446 FRANK R. LILLIE 
It might, perhaps, seem possible at first thought that the aster 
appears in this position with reference to the partial sperm nuclei 
because we have here a broken surface; this is at least a condition 
in which this particular point of the surface of the partial nuclei 
differs from the remainder of its surface. But in the entire sperm 
nucleus, where there is no broken surface, the position is always 
the same. Moreover, some ten or fifteen minutes elapses after 
entrance of the sperm head before the aster becomes visible, and 
in this time the nucleus has changed form so as to produce a 
pointed extremity (figs. 33 a, 36, 37, 40, ete.) in the position 
where the aster is to appear whether the nucleus be entire or 
partial. This is perhaps sufficient evidence of repair of the 
wounded surface. 
-We have to seek some more profound cause for this localization, 
and I believe that it must be regarded as a special case of organic 
polarity to be explained like other cases on the basis either of 
gradation or orientation of materials. From this point of view 
the nucleus would possess an immanent structure determining 
the location of aster formation and therefore the plane of division 
of the nucleus. 
3. Theory of fertilization 
I have pointed out repeatedly in these studies that fertiliza- 
tion involves two phases, viz.: an external phase prior to entrance 
of the spermatozo6n, in which. certain cortical changes are pro- 
duced in the egg, and an internal phase, following penetration, 
involving a complex series of phenomena. As I pointed out in 
the introduction, this paper is a contribution to the analysis of 
the second phase. On the basis of experiments on artificial par- 
thenogenesis and hybrid fertilization, Loeb has made a similar 
distinction of two phases, and so far the results of what we may 
call the biological and the physico-chemical analyses of fertili- 
zation are in accord. 
If we reject the centrosome theory of fertilization, as I believe 
we are compelled to do, what point of view from the side of the 
biological analysis shall we put in its place? The theory of the 
