Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/270

254 This consideration greatly simplifies the theory of Foucanlt's experiment, and makes it evident, I think, that the results of all such experiments depend upon the value of $$U,$$ and not upon that of $$V.$$

The discussion of the experiment by following a single wave, and taking account of its rotation, is a complicated process, and one in which it is very easy to leave out of account some of the elements of the problem. The principal objection to it, however, is its unreality. If the dispersion is considerable, no wave which leaves the revolving mirror will return to it. The individual disappears, only the group has permanence. Prof. Schuster, in his communication of March 11 (p. 439), has nevertheless obtained by this method, as the quantity determined by "the experiments hitherto performed," $$V^2 / (2V - U),$$ which, as he observes, is nearly equal to $$U.$$ He would, I think, have obtained $$U$$ precisely, if for the angle between two successive wave-planes of similar phase, instead of $$2\omega \lambda / V,$$ he had used the more exact value $$2\omega \lambda / U.$$

By the kindness of Prof. Michelson, I am informed with respect to his recent experiments on the velocity of light in bisulphide of carbon that he would be inclined to place the maximum brilliancy of the light between the spectral lines $$\text{D}$$ and $$\text{E},$$ but nearer to $$\text{D}.$$ If we take the mean between $$\text{D}$$ and $$\text{E},$$ we have $$K$$ denoting the velocity in vacuo (see p. 249 of this volume). The number observed was 1.76, "with an uncertainty of two units in the second place of decimals." This agrees best with the first formula. The same would be true if we used values nearer to the line $$\text{D}.$$

New Haven, Connecticut, April 1. [1886.]