GEOMETRICAL RELATIONS OF CLEAVAGE-FORMS 2 77 



the nature of the forces that determine the position of the spindle- 

 axis. Piiiigeri assumed that this position must be that of least 

 resistance to the elongation of the spindle, which is obviously in the 

 long axis of the protoplasmic mass ; and the same view has been 

 advocated by Braem and Driesch. Now, there can of course be no 

 doubt that the final direction of the spindle, like that of any body, is 

 the position of least resistance, i.e. the position of equilibrium de- 

 termined by the resultant of all the forces operating upon it. The 

 undetermined point is whether these forces are of a simple mechani- 

 cal nature, such as pressure and the like, or of a more subtle physio- 

 logical character. Roux seeks them in the "tractive forces" of the 

 protoplasmic mass modified by an innate predisposition to a partic- 

 ular form and succession of divisions that has its seat in the nucleus. 

 Heidenhain identifies them with conditions of intra-cellular tension 

 determined by the astral rays. 



It cannot be doubted that all these forces may play a part in de- 

 termining the position of the spindle, but it must be confessed that 

 the problem is still very far from a solution. In some cases Hert- 

 wig's law is directly opposed to the facts, the spindle lying trans- 

 versely to the axis of the protoplasmic mass. In other cases, as for 

 instance in the division of some Protozoa {Ejiglypha, t. Schewiakoff) 

 and in segmenting ova {Crcpidida, t. Conklin), the protoplasmic 

 elongation leads the way, and may be fully determined before the 

 spindle is formed. In still other cases the reverse is true, as in the 

 formation of the polar bodies, where the spindle forms and rotates 

 into position before the ^gg shows any corresponding change of 

 form. In many ova we can assign no mechanical cause for the rota- 

 tion, such as the pressure of deutoplasm and the like ; and even 

 when deutoplasm is present, its position is such that we should 

 expect a horizontal rather than a vertical position of the polar 

 spindles were it a mechanical result of the presence of deutoplasm. 



The ultimate determination of the planes of division is probably to 

 be sought in those influences that determine the movements of the 

 centrosomes. Sachs's law of rectangular succession is primarily a 

 result of the fact that the daughter-centrosomes typically diverge, 

 and so determine the spindle-axis, in a line which is at right angles 

 to the axis of the mother-spindle ; hence the ensuing cleavage is 

 vertical to the last.^ What we do not really understand is the prin- 

 ciple by which this typical succession is modified. The pressure- 

 experiments prove that the modifications may be produced by simple 



\ 'S4, p. 613. 



- In this we find also an explanation of the fact first observed by Roux in the frog's egg, 

 and confirmed by me in the sea-urchin egg, that the first plane of cleavage passes through 

 the sperm-track and hence approximately through the entrance-point of the spermato?:oon. 



