131 



is the relative intensity with which individuals of différent 

 size react on the causes of growth. 



The dérivation of the reaction-curve constitutes the 

 solution of part b of our problem. The solution of the 

 probletn proposed at the beginning of art. 13 is thereby 

 completed. As already mentioned the présent example was 

 chosen in such a way that z becomes a simple algebraic 



function. The conséquence is that -/ too becomes such 



a function. Indeed the reaction is inversely as the square 

 of the dimensions as is shown by the last column which 



shows the values of --- 2 • Thèse values are practically 



equal to those of the 6th col.; only the first is strongly 

 divergent. As will be shown below (Remark II) this is 



entirely due to the unavoidable uncertainty of --,- near 



z 



the limits of the frequency curve. 



Rcmark L In the preceding dérivation is involved the 

 tacit assumption that the rapidity of the growth at 

 X = 0.25, 0.75 etc. is the same as the average rapidity 

 between the limits x = and x = 0.5 ; x = 0.5 and x = 1.0 

 etc. I think that in pretty well ail cases of practice this 

 assumption is completely allowable. If however in any 

 particular case there should remain any doubt on the 

 matter, recourse might be had to well known mathema- 

 tical methods. For those not conversant with such methods 

 I would recommend interpolation for smaller intervais of 

 the X in the, thoroughly smoothed, scheme. So for instance 

 in table 2 we would obtain by graphical interpolation by 

 a large scale figure, the values of the ordinates of the 

 scheme for x = 0.25, x = 0.75 etc. If thus operating 

 with double the number of intervais, we are led to prac- 

 tically the same results as before (after multiplication of 

 ail the values by a constant, which in the présent case will 



