VIIl] 



THE SEGMENTATION OF A DISC 



359 



cell, we have no difficulty with the first two cell-divisions; for 

 we know that no bisecting partitions can possibly be shorter than 

 the two diameters, which divide the cell into halves and into 



Fig. 144. Development of Erythrotrichia. (After Berthold. 



quarters. We have only to remember that, for the sum total of 

 partitions to be a minimum, three only must meet in a point; 

 and therefore, the 'four quadrantal walls must shift a httle, pro- 

 ducing the usual httle median partition, or cross-furrow, instead 

 of one common, central point of junction. This little inter- 

 mediate wall, however, will be very small, and to all intents and 

 purposes we may deal with the 

 case as though we had now to do 

 with four ec[ual cells, each one of 

 them a perfect quadrant. And 

 so our problem is, to find the 

 shortest line which shall divide the 

 quadrant of a circle into two 

 halves of equal area. A radial 

 partition (Fig. 145, a), starting 

 from the apex of the quadrant, is 

 at once excluded, for a reason 

 similar to that just referred to; 

 our choice must lie therefore between two modes of division such 

 as are illustrated in Fig. 145, where the partition is either (as in b) 



Fig. 14.5. 



