862, his classical researches on sound, much attention has been given to the preception of musical notes, investigations having been undertaken by Mach, Preyer, Hensen, Stumpf and others. Careful experiments, not yet published, have also been carried on for several years past in the Leipsic laboratory. Luft with tuning-forks and Lorenz with an apparatus on the principle of the harmonium have been investigating the least noticeable difference in pitch in the same manner as the loudness of sound has been studied. We have seen that the ear does not readily distinguish differences in loudness; in pitch, on the contrary, small changes can be noticed with marvellous accuracy, and this whether the observer be musical

In the range most easily covered by the human voice (from about c' to c"", 256 to 1024 vibrations per second) successive notes can be distinguished when the difference between the physical stimuli isto of a vibration per sec. Where the pianoforte machine gives 24 notes the ear can distinguish over 3000. Outside the limits of the human voice the least noticeable difference in the stimulus becomes a smaller fraction of a vibration as the note is taken lower, but not in direct proportion to the rate of vibration; so Weber's law in no case holds for pitch. Experiments are being now carried on at Leipsic to determine the accuracy with which the ear can distinguish musical intervals, the notes being given in succession.

Light-sensations have been investigated at Leipsic by Kraepelin, who found that with moderate intensities a difference in the illumination of could be noticed, and that the difference must be increased too when the light was taken very faint. It is natural that the fraction should become larger as we approach the threshold of sensation, owing to the chemical process supposed to take place in the retina, and to the eye's "own light". own light". Lehmann 2 and Neiglick applied to light the so-called "method of mean graduation," a method of considerable interest to the psychologist. The observer tries to give the shade of gray

3

1 E. Kraepelin, "Zur Frage der Gültigkeit des Weber'schen Gesetzes bei Lichtempfindungen," ii. 306-326, 651-654.

A. Lehmann, "Ueber die Anwendung der Methode der mittlern Abstufungen auf den Lichtsinn," iii. 497-533.

H. Neiglick, "Zur Psychophysik des Lichtsinns," iv. 28-111; cp. W. Wundt, Bemerkungen zu vorstehendem Aufsatze," ib. 112-116.

་་

which seems to him equidistant from a lighter and a darker shade, or from white and black. If it were possible to find a sensation y as much weaker than x as it is stronger than z we could take a unit of measure and speak of one sensation as three times as strong as another, &c. The application might, further, be extended beyond the intensity of sensation, so that, for example, the hedonistic calculus could really be put in practice, and it would not be absurd to calculate, as Plato does, that a just king lives 729 times as happily as a tyrant. The fact, however, is that we are not dealing directly with sensation but with our estimates, and even these seem to me, to a certain extent, conventional. I can say that a very dark gray seems to me more like black than like white, but when I come to pick out a shade which seems equidistant from the two, I am in doubt within rather large limits, and only come to any decision by thinking of the number of differences of shade I could distinguish in each direction. If this view be correct the method is reduced to a less accurate version of that of the "least observable difference". Neiglick found that his estimate remained constant, and that other observers, varying considerably at first, finally agreed with him. He naively concludes that some persons naturally judge differences in light with accuracy, others only after practice. The fact probably is, that Neiglick, knowing the objective measure of the light, was unconsciously aided by association, and, perhaps, to an extent which invalidates his results. The other observers, comparing their results with his after the series had been completed, naturally tended next time to approximate to his judgment. It is difficult to decide that one shade of gray is equidistant from two others, but after the decision has once been made it seems quite evident, and the point is easily held in mind. Lehmann's results were disturbed by contrast, and he was led to study its influence. He found that, whatever the illuminations of two contrasted surfaces might be, the contrast was the greatest when there was a constant ratio (1: 4.76) between them. Neiglick found Weber's law to hold the more accurately the more nearly the contrast between the compared surfaces was a maximum. Schmerler1 had previously made careful experiments, determining quantitatively the saturation of a colour the most favourable to contrast. The fact which however, was already known, that contrast is not the greatest when there

1 B. Schmerler, "Untersuchungen über den Farbencontrast vermittelst rotirender Scheiben," i. 379-416.