VI [] 



OF THE POLAR FURROW 



489 



any two are related precisely as though two cells only were conjoined; the 

 centres of three contiguous cells (as c, c' and c") are related as though three 

 only were concerned; and the centres of two opposite cells are situated 

 symmetrically to one another. This is as much as to say that if there be 

 two bubbles in contact the addition of a third does not disturb their symmetry; 

 and if there be three in contact, the addition of a fourth leaves the first three 

 likewise in statu quo. Thus the triangle cc'c" is equilateral, as we already 

 know. The partition so bisects the side cc", and the angle cc'c"; and the 

 point o is the centre of gravity of the triangle. Therefore oj) — \oc" and 



Fig. 174. The geometric symmetry of a system of four cells. 



Again, in the triangle cpc", where cc" = r, pc" — ^r, and oo' (the polar 



f urrow) = -7:^ r. Once again, in the triangle soc", sc = r; and so (one of 

 V3 



2 

 the partitions) = -^ r = twice 00'. The length of the polar furrow, then, as 



V.3 

 seen in vertical projection in a system of four co-equal cells, is (theoretically) 

 just one- half that of the four intercellular partitions, and very nearly three- 

 fifths that of a c(4l-radius. 



It is worth while to remark that the universal phenomenon of a 

 polar furrow gives an appearance of bilateral symmetry to every 

 egg or embryo in its four-celled stage, no matter to what kind or 

 class or organism it belongs. 



