GEOMETRICAL RELATIONS OF CLEAVAGE-FORMS 



365 



planes according to Sachs's second rule. The first division of a homo- 

 geneous spherical egg, for example, is followed by a second division 

 at right angles to it, since each hemisphere is twice as long in the 

 plane of division as in any plane vertical to it. The mitotic figure 

 of the second division lies therefore parallel to the first plane, which 

 forms the base of the hemisphere, and the ensuing division is vertical 

 to it. The same applies to the third division, since each quadrant is 

 as long as the entire egg while at most only half its diameter. Divi- 

 sion is therefore transverse to the long axis and vertical to the first 

 two planes. 



Taken together the rules of Sachs and Hertwig, applied to the 

 egg, give us a kind of ideal type or model, well illustrated by the 



Fig. 169. Cleavage of the ovum in the holothurian Synapta (slightly schematized). [After 

 SELENKA.] 



A-E. Successive cleavages to the 32-cell stage. F. Blastula of 128 cells. 



cleavage of Synapta, described above, to which all the forms of cleav- 

 age may conveniently be referred as a basis of comparison. Numer- 

 ous exceptions to all four of these rules are, however, known, and they 

 are of little value save as a starting-point for a closer study of the 

 facts. Cleavage of such schematic regularity as that of Synapta is 

 extremely rare, both the form and the order of division being end- 

 lessly varied and in extreme cases showing scarcely a discoverable 

 connection with the "type." We may conveniently consider these 

 modifications under the following three heads : 



