Page:The New International Encyclopædia 1st ed. v. 20.djvu/467

WEBER. 391 WEBER'S LAW. in 18(10. He was mado profcs.sor of philosophy at Bn'slau in 1872. He was active in the Old C'atiiolic movement from its befjinninf;, and in 1890 7-emovod to Hoiin and was appointed vicar- fteneral I>y liisliop Keinkens. Five years later he was consecrated assistant bishop, and on Kcinkens's death in 180G he succoedod him as bishop. He has written much in relation to the Old Catholie movement and in philosophy and metapliysics. WEBER, WiLiiELM (1S04-01). A German phj'sicist. Ho was born at Wittenbcrp;, and was educated at Halle. In 1825, in association with his brother. Ernst Heinrich Weber, he published Die Wellenlehfc. He became assistant professor of physics at Halle in 1827, and professor at Gottin- gen in 1831. He was one of the seven professors of G(ittinj>en who were removed in 1837 for having I>rotested against the violation of the Constitu- tion. He held the chair of physics at Leipzig, 1843-49. when he was restored to his former posi- tion at Gottingen. While living in that city he became acquainted with Gauss, and in 1833 they jointly devised an electro-magnetic telegraph. They also founded the Magnetic Union and made many observations on terrestrial magnetism. An important achievement of Weber's is the intro- duction of the absolute system of electrical units modeled on the work of Gauss, who first de- vised such a system of units in his experiments in magnetism. Weber determined the value of the practical units in absolute measure and at the International Electrical Congress held at Paris in 1881 his system with certain modifica- tions was adopted and the volt, ampere, coulomb, and farad were defined. Weber's works were published by the Gottingen Academy of Science in 1802. A biographical sketch entitled Willielm Webrr. by Heinrich Weber, was published at Ber- lin in 1S03. 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 ditTerent sensation to the original stimulus is constant, V — IT 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 limen (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; (b) the diff'erence 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 in- creases 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 PsYCHOPiiYSlcs) : he extended its range to other sense departments and gave it the name Weber's law. Since Fechner's time the inves- tigation of the applicability of the law has been parried on by many experimenters, and its significance is attested by its prominence in the literature of psychophysics. Wundt gives a rC'Sumf- 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 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- TEXsiTY 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 fornnilation of a theory of intensity, it is possi- ble to assign the position of the discrepancy to one of three places — between stinnilus and ex- citation, between excitation and sensation, or between sensation and apperception ; these in- terpretations furnish respectively the physio- logical, psychophysical, and psychological inter- I)retations of Weber's law. (1) The psychophysical view was historically first. Fechner held that the logarithmic rela- tion which characterizes the law prevails not between physical processes themselves, but be- tween physical and psychical processes. We have no access to the final term of the physical scries, 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' psychophysics, and state the relation as s = C log. E (excitation). (2) The physiological formulation is that of G. E. Miiller, who considers the sensation to be directly proportional to its cortical excita- tion, while the 'inertia' is traceable to the be- havior of nerves under excitation, to loss of energv- 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 Uleinong. (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 i-s only a special case of the more general psychological principle of 'relativ- ity.' 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 apper- ception. (h) Ziehen replaces 'apperception' by 'asso- ciation.' A certain number of increments of intensity are added together till finally the verbal judgment, 'greater.' results l)y a process of association. If the original stimulus be large,' it takes a relatively greater increment to call forth the judgment. (cl.Meinong contends that too much emphasis has been put upon 'just noticeable differences;'