This memoir, written in 1904, clearly asserts the homopolarity of the centrosomes, and shows that the nuclear division is the result of a bipolar action, two poles of the same sign exerting their influence on opposite sides of the nucleus. It also emphasizes the important fact that diffusion, {93} and as far as we know diffusion alone, is able to produce a spindle between homologous poles. A glance at the photograph is enough to show that the spindle is formed between poles of the same sign. The lines of diffusion radiate from one centre and converge towards the other centre in curves, giving the double convergence characteristic of a spindle. The central drop merely supplies the necessary material, and should have a concentration but slightly less than that of the plasma, so as not to set up its own lines of diffusion. The photograph shows clearly that the rays of the spindle traverse the equator without any break. It has been objected that these lines form not so much a spindle as two hemi-spindles, but it is clear that these two hemi-spindles are continuous and form a single sheaf of rays uniting the two poles of concentration. This is a phenomenon entirely unknown in the magnetic or electric fields, where two poles of the same sign, one on either side of a pole of the contrary sign, give two separate spindles. In a magnetic field it is impossible to make the lines emanating from one pole converge, except to a pole of opposite sign. Hence if we admit the homopolarity of the centrosomes, we must also admit that diffusion is the _vera causa_ of karyokinesis, since, as I showed at the Grenoble Congress in 1904, diffusion and diffusion alone is capable of producing a spindle between two poles of the same sign.