§ 1. The Experimental Facts.—We can compare any two objects and pronounce them like or unlike. If the objects are disparate in kind, we are unable to say more than that they are unlike. This is the only result of comparing the brightness of the sun with the immortality of the soul. If we compare the brightness of a light with the loudness of a sound, we can say that both possess intensity; but we cannot fix any definite relation between them. For instance, we cannot affirm that the loudness of the sound is equal to the brightness of the light. On the other hand, if we compare the quantitative variations of the same kind of object in the same respect, we can pronounce more definite judgments. We can pronounce that one sound is less or more loud or equal in loudness to another. Besides this, we can compare degrees of unlikeness with definite results. We can say that one sound, C, is as much louder than B as B is louder than A. In this way we can select two sounds of different loudness, and then proceed to find a third exactly intermediate between them. We may then compare the intermediate sound, B, with each of the extremes, A and C, so as to interpose between A and B a D} unlike in loudness to A in the same degree in which, it is unlike in loudness to B; and to interpose between B and C an E unlike in loudness to B in the same degree in which it is unlike in loudness to C. It is thus possible to form a scale passing by equal gradations of unlikeness from a very faint sound to a very loud one. Similar scales can be formed for degrees of unlikeness in pitch, in the brightness of light, in weight as appreciated by pressure on the skin or by lifting, etc. Now the fundamental fact which underlies Weber's law is that equal degrees of unlikeness in sensation do not correspond to equal increase or decrease in the absolute intensity of the stimulus. If a series of increasing intensities of stimulation be denoted by R1, R2, R3, R4, and the corresponding sensations by r1, r2, r3, r4, the degree of unlikeness between r1 and 12 is equal to the degree of unlikeness between R1             R3 r3, and r4, when = or to use an equivalent formula, in R2 R4                                     R2 R1 R4 R3 some respects more convenient, when = R1 R3              Long before quantitative methods in psychology were thought of, astronomers had occasion to classify the stars according to their relative brightness. The different classes are arranged in a scale. At the top of the scale comes the brightest; the unlikeness in average brightness between this and the second class is equal to the unlikeness in average brightness between the second and third class, and so on. The corresponding intensities of the physical lights have since been determined; and it is found that they approximately form the geometrical series, 12 14 18 116, etc. Here each stimulus is the half of the preceding stimulus. Obviously 12 : 14 : : 14 : 18 and 14 : 18 :: 18:116 and 12 : 14:: 18 : 116

In experimental investigations, attention has been chiefly given to degrees of unlikeness which are barely discernible.

Within limits, the stimulus may vary without any corresponding unlikeness in the sensation becoming perceptible.* The same law holds here also. The original stimulus, whatever its absolute intensity may be, must be increased by a certain constant fraction of its own amount, before any unlikeliness in the sensation is discernible. The constant fraction is different for different kinds of sensation. In estimating weight merely by pressure on the skin, the ratio between original stimulus and increased stimulus must be 3 : 4 before an unlikeliness is perceptible ; or to use technical language, before the differencethreshold is passed. Differencethreshold is in some respects a misleading term : the facts do not warrant us in saying that there is no difference in the sensation before the threshold is passed, but that there is no discernible unlikeliness in the sensation. It is better therefore to speak of the threshold of discernment than of the threshold of difference. For brightness of white light, unlikeness only becomes discernible when the ratio of the original stimulus to the increased stimulus is 100 : 101, or, in other words, when the increment is 1/100th of the original stimulus. "If we place two candles so as throw two shadows of some object on a white surface, the shadow caused by each light will be illuminated by the other light, and the rest of the surface will be illuminated by both lights. If now we move one candle away we shall reach a point at which the shadow caused by it ceases to be visible, that is to say, we fail at this point to appreciate the difference between the surface illuminated by the near light alone and that illuminated by the near light and the far light together. If now, having noted the distance to which the candle had to be moved, we repeat the same experiment with two bright lamps, moving one lamp away until the shadow it casts ceases to be visible, we shall find that the lamp has to be moved just as far as the candle; that is to say, the least difference between the illumination of the bright lamps which we can appreciate is the same as in the case of the dimmer candles. Many similar examples might be given showing a similar result, in fact, it is found by careful observation that, within tolerably wide limits, the smallest difference of light which we can appreciate by visual sensations is a constant fraction of the total luminosity employed."*

* See Book ii., Chap, i., § 3. Mere Sensation

It should be added that a stimulus must reach a certain degree of intensity before it can produce any discernible sensation at all. Physical light or physical sound may bo too faint to be distinguishable. The point at which it is just indistinguishable, so that the least increase would make it distinguishable, is called the stimulusthreshold.

* Foster, op. cit., p. 1211.