J34 BIOLOGICAL LECTURES. 



We have, so far, been dealing with cases in which distinct 

 cleavage planes are developed, and have very largely confined 

 our attention to the planes themselves. It must be recognized, 

 however, that on account of the intimate relation usually exist- 

 ing between karyokinesis and cytoplasmic division, the arrange- 

 ment of the cleavage planes stands, to some extent at any rate, 

 in relation to the direction in which the karyokinetic spindle 

 lies, and we may carry our inquiries a little further and seek 

 to determine the cause of the positions assumed by the spin- 

 dles. Berthold's law, of course, refers only to the arrange- 

 ment of the cleavage planes ; granting the division of the cell 

 in any direction, the flattening which its surface undergoes, or 

 the shifting which it itself undergoes, is governed by the law 

 of minimal contact surfaces, and this depends on the forces 

 which we term surface tension. Now it is clear that Berthold's 

 law affects only the form and, within narrow limits, the posi- 

 tion which a cell may possess ; it does not necessarily affect 

 the plane in which that cell may divide. On the other hand, 

 Sachs' law attempts to define the direction which the spindle 

 shall occupy, the plane in which the division shall occur, and, 

 therefore, has a much deeper significance. It formulates a 

 certain number of the factors which influence the direction of 

 the division planes, the most important of these factors being 

 that of form. It has been shown, however, that exceptions 

 occur to one at least of the factors, and even so far as the fac- 

 tor of form is concerned, it is readily seen that it is not all- 

 sufficient to explain variations which occur in the cleavage of 

 ova having a similar form. Thus it does not explain why the 

 spherical yolkless ovum of an Ascidian should have a bilateral 

 cleavage, as shown by van Beneden and Julin, 1 while the appar- 

 ently similar ovum of an Echinoderm should undergo what 

 may be termed a radial cleavage ; we must go deeper, and add 

 to the factor of form that of the constitution of the cell. But 

 even this hardly suffices, for we can hardly imagine that differ- 

 ent ova from a single individual can differ very greatly in their 



1 E. van Beneden and C. Julin : La segmentation chez les Ascidiens et ses rap- 

 ports avec 1'organisation de la larve. Arch, de Biol., V, 1894. 



