74 BULLETIN: MUSEUM OF COMPARATIVE ZOÖLOGY. 
at right angles to one another — a theory often attributed to Sach — the 
rule in Asplanchna. 
(7) Rauber’s theory, that the asters of the different blastomeres exercise an 
attraction for one another, thus influencing the direction of the spindles. — 
There appears to be nothing in the cleavage of Asplanchna that would 
lead to such a conclusion as the above. Any attempt to explain the 
relative positions of asters in the different cells — in such a case, for ex- 
ample, as is shown in Figure 39 (Plate 5) — by the theory of attractions 
and repulsions among the asters, will be found to lead to. purely arbitrary 
assumptions as to which asters exercise attractions on others and which 
do not; any geueral statement of a positive nature will be found to be 
inconsistent with the facts. Moreover, the irregularities in the migrations 
of the asters, to which attention was especially called in the discussion of 
Hoidenhain's * Problem of a regular angle of rotation,” can with difficulty 
be harmonized with such a theory. 
(8) Braems principle of equal resistance at the two ends of the spindle. 
— This principle is discussed in connection with the question which 
immediately follows. 
B. What determines the Equality or Inequality of Cleavage Products ? 
C. What determines the Rate of Cleavage ? 
Owing to the similarity of the factors supposed to determine the 
relative size of the cleavage products and the time of cleavage, it will be 
well to consider together the foregoing questions. 
In regard to the first question, we have (1) the theory of Hertwig, 
stated on page 8, that the spindle tends to take a position in the middle 
of the mass of protoplasm in which it is contained, and (2) the “ principle 
of like resistance at the two ends of the spindle,” set forth by Braem, 
and stated on page 7. Since these two theories lead to similar results, 
they may be considered together. 
It certainly does not aid in understanding the cleavage of Asplanchna 
to assume that “der Kern von vornherein das Jestreben hat, sich 
gleichmässig nach beiden Seiten hin auszudehnen und somit auf eine 
üquale Zelltheilung hinzuwirken ” (Braem, 94, p. 345), nor that “der 
Kern stets die Mitte seiner Wirkungssphäre einzunehmen sucht?“ 
(Hertwig, 93, p. Ira INO differentintion into more and less yolk 
bearing regions is visible. Yet the first cleavage is unequal, and the 
second equal in one cell and unequal in the other; the third likewise 
shows both methods, with a preponderance of equal divisions ; and in 
the fourth all the divisions are again unequal. In no cleavage is there 
