the laws of the undulatory theory of light. Philosophers more able than myself to appreciate their merits, have given their testimony to the great value of his discoveries, and to the elegant means that he has employed. It is the sincere wish of us all, that these labours may be followed by others as important to science and as honourable to the University of Dublin ; an University that numbers Mr. Mac- Cullagh among the most eminent of her sons.
The Council have aw^arded the Copley Medal for the present year to Professor MacCuHagh, for his researches connected with the wave- theory of light, contained in the Transactions of the Royal Irish Academy. The grounds on which they have made this award are the following. One of the most important steps made in the physi- cal theory of light, since it was first promulgated by Huygens, is, undoubtedly, Fresnel's discovery of the laws of refraction by cry- stallized media, embodied in his ' Memoire sur la double refraction.' The object proposed by Professor MacCuUagh, in his first paper[1], was to simplify and to develope that theory. He has shown in this paper, that the elastic force of the luminiferous sether may be repre- sented, in magnitude and direction, by means of an ellipsoid, whose semiaxes are the three principal refractive indices of the medium ; and he has thence deduced, in a geometrical form, the leading results of Fresnel's theory. This ellipsoid is closely related to the genera- ting ellipsoid of Fresnel ; and by the aid of these relations, Professor MacCullagh has demonstrated, in a very simple manner, the truth of Fresnel's construction of the wave-surface, the demonstration of which had been left imperfect by its author.
In Mr. MacCullagh's next paper,, entitled " Geometrical propositions applied to the Wave-theory of Lightf," he has examined the proper- ties of a surface, which he calls the surface of indices^ and which had presented itself likewise in the researches of M. Cauchy and Sir William Hamilton ; and he has shown that it affords a general and exact construction for the interval of retardation of the two rays in their passage through a double-refracting crystal ; and thus that the forms of the rings, or isochromatic curves, which had previously been deduced only by approximate methods, may be determined generally.
The next paper of Professor MacCullagh is that "On the Double Refraction of Quartz[2];" a subject which had engaged the attention, successively, of Biot, Fresnel, and Airy. The first of these writers had determined experimentally the laws of rotatory polarization, which take place when a ray is transmitted along the axis of rock- crystal ; and the second had shown that these laws were explained by the interference of two circularly polarized rays, which are trans- mitted along the axis with different velocities. The next step in this curious subject was made by Mr. Airy, who examined the peculiar phenomena of refraction by quartz in other directions, and showed that they were accounted for by the supposition of two elliptically 'polarized rays, the ratio of the axes of these elliptical vibrations va-
