No. 641] THE BATE OF GROWTH 549 



TABLE II 

 Comparison of Constants 



First Cycle i Second Cycle \ 



\ a \ K \ a K \ 



I 175 I !0234 , 230 '.nOTC .ir! djv. 



j 220 .0193 288 .OOMl l'C.S <la.v- 



! 236 I .0180 300 .OI.'jO l2Mi day> 



1 175 ' .0260 : 230 .0231 UVl days 



C. Rates of Growth as Computed feom Values of dx/dt 

 It is unnecessary to dwell upon the prime importance 

 of the study of rates in physiological investigations. We 

 are concerned not only with what the organism is, but 

 how it came to be what it is. As soon as we begin to 

 study the problem of development, we encounter the ques- 

 tion of rates. No better means of studying the rate of 

 change in a system has yet been found than the ditTer- 

 ential calculus. 



The differential equation representing the rate of auto- 

 catalvsis is 



a, X and t represent the same values as before, but 

 h = K/a. We may proceed, therefore, to examine the 

 derivatives of the equations used above to express the 

 sizes of the animals at various time intervals. Tho vahies 

 obtained for the growth of males and fnnalrs arc sliown 

 in Figs. 6 and 7 in com]")arisoii with tlir ()l)si'i-\ cil weekly 

 increases of the animals which hav<^ hccii studitMl. The 

 computed vahies \\v\\^ (»1)tain(Ml from the tables published 

 by Kobertsoii'^ wiiieh give the vahies of I 1 K<,) . {(Ir'dt) 

 for correspoiuHiig values of /\'( / /, ). 



The rate of uTouth cf male rats on ade-iuatr .het was 

 computed for eaeh c^ele from the liuni-es in Tab],' j. The 



