VIIl] 



THE BISECTION OF A QUADRANT 



363 



one is a triangle (MAP) with two sides formed of circular arcs, 

 and the other is a four-sided figure (MOBP), which we may call 

 approximately oblong. We cannot say as yet how the triangular 

 portion ought to divide ; but it is obvious that the least possible 

 partition-wall which shall bisect the other must run across the 

 long axis of the oblong, that is to say periclinally. This, also, is 

 precisely what tends actually to take place. In the following 

 diagrams (Fig. 148) of a frog's egg dividing under pressure, that 

 is to say when reduced to the form of a flattened plate, we see, 

 firstly, the division into four quadrants (by the partitions 1, 2) ; 

 secondly, the division of each quadrant by means of an anti- 

 clinal circular arc (3, 3), cutting the peripheral wall of the quadrant 

 approximately in the proportions of three to seven ; and thirdly. 



Fig. 148. Segmentation of frog's egg, under artificial compression. 

 (After Roux.) 



we see that of the eight cells (four triangular and four oblong) 

 into which the whole egg is now divided, the four which we have 

 called oblong now proceed to divide by partitions transverse to 

 their long axes, or roughly parallel to the periphery of the egg. 



The question how the other, or triangular, portion of the divided 

 qudarant will next divide leads us to another well-defined problem, 

 which is only a slight extension, making allowance for the circular 

 arcs, of that elementary problem of the triangle we have already 

 considered. We know now that an entire quadrant must divide 

 (so that its bisecting wall shall have the least possible area) by 

 means of an antichnal partition, but how about any smaller 

 sectors of circles? It is obvious in the case of a small prismatic 



