STUDIES OF FERTILIZATION 445 
ception of the centronucleus might legitimately be extended to 
cover the present case, but this cannot be said to be true; and in 
the present state of our knowledge such an explanation would 
appear forced and merely formal. 
The formation of the sperm aster takes place on the boundary 
between nucleus and cytoplasm, and as we have seen (fig. 41), 
there are very definite quantitative relations between the bulk 
of the partial sperm nuclei and the degree of development of the 
aster and the size of the centrosome. This relation leads to the 
conclusion that if intranuclear centrosomes are the causes of the 
formation of the sperm aster, not only must they exist at every 
level, but also that they must decrease in size from the base to 
the apex of the sperm nucleus! The formation of the sperm aster 
on the boundary between nucleus and cytoplasm and the quanti- 
tative relations existing between size of the nucleus and of the 
aster demonstrate, it seems to me, that the centrosome and aster 
owe their existence to an interaction between nucleus and cyto- 
plasm, and not to any third element. All the observed relations 
in the case of Nereis harmonize with this point of view. 
The production of astrospheres remote from the nucleus in the 
experiments of Morgan (’96 and ’99) and others show, it is true, 
that the nucleus is not necessary for the production of such phe- 
nomena. These asters are apparently very temporary formations, 
and evidence that their central bodies may divide like the centro- 
some of the sperm aster, or other centrosomes associated with 
nuclei, is lacking. Nevertheless, it seems probable that funda- 
mentally similar physiological causes are at the foundation cf 
both sets of phenomena, and we can only assert our profound 
ignorance of what these causes really are. 
2. The polarity of the sperm-nucleus 
We may use the term polarity to describe the fact that the 
sperm aster arises invariably at the most basal point of the sperm 
nucleus, whether it be entire or partial. This phenomenon cor- 
responds accurately to the general features of polarity of ova or 
lower organisms, as, for instance, the formation of oral organs 
at the oral end of a cut piece, etc. 
