MACCULLAGH, James (1809-1846), one of the most elegant geometers of modern times, was born in 1809, near Strabane, Ireland. After an exceptionally brilliant undergraduate career in Trinity College, Dublin, he was elected fellow in 1832. From 1832 to 1843 he held the chair of mathematics; and during his tenure of this post, for which he was specially fitted, he improved in a most marked manner the position of his university as a mathematical centre. In 1843 he was transferred to the chair of natural philosophy, for which he was not nearly so well qualified. Overwork, mainly on subjects beyond the natural range of his powers, induced mental disease; and he died by his own hand in 1846. His Works have been published in a collected form (Dublin University Press Series, 1880). Their distinguishing feature is the geometry,—which has rarely been applied either to pure space problems or to known physical questions such as the rotation of a rigid solid or the properties of Fresnel’s wave-surface with such singular elegance. In this respect his work takes rank with that of Poinsot. No higher praise could be given. One specially remarkable geometrical discovery of Maccullagh’s is that of the “modular generation of surfaces of the second degree”; and a noteworthy contribution to physical optics is his “theorem of the polar plane.” But his methods, which, in less known subjects, were almost entirely tentative, were altogether inadequate to the solution of the more profound physical problems to which his attention was mainly devoted, such as the theories of double refraction, of crystalline reflexion, &c. Here not only are the utmost powers of analysis required, but also the highest physical knowledge; and in consequence Maccullagh’s work was entirely overshadowed by ...