WEBERS LAW. In the 30's of the last century E. H. Weber (q.v.) made the dis covery that a subject who could barely distin guish between lifted weights of 29 and of 30 ounces could also batch: distinguish between weights of 29 and 30 drachms. Similar results were obtained in the case of cutaneous pressure and in the visual measurement of short lines. That is, it appeared in each case that the just noticeable increment of a stimulus was not a constant, but bore instead a constant ratio to the strength of the stimulus itself. This gen eralization, which is Weber's law, is a precise statement of the fact which is familiar to us in such cases as that of the tiddng of a watch, quite inaudible on the noisy street though it may be very loud In the silence of the bedroom. The ratio of the barely observable increment or dif ference limen to the stimulus is dependent on the kind of stimulus used. For pressures on the tip of the finger it is nearly 0.05, for noise loud aesses it is about 0.33, for lifted weights, 0.033, and for brightness, 0.01. Weber's law is only an approximation at best It is badly in error for very great or very small stimuli; even for those of moderate intensity it presupposes a complete adaptation of the percipient organ. It is not in general valid for other attributes of sense than intensity, although it seems to hold good for visual extension. In the pitch of tones, for instance, the just noticeable increment is about .75 vibrations per second for a consider able range of the scale. In so far as we are able to equate easily noticeable intervals in dif ferent parts of an intensity scale, it appears that these obey the same law as just noticeable intervals; that equal-appearing intervals between stimuli are proportional to the intensity of the stimuli evoking the lower terms of the intervals, and are made up of an equal number of just noticeable intervals. This assemblage of facts was raised by G T. Fechner (q.v.) to the dig nity of a necessary law expressing the relation ship of mind and matter lie represented the fact that a constant increment of a sensation is produced by a fixed proportional change in the stimulus by the formula , where 4 is the stimulus inducing the sensation We obtain from this at once log I) log it —lot =f, Ong i, 4).
As is depends only on 4, and is depends only on ss in the same, we get .4 =c 0, (log 4 — c), and 4 =a4 (logThere — c , where cis the value of log i for ore/ (log — ) — nog is— 0 (log i, — log 4), so that 1 satisfies the functional equation 0 (x) —0 (0-1 (r— Differentiating with respect to x, (x) .s r (x — y), which is only possible for all values of x and 7 if ei (x) is some constant such as or if 1 (x) is of the form Ks • + Ks. It is easily seen that =c O. We thus get s, — s= IC, (log —log By the proper choice of units this becomes c= S log a. Fechner's law is, then, that the sensa tion varies as the logarithm of the stimulus.
There are several serious objections to Fechner's treatment of the law. In the first
place, it is more than probable that the basis of the phenomena observed lies rather in the make-up of the nervous system than in the transition from the physical phenomena of the nervous system to the percipient mind. Even Wundt's explanation of the facts by appercep tion is vitiated by the appearance of the same logarithmic formula in the reactions of the nervous system of a decerebrized frog. Sec ondly, what is being determined in the mind of the subject of an experiment on discrimination is not the difference between two mental states, but the awareness of that difference, which is altogether another thing. The existence of limina is in itself enough to refute Fechner's opinion that it is actually the difference between two mental states which is reported, for things identical with the same thin are identical with one another, whereas a we't t of 61 drachms is sensibly equal to the discnminabk weights of 60 and 62 drachms. In the third place, whik measurement of sensations is a conceivable thing, it is most assuredly not done directly, so that the whole interpretation of Fechuer's law remains indeterminate until a thorough logical analysis is made of the processes involved in our actual measurement of the intensity of sen sation.
The general types of method used in experi ments and investigations on Weber's law are that of just noticeable differences, where two stimuli are gradually separated or approximated until their difference appears or disappears; that of average error, in which the average error of the observer in selecting a variable stimulus equal to a given fixed stimulus is taken as the index of the just noticeable difference or limen; that of equivalents, which differs from that of average error only in that the stimuli are applied sim ultaneously to ditTerent parts of the body rather than successively to the same part ; that of mean gradations, in which a supraliminal interval is bi•ected; and that of right and wrong cases. in %Ouch the mean position of the initial stimulus limen or the difference linen is determined by ascertaining throughout a series of trials for each intensity of stimulus or magnitude of stimulus difference the proportion of cases in which its presence or absence is rightly (See Lim INA ; PSYCHOPH YSICII). J. R. L., 'Examen critique de la loi pity chophysique (Paris 1883); Fechner, G. T., 'Elemente der Psychophysatl (Leipzig 1889); Fullertan and Cattell, 'On the Perception of Small Differences' (Philadelphia 1892); Kidpe, O.. Outlines of Psychology' (tr. New York /909): Meinong, A. OnZeitschnft Psychol ogee, Vol. XI, I896); Muller, 'Grundlegung der Psychophysile (Berlin 1878); S.
'Text-Book of Experimental P (2d ed., Cambridge. 1911) ; Titchener. xperi mental Psychology' (New York 1905): Winidt. W.. 'Grundnige derphysiologischen Psycho/o gle' 1908-11) ; Ziehen, T., 'Leitfaden der ph ologischen Psychologie (10th ed.. Jena 19114).