The Infusoria have long been known to multiply by spontaneous fission, external germination, and the production, internally, of variously formed bodies, which many observers, somewhat hastily, have described under the name of “embryoes.” The phenomena of “encysting,” “conjugation,” and “alternate generation” (so called), which these animals frequently exhibit, and the relation, real or supposed, between such processes and their various modes of propagation, have, from time to time, afforded subject-matter for not a little controversy. Stein’s theory of Acinetism, once universally received, then skilfully assailed by Lachmann and Cienkowsky, and again defended by D’Udekem, has now virtually been abandoned by its distinguished author. But, although some knowledge was gained, and many false notions dispelled by these and other investigations, it is surprising how little, before 1858, had really been done towards proving the occurrence among the Infusoria of a true reproduction, similar to that which takes place in all the higher classes of animals. An English anatomist had, in 1851, recorded the presence of ova and spermatozoa in one of the marine sponges (Tethya), thus, for the first time, showing that the Protozoa formed no exception to the four remaining sub-kingdoms of animals in the possession of these essential elements. Five years later his observations were corroborated by Lieberkühn, in the case of the fresh-water sponge (Spongilla). Even then, the existence of generative elements still remained to be demonstrated in the Infusoria—a class which might well be considered as ranking above sponges in the scale of organisation. Ehrenberg, it is true, had described their “nucleus” as a male organ—an opinion which received a qualified support from Stein, though it met with less favour at the hands of other observers. And the late Johannes Müller, with some of his most able pupils, took note of various minute filaments seen by them within the bodies of several Infusoria, which filaments they were disposed to regard as spermatozoa. Such researches and conjectures, in themselves by no means useless, were very far from settling the questions really at issue; for it has now conclusively been shown that the nucleus does not perform the function of a testis, and that Müller’s filaments were, in all probability, parasitic organisms, belonging to the lower Algæ.