GEOMETRICAL RELATIONS OF CLEAVAGE-FORMS 377 



same plane, is correlated with a deeply lying law of growth affecting 

 the entire formation of the body. We can7iot comprehend the forms 

 of cleavage without reference to the end-result ; and thus these phe- 

 nomena acquire a certain teleological character so happily expressed 

 by-LilHe (p. 370). This has been clearly recognized in various ways 

 by a number of recent writers. Roux ('94), while seeking to explain 

 many of the operations of mitosis on a mechanical basis, holds that 

 the position of the spindle is partly determined by " immanent " 

 nuclear tendencies. Braem ('94) recognizes that the position of the 

 spindle is determined not merely as that of least resistance for the 

 mitotic figure, but also for that of the resulting products. I pointed 

 out ('92) that the bilateral form of cleavage in annelids must be 

 regarded as a "forerunner" of the adult bilaterality. Jennings ('97) 

 concludes that the form and direction of cleavage are related to the 

 later morphogenetic processes ; and many similar expressions occur 

 in the works of recent students of cell-lineage.^ 



The clearest and best expression of this view is, however, given by 

 Lillie ('95, '99), who not only correlates the direction and rate of 

 cleavage, but also the size-relations of the cleavage-cells with the 

 arrangement of the adult parts, pointing out that in general the size, 

 as well as the position, of the blastomeres is directly correlated with 

 that of the parts to which they give rise, and showing that on this 

 basis " one can thus go over every detail of the cleavage, and know- 

 ing the fate of the cells, can explain all the irregularities and peculi- 

 arities exhibited." 2 Of the justice of this conclusion I think any one 

 must be thoroughly convinced who carefully examines the recent 

 literature of cell-lineage. It gives no real explanation of the phenom- 

 ena, and is hardly more than a restatement of fact. Neither does it 

 in any way lessen the importance of studying fully the mechanical 

 conditions of cell-division. It does, however,, show how inadequate 

 have been most of the attempts thus far to formulate the " laws " of 

 cell-division, and how superficially the subject has been considered by 

 some of those who have sought for such *' laws." 



We now pass naturally to the second or promorphological aspect 

 of cleavage, to a study of which we are driven by the foregoing con- 

 siderations. 



^ Conklin ('99) believes that many of the peculiarities of cleavage may be explained by 

 the assumption of protoplasmic currents which " carry the centrosomes where they will, and 

 control the direction of division and the relative size and quality of the daughter-cells," 

 I.C., p. 90. He suggests that such currents are of a chemotropic character, but recognizes 

 that their causation and direction remain unexplained. 



=^ Cf- ('95). P- 39- 



