WEBER'S LAW. In psychology, the formula expressing the relation of sensation to intensity of stimulus. In 1834 E. B. Weber proposed the theorem that the ratio of the increment of stimulus necessary to give a noticeably different sensation to the original stimulus is constant, or, as he expressed it, C, where V is the comparison stimulus, U the standard stimu lus, and C a constant. The principle may be briefly termed that of the constancy of the rela tive difference linen (see LimEx) ; it can be more explicitly stated in other forms, e.g. (a ) if sensations increase in intensity by equal amounts, their stimuli increase by relatively equal amounts; (11) the difference which is relatively the same for stimulus is absolutely the same for sensation ; or (e) the intensity of the stimulus increases in geometrical ratio as the intensity of the apperceived sensation in creases in arithmetical ratio. The validity of this theorem was confirmed by Gustav recliner by the use of other psyehophysical methods (Weber had used that of minimal changes; see : he extended its range to other sense departments and gave it the name Weber's law. Since Feehner's time the inves tigation of the applicability of the law has been carried on by many experimenters, and its significance is attested by its prominence in the literature of psychophysies. Wundt gives a r6sumt of its applicability as follows: The law has its most satisfactory application and its widest range in noke intensities; it has a less extended application in the modalities of vision, pressure, movement, taste, and smell; its valid ity in temperature and organic sensation is yet uncertain. In all modalities there are varia tions from the law at small and at great intensities. For quantitative results, see IN TENSITY OF SENSATION.
When a stimulus acts upon the organism and its intensity is consciously noted, four factors may be distinguished, viz. stimulus, excitation, sensation, and apprehension, or apperception of the sensation. Now the facts of \Veber's law show that somewhere in this series of steps there is an 'inertia' or lag. Accordingly, in the
formulation of a theory of intensity, it is possi ble to assign the position of the discrepancy to one of three places—between stimulus and ex citation, between excitation and sensation, or between sensation and apperception; these in terpretations furnish respectively the physio logical, psychophysical, and psychological inter pretations of Weber's law.
( I ) The psychophysical view was historically first. Fechner held that the logarithmic rela tion which characterizes the law prevails not betNren physical processes themselves, but be tween physical and psychical processes. We have no access to the final term of the physical series, the cortex, and hence we are compelled to state the logarithmic relation in terms of stimulus and sensation, i.e. s (sensation) = C log. r (stimulus) ; but we have reason to sup pose that, except at the upper and lower limits of intensity, the cortical excitation is directly proportional to the intensity of the stimulus, and hence we can pass from 'external' to 'inter nal' psyehophysics, and state the relation as s = C log. E (excitation).
(2) The physiological formulation is that of G. E. who considers the sensation to he directly proportional to its cortical excita tion, while the 'inertia' is traceable to the be havior of nerves under excitation, to loss of energy in transmission, etc. The formula is thus s = E = C log. r.
(3) The psychological interpretation has taken three forms: the theories of Wundt, Ziehen, and Meinong.
(a) Wundt says that there are instances (method of mean gradations) in which sensation is directly proportional to its stimulus, and a single instance of this sort is enough to con trovert the physiological interpretation. For Wundt, Weber's law is only a special case of the more general psychological principle of `relativ ity.' Intensitie. are always judged relatively; we estimate the intensity of a sensation always with reference to sonic other intensity. This comparison of intensities is a matter of apper ception.