very small, it might nevertheless be amply sufficient to transmit the tendencies of heredity. Nägeli and Pflüger rightly asserted, at a later date, that the amount of the substance which forms the basis of heredity is necessarily very small, for the fact that hereditary tendencies are as strong on the paternal as on the maternal side, forces us to assume that the amount of this substance is nearly equal in both male and female germ-cells. Although I had not published anything upon the point, I was myself inclined to ascribe considerable importance to the cell-substance in the process of fertilization; and I had been especially led to adopt this view because my investigations upon _Daphnidae_ had shown that an animal produces large sperm-cells with an immense cell-body whenever the economy of its organism permits. All _Daphnidae_ in which internal fertilization takes place (in which the sperm-cells are directly discharged upon the unfertilized egg), produce a small number of such large sperm-cells (_Sida_, _Polyphemus_, _Bythotrephes_); while all species with external fertilization (_Daphnidae_, _Lynceinae_) produce very small sperm-cells in enormous numbers, thus making up for the immense chances against any single cell being able to reach an egg. Hence the smaller the chances of any single sperm-cell being successful, the larger is the number of such cells produced, and a direct result of this increase in number is a diminution in size. But why should the sperm-cells remain or become so large in the species in which fertilization is internal? The idea suggests itself that the species in this way gains some advantage, which must be given up in the other cases; although such advantage might consist in assisting the development of the fertilized ovum and not in any increase of the true fertilizing substance. At the present time we are indeed disposed to recognize this advantage in still more unimportant matters, but at that time the ascertained facts did not justify us in the assertion that fertilization is a mere fusion of nuclei, and M. Nussbaum[109] quite correctly expressed the state of our knowledge when he said that the act of fertilization consisted in ‘the union of identical parts of two homologous cells.’