That is an outline of the famous gastræa-theory, that Haeckel discovered when he was engaged in studying the calcisponges. It was first published in his large _Monograph on the Calcispongiæ_ in 1872, elaborated in his _Studies of the Gastræa-theory_ in 1873, 1875, and 1876 (published in one volume in 1877), and generally expounded, together with the biogenetic law, in (amongst other works) his polemical essay, “The aims and methods of modern embryology” (1875). This discovery, in Haeckel’s opinion, now made the biogenetic law a real search-light in the exploration of the obscure past. It indicated a third critical point in the great genealogical tree. Already we had the root (the monera) and the crown (man); now we had the point from which the various real animal stems radiated like the umbellate branches of a single large bloom. Through it the Darwinian system had been converted into the greatest practical reform of animal classification. If this gastræa-theory was correct, it was an incalculable gain for zoology. The difficulty of it, on the other hand, lay in the infinite modifications of the embryonic processes in detail that had been brought about by cenogenesis; almost everywhere this had more or less obscured the original features. On the whole it gave rise to the greatest and most far-reaching discussion that has taken place in zoology for the last thirty years, apart from the Darwinian theory itself. To-day, at the close of these three decades, there are only two alternatives. One is that there is still an absolutely mysterious and hidden law of ontogeny, that compels countless animals over and over again to pass through these embryonic forms and assume a likeness to the gastræa. After all the eagerness with which the whole school of embryologists opposed to Haeckel have sought, up to our own day, to establish such a direct law, we have not yet got the shadow of a clear formulation of it. The other alternative is that Haeckel is right in believing that he has discovered the correct formula in his phylogenetic interpretation of embryonic processes in accordance with the biogenetic law. If that is so, the gastræa-theory is the crown of all his labours in technical zoology proper. Let us wait another thirty years.