very nearly equal the subject will often fail to recognize which is the greater, saying sometimes that A is greater, sometimes that B is greater. When in a large number of trials the right and wrong guesses exactly balance one another we may conclude that the difference between the two stimuli is not appreciable by the sense. On the other hand, as soon as the number of correct guesses definitely exceeds half of the total number of cases, it may be inferred that there is a certain subjective appreciation of difference. This method was first employed by Vierordt. The third method, that of average errors, is very similar to the one just explained. Here a certain weight (to take a concrete example) is laid upon the hand of the person experimented upon, and he is asked, by the aid of subjective impression alone, to fix upon a second weight exactly equal to the first. It is found that the second weight sometimes slightly exceeds the first, sometimes slightly falls below it. Whether above or below is of no consequence to the method, which depends solely on the amount of the error. After a number of experiments, the different errors are added together, and the result being divided by the number of experiments gives us the average error which the subject may be calculated upon to make. This marks the amount of stimulus which is just below the difference-threshold for him. This method was first employed by Fechner and Volkmann. The different methods were first named, and the theory of their application developed by Fechner in his Elemente der Psychophysik (1860).
A number of experimental variations have since been devised by Wundt and others, but they are all reducible to the two types of the “gradation” and “error” methods. These methods have been chiefly applied to determine the relation of the difference-threshold to the absolute magnitude of the stimuli employed. For a very little reflection tells us that the smallest perceivable difference is not an amount whose absolute intensity is constant even within the same sense. It varies with the intensity of the stimuli employed. We are unable, for example, to recognize slight differences in weight when the weights compared are heavy, though we should be perfectly able to make the distinction if the weights compared were both light. Ordinary observation would lead us, therefore, to the conclusion that the greater the intensity of the original stimulus at work the greater must be the increase of stimulus in order that there may be a perceptible difference in the resulting sensation. Weber was the first (after a prolonged series of experiments) to clothe this generality with scientific precision by formulating the law which has since gone by his name. He showed that the smallest perceptible difference is not absolutely the same, but remains relatively the same, that is, it remains the same fraction of the preceding stimulus. For example, if we can distinguish 16 oz. and 17 oz., we shall be able to distinguish 32 oz. and 34 oz., but not 32 oz. and 33 oz., the addition being in each case 116 of the preceding stimulus. This fraction (supposing it to be the difference-threshold of the muscular sense) remains a constant, however light or however heavy the weights compared. The law may be formulated thus:—The difference between any two stimuli is experienced as of equal magnitude, in case the mathematical relation of these stimuli remains unaltered. Or, otherwise expressed, in order that the intensity of a sensation may increase in arithmetical progression the stimulus must increase in geometrical progression. It is also expressed by Fechner in the form—The sensation increases as the logarithm of the stimulus.
The law has been variously interpreted. Fechner himself designated it the psycho-physical law, and treated it as the fundamental formula of the relation between body and mind, thus assigning to it an ontological dignity and significance. But in this “psycho-physical” interpretation of his results he has not had a numerous following. Wundt interprets the law in a purely “psychological” sense, making it a special instance of the general law of relativity which governs our mental states. Introspection can give us no information as to the absolute intensity of the stimulus; for a stimulus is known in consciousness only through its sensational resultant. Hence, he argues, we can only compare one psychical state with another, and our standard of measurement is therefore necessarily a relative one; it depends directly upon the preceding state with which we compare the present. Others (e.g. G. E. Müller) have attempted to give the law a purely physical or “physiological” explanation. Instead of holding with Fechner that the law expresses a recondite relation between the material and the spiritual world, they prefer to regard the quantitative relation between the last physical antecedent in the brain and the resultant mental change as prima facie one of simple proportion, and to treat Weber's law as holding between the initial physical stimulus and the final action of the nerve-centres. According to this interpretation, the law would be altogether due to the nature of nervous action. As a nerve, says Sully, after a temporary degree of stimulation temporarily loses its sensibility, so the greater the previous stimulation of a nerve the greater is the additional stimulus required to produce an appreciable amount of sensation.
