No. 641] 



THE BATE OF GROWTH 



541 



log =K{t — i,), 



in which x represents the weight of the animals at time 

 f, a represents their weight at the end of the cycle, is 

 the time at which the weight, is one half a, and K is a 

 constant. 



Although the quantitative relationships of this growth 

 rate have been ably discussed by Hatai,'^ it will be shown 

 subsequently that there are numerous reasons for using 

 the above-mentioned formulas for computing growth. 

 The computation of these and other growth rates studied 

 in this paper have been made with the aid of tables pub- 

 lished by Robertson.* 



Table I contains data on the growth of white rats in 

 the first year of life. The data for the rats were taken 

 from Donaldson's tables 63 and 64. 



The equations for the growth of the animals are as 

 follows : 



Males, first cycle, log oosZZ'i " -^'^^^ " - '^'^'^ 



Males, second cycle, log 7,-^^^ =.0123 — 2\',i) 



Females, first cycle, log yf^^— =.02U(t — 61) 



It will 1)0 noticed the ca lciil;i t iou of the second 



cycle involves a cliaiiuc cf ilic axes of tlie coordinates 

 so that the new point of origin is near the point at which 

 the first cycle of growth ended. Tlu' fir^t cycle of growth 

 in the female appears to terminate somewhat earlier than 

 that in tlio male and the value of K, the constant, was 

 uieater in the growth curve of the female. These rela- 

 tii.ii- auiee with the repeated observation that in early 

 lile I he leniale grows more rapidly than the male. In the 



(M.nd rxcle the female uT.nv- h->. vapidly than the male. 



