No. 546] SHORTER ARTICLES AND DISCUSSION 367 



the nuclear material of a given cell increased when that cell 

 divides? Or, what is essentially the same, when several cells 

 are present, as usually in a developing egg : In what proportion 

 is the total nuclear material increased when all of the cells 

 divide once? It appears to me that these questions are the 

 ones that have been in mind when it has been held that the nu- 

 clear material increases nearly 100 per cent, at each cleavage, 

 so that the relation of the ratio used by Conklin to the ratio 

 implied by them is of interest. 



The ratio implied in the questions just set forth— the ratio 

 of increase in the nuclear material of a given cell after that cell 

 has divided — is of course obtained by dividing the nuclear vol- 

 ume of the two resulting cells by this volume in the mother cell ; 

 or by dividing the total nuclear volume of the egg after all its 

 cells have divided once by the total volume before the cells 

 divided. (Inclusion of several cells, each of which divides once, 

 of course does not of itself alter the ratio.) Performing these 

 operations for the mean nuclear volumes in Crepidula, as given 

 in Conklin 's Table 9, one finds the ratios in question to be for 

 the second cleavage 1.40, for the third 1.25, for the fourth 1.19, 

 for the fifth 1.89. That is, in passing from the 2-cell to the 4-cell 

 stage, the nuclear volume of each mother cell increases 40 per 

 cent. ; in passing from the 4-cell to the 8-cell stage, the increase 

 is 25 per cent. ; from the 8- to the 16-cell stage it is 19 per cent. ; 

 from the 16- to the 32-cell stage it is 89 per cent. These ratios 

 are not 100 per cent, at each division, but they approach it more 

 nearly than the ratio Conklin employs. If we average the in- 

 crease for these four cleavages, we find the mean to be 43 per 

 cent. That is, at each cleavage, the nuclear volume of the cell 

 increases on the average by 43 per cent. 



It may be noted that even with an absolutely constant ratio 

 between the nuclear volume in a given cell before cleavage and 

 that in its products after cleavage, the ratio employed by Conk- 

 lin would, as a rule, if I have correctly interpreted it. decrease 

 rapidly as we pass to later cleavage stages. The relation be- 

 tween the two ratios would be that shown by the following 

 formula, in which x = Conklin 's ratio; r = the (constant) ratio 

 of the nuclear volume after division of a given cell to the nuclear 

 volume before that division; « = the number of the cleavage 



