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a. is it possible to assign other quantifies z, pure func- 

 tions of X, which are normally spread? 



h. is it possible to find the way in which the déviations 

 dépend on the size of the individual? 



The importance, especially of the last question will be 

 apparent, if we try to realize its true meaning in those 

 cases where, as for plants and animais or parts thereof, 

 there is groivth. 



For individuals of one determined size, under the influence 

 of one cause, I call growth the average increase in size 

 of ail thèse individuals; 



fluctuations the individual déviations from the average. 



In most of the cases it will presumably be permissible 

 to assume that the average of the fluctuations (thèse being 

 ail taken positively) is proportional to the growth; in 

 other words that the average fluctuation is a certain per- 

 centage of the growth. In what follows we will assume 

 that it is so. The conséquence will be that the growth 

 will be proportional to the total déviation and we may 

 formulate our question b: is it possible to find the way 

 in which the growth dépends on the size? 



Suppose the question solved we might then for instance 

 find that the growth for plants of a certain size becomes 

 ail but zéro and we would thus be led, by the simple 

 considération of the frequency curve of the plants harvested 

 at an arbitrary epoch, to the conclusion that there is a 

 period of rest in the growth at the time at which the 

 plants reach such and such a size. Our attention might 

 thus, in quite a new way, be drawn to interesting détails 

 in the process of growing. 



Coming back now to our questions a and b themselves, 

 I will develop their solution by the considération of a 

 particular example: 



Suppose we hâve obtained from the observation of 



