;')() Robertson, Further Explanatory Remarks Concerning etc. 



temperature or mass, and consequently the autocatalytic formula 

 of growth can only legitimately he applied to the growth of mass. 



b) Since, as Moeser very justly points out, temperature, 

 moisture, and a number of other factors have an influence upon 

 growth, and we usually possess little certainty all that of these factors 

 are maintained constant during the growth of a single individual, 

 it is safer, in order to eliminate fluctuating variations due to these 

 uncontrolled variables, to measure and average the growth of a 

 very large number of individuals, rather than to depend as Moeser 

 does, upon measurements made upon a single individual. 



c) In order to avoid assuming that the maximum increment 

 in growth occurs at the middle of a growth-cycle (i. e. when the 

 total growth due to the cycle is half completed) Moeser suggests 

 the following modification of my formula. 



The differential equation which expresses the progress of an 

 autocatalytic (monomolecular) reaction is the following: 



-^ = Kx(A-x) ........ (1) 



in which x is the mass which has undergone transformation (= growth) 

 at time t and A is the final mass which has undergone transformation 

 at the end of the reaction (i. e. the total growth at the end of the 

 growth-cycle). 



Integrating, we obtain : 



In-^-, =KAt + C ...... (2) 



J\. X 



where C is the constant of integration. 



In my derivation of the growth formula I proceeded as follows : 

 Since the value of C must be the same for all values of x let us 

 make x = 1 / 2 A and let t 1 be the corresponding value of t, then 

 from equation (2) we have: 



KAti-fC^o ......... (3) 



hence : 



C=--KAt 1 .......... (4) 



and equation (2) becomes: 



t-t 1 ) ...... (5) 



Moeser, however, proceeds from equation (2) as follows: 

 When t = o let x = v, then when t = o we have: 



(6) 



A v 



hence (2) becomes 3 ): 



Inw^^^KACt-tJ (7) 



3) For the constant A, Moeser employs the symbol V. 



