The meaning of the photometric experiments will now be understood. A candle placed at a certain distance from a sheet of paper illuminates it in a certain way: you double the distance and find that four candles are required to produce the same effects, sensation. From this you conclude that if you had doubled the distance without increasing the intensity of the luminous source, the resultant illumination would have been only one-fourth as bright. But it is quite obvious that you are here dealing with the physical and not the psychological effect. For it cannot be said that you have compared two sensations with one another: you have made use of a single sensation in order to compare two different luminous sources with each other, the second four times as strong as the first but twice as far off. In a word, the physicist never brings in sensations which are twice or three times as great as others, but only identical sensations, destined to serve as intermediaries between two physical quantities which can then be equated with one another. The sensation of light here plays the part of the auxiliary unknown quantity which the mathematician introduces into his calculations, and which is not intended to appear in the final result. [Sidenote: The psychophysicist claims to compare and measure sensations. Delbœuf's experiments.] But the object of the psychophysicist is entirely different: it is the sensation of light itself which he studies, and claims to measure. Sometimes he will proceed to integrate infinitely small differences, after the method of Fechner; sometimes he will compare one sensation directly with another. The latter method, due to Plateau and Delbœuf, differs far less than has hitherto been believed from Fechner's: but, as it bears more especially on the luminous sensations, we shall deal with it first. Delbœuf places an observer in front of three concentric rings which vary in brightness. By an ingenious arrangement he can cause each of these rings to pass through all the shades intermediate between white and black. Let us suppose that two hues of grey are simultaneously produced on two of the rings and kept unchanged; let us call them A and B. Delbœuf alters the brightness, C, of the third ring, and asks the observer to tell him whether, at a certain moment, the grey, B, appears to him equally distant from the other two. A moment comes, in fact, when the observer states that the contrast A B is equal to the contrast B C, so that, according to Delbœuf, a scale of luminous intensities could be constructed on which we might pass from each sensation to the following one by equal sensible contrasts: our sensations would thus be measured by one another. I shall not follow Delbœuf into the conclusions which he has drawn from these remarkable experiments: the essential question, the only question, as it seems to me, is whether a contrast A B, formed of the elements A and B, is really equal to a contrast B C, which is differently composed.