Thus we can understand that the number of chromosomes remains the same in every cell-generation throughout development, as it is the same in all the individuals of a species. The numbers are known for many species: in some worms there are only two or four chromosomes, while in other related worms there are eight; in the grasshopper there are twelve, and in a marine worm, Sagitta, eighteen; in the mouse, the trout, and the lily there are twenty-four; in some snails thirty-two; in the sharks thirty-six, and in Artemia, a little salt-water crustacean, 168 chromosomes. In Man the chromosomes are so small that their normal number is not certain—sixteen have been counted. This counting can only be done during the process of nuclear division, for afterwards the chromosomes flow indistinguishably together, or rather apart, only to reappear, however, in the old form and number whenever the nucleus again begins to divide.

It remains to be told what becomes of the centrosphere in cell-division. As soon as the formation of the daughter-nuclei has been brought about by the divergence of the split halves of the loops, the spindle figure begins to retrograde, its threads become pale and gradually disappear, as does the whole radiate halo of the centrosphere ([Fig. F and G]). The cell-body has by this time also divided in the equatorial plane of the nuclear spindle, and the centrosome remains usually as a very inconspicuous pale body lying in the cytoplasm close to the nucleus, reawakening to renewed activity when cell-division is about to recommence ([G, csph]).

These, briefly, are the remarkable processes of nuclear division. Their net result is obvious; the chromatin substance is divided between the daughter-nuclei with the greatest conceivable accuracy.

It is not so easy to understand the mechanism of this partition, and there are various divergent theories on this point. According to the older idea of Van Beneden, the spindle fibres work like muscles, and by contracting draw the halves of the chromosomes which adhere to them towards the pole, while the rest of the fibres radiating out from the polar corpuscles act as resisting and supporting elements. This view, with many modifications however, has still its champions, and M. Heidenhain in particular has made a notable attempt to establish it and to work it out in detail. Opposed to it stand the views of those who, like O. Hertwig, Bütschli, Häcker, and others regard the rays not as specific elements which were pre-formed in the cell, but as the expression of the orientation of certain protoplasmic particles—an orientation evoked by forces which have their seat within the central corpuscles, and act in the manner of magnetic or electric forces. That the central corpuscles are centres of attraction seems to me hardly open to doubt, and I cannot regard the regular arrangement of the chromosomes in the equatorial plane of the spindle as due to a mere adhesion to contractile threads. Some still unknown forces—chemotactic or otherwise—must be at work here. Later on we shall study the phenomenon of the migration of the sperm-nucleus into the ovum, when it is accompanied by its central body and its halo of rays. Häcker seems to me justified in inferring from this phenomenon alone that the sudden origin of the rays is due to forces resident in the central corpuscle. But undoubtedly even this 'dynamic' explanation of karyokinesis is still only at the stage of hypothesis and reasoning from analogy, and is far removed from a definite knowledge of the forces at work.

For the problems with which we are here chiefly concerned, the problems of heredity, it is enough to know that the cells of multicellular organisms possess an extremely complex apparatus for division, whose chief importance lies in the fact that through it the chromatin units of the nucleus are divided into precisely equal parts, and so separated from each other that one half forms one daughter-nucleus, the other half the other. It is not merely that there is an exact division of the whole chromatin in the mass, which could have been effected much more simply, but that there is a regulated distribution of the different qualities of the chromatin, as we shall see later.

It must here be emphasized that the splitting of the chromosomes does not depend on external forces, but on internal ones involved in their organization, and in the definite attractions and repulsions of their component particles which come about in the course of growth. The chromosomes do not split like a trunk that has been broken open with an axe, but rather like a tree burst apart by the frost, that is, by the freezing of the water within itself. I consider it very important that we should recognize this, even though we do not yet know what the forces are that have control in this case, because it leads us to conclude that the structure of the chromosomes is extremely complex, that they are, so to speak, a world in themselves, that they possess an infinitely complex and delicate though invisible organization, in which intrinsic chemico-physical forces produce the regulated succession of changes which we observe. We shall afterwards see that we are led to the same conclusion from another direction—that is, from the phenomena of inheritance. We shall then recognize that the rod- or loop-shaped chromosomes cannot be simple elements, but are composed of linear series of 10, 20, or more globular single-chromosomes, each of which represents a particular kind of chromatin or hereditary substance. If we consider this carefully, we shall see that it would hardly be possible to think out a mode of nuclear division which would so exactly and securely fulfil the purpose of conveying these many kinds of chromatin to the two daughter-nuclei in like proportions as does the mechanism of distribution actually brought about by nature. The longitudinal splitting of the rods halves the chromosomes, and the spindle apparatus secures the proper distribution of the halves between the two daughter-nuclei.

So much, at least, is certain, that no such complicated mechanism for 'mitotic' division would have arisen if the very precise division of a substance of the highest importance had not been concerned, and in this conclusion lies the first hint of the interpretation of the chromatin substance as the bearer of the hereditary qualities.

We are now familiar with the cell-nucleus and the apparatus for its division, and we are thus fully prepared to begin the study of the phenomena of 'fertilization.' Here also the processes depend essentially on the behaviour of the cell-nuclei, for even the first observations made by O. Hertwig on the behaviour of the spermatozoon after it has penetrated into the ovum led to the suggestion that the essential fact is the union of two nuclei; and numerous later, more and more deeply penetrating researches have furnished abundant evidence that the so-called 'fertilization' is essentially a nuclear fusion.

Let us begin with O. Hertwig's observations on the ovum of the sea-urchin. Eggs of this animal, which have been taken out of the ovary of the female, may easily be fertilized artificially by pouring over them spermatic fluid taken from a male, and diluted with sea-water. Before this is done only one nucleus can be observed in the ovum, but shortly afterwards two nucleus-like structures of unequal size can be seen within the ovum, and the smaller is surrounded by a circle of rays. Hertwig rightly interpreted this smaller nucleus as the modified remains of the penetrating spermatozoon, which then slowly approaches the nucleus of the egg, and ultimately fuses with it to form a 'segmentation nucleus.' From this starts the so-called 'segmentation' of the ovum, that is, the series of repeated divisions resulting in the formation of an ordered mass of cells, which by continued division of cells builds up the embryo.

Simple as this process of nuclear conjugation may seem, it was by no means so easy to recognize, and several investigators, especially Auerbach, Schneider, and Bütschli, had seen stages of the process at an earlier date without arriving at the true interpretation of the phenomena. This was chiefly due to the fact that, in addition to the phenomena of fertilization proper, which we have briefly sketched, other nuclear changes take place in the maturing ovum, and these are not very easy to distinguish from the former; we refer to the phenomena of the so-called 'maturation of the ovum.' When the ovum-cell has attained its full size within the ovary it is not yet capable of being fertilized, but must first undergo two processes of division, to the right understanding of which Hertwig's investigations, and afterwards those of Fol, have contributed much.