58 BL'LLETIX : MUSEUM OF COMPARATIVE ZOOLOGY. 



III. Discussion of the Bearing of the Observations on the 



Problems. 



In the following discussion I shall adopt in general the order pursued 

 in my " Statement of Problems," taking up successively the various 

 theories in regai-d to cleavage and gastrulation, and pointing out what 

 bearing the observations above detailed have upon these theories. This 

 •will be followed by a resume of the general conclusions which may be 

 drawn from the work. 



We will therefore first take up a discussion of the cleavage, and of the 

 theories bearing upon it. 



1. Cleavage. 

 A. The Direction of Cleavage. 



(1) BerthoMs theory of surfaces of least area. (See page 4.) — The 

 two- and four-cell stages in Asplanchna agree well with the conditions 

 demanded by the law of least surfaces. The peculiar arrangement of 

 blastomeres in the four-cell stage, agreeing as it does with the four-cell 

 stage of animals of the most various systematic positions, and with the 

 four-cell stage of many plants, seems probably due to some very general 

 law. In all these cases only three cells meet along one common line. 

 As this is the arrangement demanded by the principle of least surfaces, 

 the conclusion seems perhaps justifiable that this principle of least sur- 

 faces is that common law. 



The eiirht-cell stage also fulfils the requirements of the principle of 

 least surfaces. But from this stage onward, many of the conditions 

 found are irreconcilable with the view that this principle is a determining 

 factor. Six of the cells in the eight-cell stage divide in a manner that 

 squarely defies the principle of least surfaces. Nor does the arrange- 

 ment of cells in the resting periods agree better with the principle. As 

 pointed out on page 30, the flat, almost disk-shaped form taken by the 

 cells of quadrant D during the ten-cell stage (Figs. 23 and 2.5, Plate 3) 

 and the sixteen-cell stage (Figs. 31 and 32, Plate 4) is widely at vari- 

 ance with the demands of the principle of least surfaces. The form 

 of the cells in quadrants A, B, and C during their resting period in the 

 sixteen-cell stage (Figs. 30 and 34) is equally impossible of explanation 

 on the least surfaces theory. "Many other cases could be adduced in 

 which this principle is contradicted, but a fuller discussion of these cases 

 will be given under the next theory (Hertwig's law). In general, any 

 case which is not in agreement with Hertwig's law is likewise inexplicable 



