221. 



As a matter of fact this identity, or approximate iden- 

 tity, will not exist at ail but in a few very exceptional 

 cases. 



As a conséquence thereof Pearsons formulae will lose 

 their rational character. 



The reason is that to substitute the expression 



(7) a„ + «1 a; 4- «2 x^ 



for F (x) and for a long range of values of x, is permis- 

 sible (even as an approximation) only in quite excep- 

 tional cases. 



If it be permissible to substitute the expression (7) for 

 F (x), why not for 



F {X) 



which would make the équation (3) still simpler, or, sim- 

 plest of ail, why not take (7) for the ordinatès of the 

 frequency-curves themselves. 



The only possible answer is, that expérience shows that 

 Pearsons assumption leads to équations which can be 

 made to represent tolerably a great number of observed 

 frequency-curves, whereas the other assumptions do not. 



But this is équivalent to admitting that Pearsons 

 curves are purely empirical; which is just what I maintain. 



It settles Point IL ') 



In Conclusion. As Prof. Pearson now dérives his own 

 theory from mine, it need not be said that every objection 

 raised by him against my gênerai theory bears directly on 

 his own. 



Of the objections contained in his paper against the 

 spécial case (causes proportional to some power of x -f- x) 



1) The same reasoning still holds of course in the case that 

 more terms of a Maclaurin expansion are included. 



