217 



a normal frequency curve, then other characters propor- 

 tional to any function (p {x) of that character will be 

 generally distributed according to an asymmetrical fre- 

 quency curve. 



This remark is undoubtedly correct and, rightly translated 

 into a matheraatical formula, vvould lead to the following 

 équation 



,., h ^, . ^ — k" [F(x) — MY 



(1) y z=z —- F' {X) e 



F (x) being the solution for z of the équation x — fp (s). 



Now this équation is no other than the fundamental 

 équation at which I arrived in my paper (p. 16). 



If, notwithstanding this, I still feel justifled in claiming 

 my part in the ownership of this formula, it is on the 

 ground that Prof. E d g e w o r t h's remark, correct though it 

 be, is still not équivalent to a gênerai theory. 



It does not prove that (1) must be the gênerai équation 

 of frequency curves. Prof. Edgewo.rth expressly says 

 that it is not (l.c. p. 8). Nor does the theory, and this is 

 the ail important point, connect thèse curves in any way 

 with the causes, which give rise to them. 



The gênerai theory involves the solution of this problem 

 (and its reverse): 



„0n certain quantifies x, which at starting are equal, 

 „there come to operate certain causes of déviation, the 

 „effect of which dépends in a given way on the value 

 „of x. What will be the frequency-curve produced?" 



It is this problem which I treated in my paper and of 

 which the gênerai solution is given p. 15 — 16. It leads to 

 the identical équation (1), when the effect of the causes 

 is proportional to 



1 

 F' [x) 



The différence m the signiflcance of the resuit, however, 

 is évident. 



