Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/268

 the student. An exception, however, must be made with respect to the statements concerning the electromagnetic theory of light. We are told (p. 450) that the English theory, founded by Maxwell and represented by Glazebrook and Fitzgerald, makes the plane of polarization coincide with the plane of vibration, while Lorentz, on the basis of Helmholtz's equations comes to the conclusion that these planes are at right angles. Since all these writers make the electrical displacement perpendicular to the plane of polarization, we can only attribute this statement to some confusion between the electrical displacement and the magnetic force or "displacement" at right angles to it. We are also told that Glazebrook's "surface-conditions" which determine the intensity of reflected and refracted light are different from those of Lorentz,—a singular error in view of the fact that Mr. Glazebrook (Proc. Camb. Phil. Soc., vol. iv, p. 166) expressly states that his results are the same as those of Lorentz, Fitzgerald, and J. J. Thomson. We have spent much fruitless labor in trying to discover where and how the expressions were obtained which are attributed to Glazebrook, but in which the notation has been altered. They ought to come from Glazebrook's equations (24)–(27) (loc. cit.), but these appear identical with Lorentz's equations (58)–(61) (Zeitschrift f. Math. u. Phys., vol. xxii, p. 27). They might be obtained by interchanging the expressions for vibrations in the plane of incidence and at right angles to it, with two changes of sign.

The reader must be especially cautioned concerning the statements and implications of what has not been done in the electromagnetic theory. These are such as to suggest the question whether the author has taken the trouble to read the titles of the papers which have been published. We refer especially to what is said on pages 248, 249 concerning absorption, dispersion, and the magnetic rotation of the plane of polarization.

In the Experimental Part, with which the treatise closes, we have a comparison of formulæ with the results of experiments by the author and others. The author has been particularly successful in the formula for dispersion. Li the case of quartz (p. 545), the formula (with four constants) represents the results of experiment in a manner entirely satisfactory through the entire range of wave-length from 2.14 to 0.214. Those who may not agree with the author's theoretical views will nevertheless be glad to see the results of experiment brought together, and, so far as may be, represented by formulæ.