58 BULLETIN: MUSEUM OF COMPARATIVE ZOÖLOGY. 
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 regard to cleavage and gastrulation, and pointing out what 
bearing the observations above detailed have upon these theories, This 
will be followed by a résumé 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 Oleavage. 
(1) Berthold’s 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 varions 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 eight-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 25, Plate 3) 
stage (Figs. 31 and 32, Plate 4) is widely 
at varl- 
and the sixteen- cell 
ance with the demands of the principle of least surfaces. The form 
of the cells in quadrants A, B, and O during their resting period in the 
sixteen-cell stage (Figs. 30 and 34) is equally impossible of explauation 
on the least surfaces ‘theory. 
Many other cases could be adduced in 
which this principle is contradicted, but a fuller discussion or 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 
