# The New International Encyclopædia/Weber's Law

Edition of 1905. See also Weber-Fechner law on Wikipedia; and the disclaimer.
WEBER'S LAW. In psychology, the formula expressing the relation of sensation to intensity of stimulus. In 1834 E. H. 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,
| V—U |
| | = | C, |
| U |
where V is the comparison stimulus, U the standard stimulus, and C a constant. The principle may be briefly termed that of the constancy of the relative difference limen (see Limen); 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; (b) the difference which is relatively the same for stimulus is absolutely the same for sensation; or (c) the intensity of the stimulus increases in geometrical ratio as the intensity of the apperceived sensation increases in arithmetical ratio. The validity of this theorem was confirmed by Gustav Fechner by the use of other psychophysical methods (Weber had used that of minimal changes; see Psychophysics): he extended its range to other sense departments and gave it the name Weber's law. Since Fechner's time the investigation 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 psychophysics. Wundt gives a
résumé of its applicability as follows: The law has its most satisfactory application and its widest range in noise intensities; it has a less extended application in the modalities of vision, pressure, movement, taste, and smell; its validity in temperature and organic sensation is yet uncertain. In all modalities there are variations from the law at small and at great intensities. For quantitative results, see Intensity 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 Weber'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 possible to assign the position of the discrepancy to one of three places — between stimulus and excitation, between excitation and sensation, or between sensation and apperception; these interpretations furnish respectively the physiological, psychophysical, and psychological interpretations of Weber's law.
(1) The psychophysical view was historically first. Fechner held that the logarithmic relation which characterizes the law prevails not between physical processes themselves, but between 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 suppose 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 ‘internal’ psychophysics, and state the relation as s = C log. E (excitation).
(2) The physiological formulation is that of G. E. Müller, who considers the sensation to be directly proportional to its cortical excitation, while the ‘inertia’ is traceable to the behavior 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 controvert the physiological interpretation. For Wundt, Weber's law is only a special case of the more general psychological principle of ‘relativity.’ Intensities are always judged relatively; we estimate the intensity of a sensation always with reference to .some other intensity. This comparison of intensities is a matter of apperception.
(b) Ziehen replaces ‘apperception’ by ‘association.’ A certain number of increments of intensity are added together till finally the verbal judgment, ‘greater,’ results by a process of association. If the original stimulus be large, it takes a relatively greater increment to call forth the judgment.
(c) Meinong contends that too much emphasis has been put upon ‘just noticeable differences;’
such differences may not be equally great or equally noticeable. We must distinguish between difference and ‘differentness’ or diversity. In an arithmetical series one obtains an expression of the former category, in a geometrical series an expression of the latter. The mind takes note of diversity, not of difference; e.g. it notes not that an intensity difference of 2 less 1 equals one of 101 less 100, but rather that the relation of 2 to 1 is like that of 200 to 100.
Bibliography. Delbœuf, Examen critique de la loi psychophysique, sa base et sa signification (Paris, 1883); Elements de psychophysique générale et spéciale (Paris, 1883); Fechner, Elemente der Psychophysik (1860; new ed., Leipzig, 1889); In Sachen der Psychophysik (Leipzig, 1877); Revision der Hauptpunkte der Psychophysik (Leipzig, 1882); G. E. Müller, Grundlegung der Psychophysik (Berlin, 1878); Fullerton and Cattell, On the Perception of Small Differences (Philadelphia, 1892); Külpe, Outlines of Psychology (London and New York, 1895); Meinong, Zeitschrift für Psychologie (1896, xi., 81, 230, 353); E. H. Weber, Der Tastsinn und das Gemeingefühl, in Wagner's Handwörterbuch der Physiologie, iii. (1851); Annotationes Anatomicæ (Leipzig, 1846); Wundt, Grundzüge der physiologischen Psychologie (Leipzig, 1893, i., 332); Philosophische Studien, ii. (1885, 1); Th. Ziehen, Introduction to Physiological Psychology (Eng. trans., London, 1892, 49-60); Leitfaden der physiologischen Psychologie (4th ed., Jena, 1898).