Page:Scientific Papers of Josiah Willard Gibbs.djvu/29

Rh As already remarked, the exposition of the theory of dyadics given in the vector analysis is not in accord with Grassmann's system. In a footnote to the address referred above, Professor Gibbs shows the slight modification necessary for this purpose, while the subject has been treated in detail and in all generality in his lectures on multiple algebra delivered for some years past at Yale University.

Professor Gibbs was much interested in the application of vector analysis to some of the problems of astronomy, and gave examples of such application in a paper, "On the Determination of Elliptic Orbits from Three Complete Observations" (Mem. Nat. Acad. Sci., vol. iv, pt. 2, pp. 79-104). The methods developed in this paper were afterwards applied by Professors W. Beebe and A. W. Phillips to the computation of the orbit of Swift's comet (1880 V) from three observations, which gave a very critical test of the method. They found that Gibbs's method possessed distincts advantages over those of Gauss and Oppolzer; the convergence of the successive approximations was more rapid and the labor of preparing the fundamental equations for solution much less. These two papers were translated by Buchhols and incorporated in the second edition of Klinkerfues' Theoretische Astronomie.

Between the years 1882 and 1889, five papers apeared in The American Journal of Science upon certain points in the electromagnetic theory of light and its relations ot the various elastic theories. These are remarkable for the entire absence of special hypotheses as to the connection between ether and matter, the only supposition made as to the constitution of matther being that it is fine-grained, and that it does disturb in some manner the electrical fluxes in the ether. By methods whose simplicity and directness recall his thermodynamic investigations, the author shows in the first of these articles that, in the case of perfectly transparent media, the theory not only accounts for the dispersion of colors (including the "dispersion of the optic axes" in double refracting media), but also leads to Fresnel's laws of double refraction for any particular wave-length without neglect of the small quantities which determine the dispersion of colors. He proceeds in the second paper to show that circular and elliptical polarization are epxlained by taking into account quantities of a still higher order, and that these in turn do not disturb the explanation of any of the other known phenomena; and in the third paper he deduces, in a very rigorous manner, the general equtions of monochromatic light in media of every degree of transparency, arriving