JOSIAH WILLARD GIBBS. xxi 



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 to 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 distinct advantages over those 

 of Gauss and Oppolzer; the convergence of the successive approxi- 

 mations was more rapid and the labor of preparing the fundamental 

 equations for solution much less. These two papers were translated 

 by Buchholz and incorporated in the second edition of Klinkerfues' 

 Theoretische Astronomie. 



Between the years 1882 and 1889, five papers appeared in The 

 American Journal of Science upon certain points in the electro- 

 magnetic theory of light and its relations to 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 matter being that 

 it is fine-grained with reference to the wave-length of light, but 

 not infinitely 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 doubly 

 refracting media), but also leads to Fresnel's laws of double refrac- 

 tion 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 polariza- 

 tion are explained 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 equations of mono- 

 chromatic light in media of every degree of transparency, arriving 



* Astronomical Journal, vol. ix, pp. 114-117, 121-124, 1889. 



