Skcw frequcncy curvcs in Biology 

 and Statistics 



by 



J. C. KAPTEYN, Ph. D.; Se. D. 



Professer of Astronomy at Groningen. 



1. Introduction. The substance of the following paper 

 was delivered as a lecture before the scientific section of 

 the Physical society of Groningen on 14 October 1916. 

 It was meant as a popular exposition of the investigations 

 contained in two more extensive papers published by 

 the Astronomical Laboratory at Groningen, the fîrst of 

 which (by J. C. Kapteyn) appeared in 1903, the second 

 (by J. C. Kapteyn and M. J. van Uven) in 1916^). 

 In what follows I will refer to thèse papers as first and 

 second paper. 



In writing my part of the second paper — and as a 

 matter of fact even already in the first — I tried, as 

 much as was in me, to avoid any superfluous mathematical 

 development. I found however, that, if we wish to develop 

 the theory in as rigourous a form as possible, it is not 

 well possible to avoid some, to the gênerai reader very 

 formidable looking formulae. As I know very well that 

 this fact will be much in the way of a somewhat extensive 

 application of the theory, I resolved, even at the time of 

 writing the second paper, to work out also a popular 



') Printed by Hoitsema Brothers, Groningen. 



