74 BULLETIN : MUSEUM OF COMPARATIYE ZOOLOGY. 



at right angles to one another — a theory often attributed to Sach — the 

 rule in Asplauchna. 



(7) Ratiber's theonf^that the asters of the different hlastomeres exercise an 

 attraction for one another, thus influencing the direction of the spindles. — 

 There appears to be nothing in the cleavage of Asplauchna 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 general 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 

 Heideuhaiu's " Problem of a regular angle of rotation," can with difficulty 

 be harmonized with such a theory. 



(8) Braetns principle of equal rfsistajice at the tivo ends of the spindle. 

 — This principle is discussed in connection with the question which 

 immediately follows. 



B. What determiiies the Equality or Inequcdity 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 Bestreben hat, sich 

 gleichmassig nach beiden Seiten bin auszudehnen und somit auf eine 

 aquale Zelltheilung hinzuwirken " (Braem, '94, p. 3-i5), nor that "der 

 Kera stets die Mitte seiner Wirkungssphare eiuzunehmen sucht " 

 (Hertwig, '93, p. 172). Xo differentiation 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 



