WILCOX : SPERMATOGENESIS. 29 
geneous, or. if they are not homogeneous, that there is an exact halving 
of the component particles of the elements of the Vierergruppe. But 
Brauer considers the four elements of a group identical because they all 
arise, by two divisions, from one. 
Again, if this whole process be only to secure a reduction of the mass 
of chromatin, the doubling of the chromatic elements, and the long, 
laborious process of mitosis would be unexplained and unjustified, as 
Weismann has pointed out; for a halving of the mass could be brought 
about by amitotic division. According to Weismann, the formula for 
Brauer's Vierergruppe would be (Häcker, '93) 5 at. We start 
with one element, a; this undergoes two longitudinal splittings, and 
then two separations by the two maturation divisions, and we then have 
just what we started with. The series formulated would be 
a aa a 
a aa a 
a 
a 
ala 
But Henking, Weismann, Häcker, Rückert, vom Rath, and others 
allow only one longitudinal splitting, and their formula for the Vierer- 
gruppen, as stated by Häcker (93), and accepted by vom Rath (93), 
is : "E This evidently permits only one reduction division in the 
A | 
Weismannian sense. Vom Rath and Weismann are therefore inconsistent 
when they hold to a longitudinal splitting in the spirem condition, and 
yet consider both maturation divisions as reductions. If the Vierer- 
gruppen have the formula E HZ there are but two sorts of ids, a and 
6, and it is simply impossible to get more than one reduction division. 
a 
If from the nucleus - arises by division two nuclei, 3 and 
) 
this is by Weismann's own definition an equation division, and only 
when these two cells become by division the four ultimate products of 
maturation a, b, a, b, can we speak of a redüction. 
Hücker at first considered both divisions as reductions (92), but 
later (93) he rightly came to the conclusion that the longitudinal 
splitting in the spirem stage was a preparation for one division, and 
that the final separation of the sister elements thus produced oonsti- 
tutes an equation division, —a “modified equation division," he calls 
it, because the splitting, which ordinarily occurs at the equator of the 
spindle is here precociously introduced in the spirem condition. 
