128 



BIOLOGICAL LECTURES. 



w 



FIG. 2. (After Sachs.) 



planes divide it into two parts, a third plane at right angles 

 to the first two dividing the middle cell (Fig. 2, B) ; where 

 it is club-shaped the arrangement of the 

 division planes is that shown in Fig. 2, C' } 

 and, finally, not to multiply examples, where 

 it has a tetrahedral form the four resulting 

 cells are also arranged in a tetrahedral man- 

 ner (Fig. 2, D). 



We have, then, as the first thesis that the 

 direction and arrangement of the cleavage 

 planes is dependent, to some extent at least, 

 upon the form of the original mass. To this Sachs adds two 

 other theses to the effect that there is a tendency for cells to 

 be equally divided, and that successive cleavage planes tend 

 to be arranged at right angles to those which precede them. 

 These three theses may be grouped together and spoken of as 

 Sachs' law of right-angled division. 



Let us now, following Sachs' example, apply this law to a 

 comparatively simple case, noting the result with the view to 

 observing if it agrees with what 

 is actually found in Nature. For 

 this purpose Sachs chooses a disc 

 of protoplasm with an elliptical 

 outline (Fig. 3) which is to un- 

 dergo division only at right an- 

 gles to the surface, i.e., only in 

 two planes. The first two divi- 

 sions will naturally correspond 

 with the longer and shorter axes 

 of the ellipse, and will divide it 

 into four segments. 



FIG. 3. (After Sachs.) 



To carry out the law the succeeding 



divisions will necessarily fall into two series ; in the first place 

 there will be a series of cleavage planes which form ellipses 

 (/, /) confocal with one another and with the periphery of the 

 original elliptical disc of protoplasm, and secondly, crossing 

 these there will be two series of planes (a, A, a), each of 

 which consists of a number of confocal hyperbolas arranged 

 around one of the foci (/) of the original ellipse. Sachs 



