220 



the true gênerai équation of the frequency curves is not 

 Prof. Pearson's équation, but simply the équation of 

 the curves of Edge worth-Kaptey n '), The identity is 

 only hidden by the fact that it is the differential équation, 

 whereas I derived at once the équation in its finite form. 

 Everybody may convince himself of the fact by simply 

 differentiating équation (1). In order to accomodatc to Prof. 

 Pearsons notation in équation (8) he has only, to substitute : 



f{x) for Fix) — ^) 



so that this équation becomes: 



(5) y = — -^- /■■ (X) e ~2o~' ^^ ^'^^^^ 



and further to introduce Pruf. Pearsons abbrcviation 

 (p. 178) 



(6) F (r) — ^^ ^^^ 



This proves point I. 



As to point IL 



One would naturally imagine that, if it be true, as 

 shovvn just now, that Prof. Pearson dérives his own 

 curves from those given by myself, both curves must be 

 identical ; the only possible différence being that my for- 

 mulae must be rigorous, whereas Prof. Pearson's, in 

 which only a few terms of M a c 1 a u r i n's séries are used, 

 must be only more or less approximate. 



1) If Prof. Edgeworth lias no objection I will gladly adopt 

 this denonaination applied to thera by Prof. Pearson. 



2) This does noI raean, as Prof. P e a r s o n erroneously supposes, 

 that we choose the mode as the origin (p. 178). 



