STUDIES IN STATISTICAL REPRESENTATION. 



On the Nature and Computation of the Curve 



y = Ax- e™» 



By G. H. Knibbs, c.m.g., f.s.s., f.r.a.s., etc., 





stati- 



The curve and its origination. 



Synthesis of the curve. 



Points of inflexion of constituent c 



Variety of the form of curve. 



Logarithmic homologue of curve. 



Critical points of curve. 



Determination of constants of cur\ 



Weight of results. 



Algorithm of practical solution. 



Integral of the curve. 



of integration. 



lues of abscissa. 



Partieuls 

 The cons 

 Approxi, 



MI.-. 



1. The curve and its origination.— A single expression 

 which, by variations of its constants, will reproduce the 

 great majority of the curves required to represent data 

 furnished by physical observations and statistical enumer- 

 ations has certain obvious advantages, and an appropriate 

 study of the nature of the variation of the constants of such 

 an expression would unquestionably go far to facilitate 

 their rational interpretation, and reveal their inter-rela- 

 tions. I propose to shew that a single expression will cover 

 a great range of requirements, excepting however those 

 curves which, following Helguero, 1 may be called dimorphic 