Weber's law, it must be added, holds only within certain limits. In the “chemical” senses of taste and smell experiments are almost impossible. It is not practicable to limit the amount of the stimulus with the necessary exactitude, and the results are further vitiated by the long continuance of the physiological effects. The same considerations apply with still more force to the organic sensations, and the results in the case of temperature sensations are completely uncertain. The law is approximately true in the case of sight, hearing pressure, and the muscular sense — most exactly in the case of sound. As this is the sense which affords the greatest facilities for measuring the precise amount of the stimulus, it may perhaps be inferred that, if we could attain the same exactitude in the other senses, with the elimination of the numerous disturbing extraneous influences at work, the law would vindicate itself with the same exactitude and certainty. It is further to be noted, however, that even in those senses in which it has been approximately verified, the law holds with stringency only within certain limits. The results are most exact in the middle regions of the sensory scale; when we approach the upper or lower limit of sensibility they become quite uncertain.
Literature. — Weber's investigations were published as “Der Tastsinn und das Gemeingefühl,” in Wagner's Handlewörterbuch der Physiologie, iii. (1846). Fechner's Elemente der Psychophysik (1860) contains an elaborate exposition of the whole subject. He replied to his critics in two later works, In Sachen der Psychophysik (1877) and Revision der Hauptpunkte der Psychophysik (1882). Delbœuf's Étude psychophysique (1873), Examen critique de la loi psychophysique (1883), and Elements de psychophysique générale et speciale (1883), and G. E. Müller's Zur Grundlegung der Psychophysik (1878) are also important documents; and the subject is fully treated in Wundt's Grundzüge der physiologischen Psychologie (ed. 1902–1903), and “Über die Methode d. Minimaländerungen,” in Philos. Stud. (Leipzig, 1883), or, more popularly, in his Human and Animal Psychology (2nd ed., 1892), Lectures 2, 3, 4. See also Ladd's Physiological Psychology (1887), which is based upon Wundt; Meinong. in Zeitschr. für Psychologie, xi. (1896); Ziehen, Leitfaden der physiologischen Psychologie (7th ed., Jena, 1906); E. B. Titchener, Experimental Psychology (ii., 1905); Professor James Ward's “Attempt to Interpret Fechner's Law,” in Mind, i. 452 sqq.; and generally textbooks of psychology, e.g. G. F. Stout's Manual of Psychology, bk. ii. ch. 7 (following Meinong); James's Principles of Psychology, ch. 13; Külpe’s Outlines of Psychology, part i. chap. 1 and 3. (A. S. P.-P.)
WEBSTER, ALEXANDER (1707–1784), Scottish writer and
minister, son of James Webster, a covenanting minister, was
born in Edinburgh in 1707. Having become a minister in the
church of Scotland, he propounded a scheme in 1742 for providing
pensions for the widows of ministers. The tables which he
drew up from information obtained from all the presbyteries
of Scotland were based on a system of actuarial calculation that
supplied a precedent followed by insurance companies in modern
times for reckoning averages of longevity. In 1755 the government
commissioned Webster to obtain data for the first census
of Scotland, which he carried out in the same year. In 1753
he was elected moderator of the General Assembly; in 1771
he was appointed a dean of the Chapel Royal and chaplain to George III. in Scotland; and he died on the 25th of January 1784.
Webster published in 1748 his Calculations, setting forth the principles on which his scheme for widows' pensions was based; he also wrote a defence of the Methodist movement in 1742, and Zeal for the Civil and Religious Interests of Mankind Commended (1754).
WEBSTER, BENJAMIN NOTTINGHAM (1797–1882), English
actor, manager and dramatic writer, was born in Bath on the 3rd of September 1797, the son of a dancing master. First appearing as Harlequin, and then in small parts at Drury Lane, he went to the Haymarket in 1829, and was given leading comedy character business. He was the lessee of the Haymarket from 1837; he built the new Adelphi theatre (1859); later the Olympic, Princess's and St James's came under his control; and he was the patron of all the contemporary playwrights and many of the best actors, who owed their opportunity of success to him. As a character actor he was unequalled in his day, especially in such parts as Triplet in Masks and Faces, Joey Ladle in No Thoroughfare, and John Peerybingle in his own dramatization of The Cricket on the Hearth. He wrote, translated or adapted nearly a hundred plays. Webster took his formal farewell of the stage in 1874, and he died on the 3rd of July 1882. His daughter, Harriette Georgiana (d. 1897), was the first wife of Edward Levy-Lawson, 1st baron Burnham; and his son, W. S. Webster, had three children—Benjamin Webster (b. 1864; married to Miss May Whitby), Annie (Mrs A. E. George) and Lizzie (Mrs Sydney Brough)—all well known on the London stage, and further connected with it in each case by marriage.
WEBSTER, DANIEL (1782–1832), American
statesman, was born in Salisbury (now Franklin), New Hampshire, on the
