VIII] THE SEGMENTATION OF A DISC 369 



This is as much as to say that, supposing each cell tends to 

 divide into two halves when (and not before) its original size is 

 doubled, then, in our flattened disc, the triangular cell T will tend 

 to divide when the radius of the disc has increased by about a 

 third (from 1 to 1-345), but the quadrilateral cell, Q, will not tend 

 to divide until the linear dimensions of the disc have increased 

 by about a half (from 1 to 1-517). 



The case here illustrated is of no small general importance. 

 For it shews us that a uniform and symmetrical growth of the 

 organism (symmetrical, that is to say, under the limitations of a 

 plane surface, or plane section) by no means involves a uniform 

 or symmetrical growth of the individual cells, but may, under 

 certain conditions, actually lead to inequality among these; and 

 this inequality may be further emphasised by differences which 

 arise out of it, in regard to the order of frequency of further 

 subdivision. This phenomenon (or to be quite candid, this 

 hypothesis, which is due to Berthold) is entirely independent of 

 any change or variation in individual surface tensions ; and 

 accordingly it is essentially different from the phenomenon of 

 unequal segmentation (as studied by Balfour), to which we have 

 referred on p. 348. 



In this fashion, we might go on to consider the manner, and 

 the order of succession, in which the subsequent cell-divisions 

 would tend to take place, as governed by the principle of minimal 

 areas. But the calculations would grow more diSicult, or the 

 results got by simple methods would grow less and less exact. 

 At the same time, some of these results would be of great interest, 

 and well worth the trouble of obtaining. For instance, the precise 

 manner in which our triangular cell, T, would next divide would 

 be interesting to know, and a general solution of this problem is 

 certainly troublesome to calculate. But in this particular case 

 we can see that the width of the triangular cell near P is so 

 obviously less than that near either of the other two angles, that 

 a circular arc cutting off that angle is bound to be the shortest 

 possible bisecting line; and that, in short, our triangular cell 

 will tend to subdivide, just like the original quadrant, into a 

 triangular and a quadrilateral portion. 



But the case will be different next time, because in this new 



T. G. 24 



