120 



pendent in the case of the diameters, then they cannot 

 longer be considered to be independent in the case of 

 the volumes. 



The difficulty of understanding, how it cornes to pass 

 that the volumes necessarily give a skew curve, in the 

 case that the diameters give a normal one, is thereby 

 removed. 



10. Skew curves generated by causes \vhose effect 

 dépends on size. The net resuit of the preceding article 

 may be considered to be that, wherever causes are at 

 work, the effect of which dépends on the size of the 

 individuals, there we must expect skew curves. The con- 

 séquence must be that, whereas the reasoning of arts 4 — 7 

 might seem to lead to the conclusion that the normal 

 frequency-curves must be the rule in nature, we will 

 conclude now that they must be the exception. For it 

 will be clearly perceived that, even if we assume the 

 effect of certain causes in producing déviations in certain 

 quantities x, to be independent of the value of x, this 

 cannot be the case with quantities proportional to x~. x^, 



— etc., or more generally with any quantities whatever 



X 



depending on x, which are not proportional to x itself. 



We thus are led to consider the reverse of the former 

 difficulty, that is: how is it, that normal curves, or at 

 least curves but imperceptly différent from normal curves 

 are so common in nature. 



The answer seems not difficult to give. 



In the case of our example it would be as follows: 



As long as the variations in the diameters of the berries 

 are small as compared to the diameters themselves, the 

 effect of the several causes of growth in volume, which 

 dépend on the size of the berries, must be httle différent 

 too. Suppose for instance that the diameters of ail our 

 berries ranged only from 7 to 8mm, then the effect of 



