540 THE AMiERICAN NATURALIST [Vol. LV 



idly growing apricot shoots. In each case the rate was 

 proportional to a function of the final length of the shoot. 

 The shoots which had a greater final length at the end 

 of the season grew more rapidly from the start than their 

 shorter neighbors, though the growing periods of the two 

 samples were the same. The particular point of interest 

 lay in the fact that the equations representing the growth 

 rates had the same value for the constant of the reaction, 

 differing only in the value of the constant expressing the 

 final length of the shoots. 



The present paper attempts to supplement this work 

 by investigating the growth of organisms which reached 

 approximately mature size after being subjected to con- 

 ditions which suppressed growth in early life. 



In the former case the difference between the two lots 

 was in their final size ; in the present case the difference 

 betw^een the two lots was in the time required to make 

 equivalent body weight. 



A. The Eate of Growth of Eats ox Adequate Diets 

 The growth of the white rat has been so completely 

 studied by many investigators that no extended discus- 

 sion of the subject is required. 



The rate of growth of rats varies slightly in different 

 lots, but in general it follows the course of a differential 

 equation. In later paragraphs I shall show that the 

 equations used are those which express an autocatalytic 

 reaction. The rate at which each sex grows is quite char- 

 acteristic. The females grow^ relatively faster in early 

 life than the males, come sooner to maturity, and weigh 

 less at maturity than the males. 



The growth of a white rat in the first year comprises 

 two cycles. The first cycle, covering approximately 150 

 days, consists of a rapid increase in the weight and size 

 of the body. The second cycle, covering the remaining 

 200 days, consists of a thickening of the body and a 

 deposition of fat. The growth of rats in each of these 

 cycles may be expressed by the equation 



