Page:Russian Realities and Problems - ed. James Duff (1917).djvu/193

 the domain of mathematics was supplemented by another, produced by the genius of Lobachevsky (1826): his "pan-geometry," which revealed an entirely new and comprehensive conception of space, eventually found some partisans among Russian mathematicians, for instance, Vashchenko, and Zacharchenko.

During the same period the evolution of independent Russian thought concerning the real world in its natural and historical aspect can also be exemplified. Such a knowledge supposes a theoretical conception of Reality as an object of experience, and experience, from an epistemological and even practical point of view, becomes a problem in itself.

The most scientific mathematical treatment of natural phenomena could, however, be applied only to some of them: it turned out to be particularly successful in mechanics. Following Bernoulli and Euler, some Russian scholars contributed to this subject: thus Ostrogradsky wrote papers on the propagation of undulatory motion in a cylinder and on the motion of an elastic body; and more recently Lyapunov solved the problem of the figures of equilibrium not very different from ellipsoids exhibited by a homogeneous and liquid mass with a rotatory movement.

Mathematics and mechanics were applied also to astronomical investigations: one of the colleagues of Bernoulli—the Frenchman Delisle—and Rumovsky a Russian pupil of Euler, began this work; but it was organized somewhat later, after the foundation of the