STATISTICAL METHODS IN STELLAR ASTRONOMY 



BY JACOBUS CORNELIUS KAPTEYN 



[Jacobus Cornelius Kapteyn, Professor of Astronomy, University of Groningen, 

 Holland, since 1878. b. Barneveld, Holland, 1851. Ph.D. 1875. Assistant at the 

 Observatory at Leiden, 1875-78. Member of Academy of Sciences, Amsterdam; 

 Royal Astronomical Society; and various other scientific societies. Author of 

 The Cape Photographic Durchmusterung (together with Director Gill) ; Determin- 

 ation of Parallaxes and Proper Motions ; Motion of the Solar System ; Distri- 

 bution of Stars in Space; Determination of Latitude; Methods of Measuring Star 

 Photographs; and numerous other articles on astronomy and mathematics.] 



THE remark has been made several times lately: "The nineteenth 

 century has brought the problem presented by the motions in our 

 solar system to a certain issue. It will be the task of the twentieth 

 to attack the problem of the arrangement and motions in the stel- 

 lar universe." Science has put astronomers in the possession of new 

 weapons eminently suitable for the purpose: 

 Photography which dreads no numbers. 

 Spectroscopy which does not care for distance. 

 Is it possible with their aid even now to make some plan of cam- 

 paign? 

 That is: 



Can any way be suggested for the solution of what a famous 

 astronomer recently very conveniently called the sidereal problem? 



You will forgive me if, in trying to answer this broad question, 

 I wholly restrict myself to presenting my own views on the matter. 

 I am sure that nobody can appreciate more highly than I do, what, 

 to mention only a few of the most recent investigations, such men 

 as Schiaparelli, Newcomb, Seliger, Kobold, Easton, are doing, but 

 want of time utterly prevents me from discussing their methods in so 

 far as they differ from my own. 



From an astrometrical point of view the problem in its simplest 

 form comes to this: to determine for every individual star its posi- 

 tion, velocity, and mass. 



For practical reasons we may add: its total quantity of light, 

 which in what follows we will call its luminosity, though we thus 

 encroach somewhat on the domain of astrophysics. If we assume, 

 as there is ample reason to do, that Newton's law holds good for 

 the whole of the stellar universe, then these data determine the past, 

 the present, and the future arrangement of the stars in space. 



We may safely assume that the problem will never be completely 

 solved in this form; for the mass of data, even if it could ever be 

 obtained, would be so overwhelming, that it would defy any detailed 

 mathematical treatment. 



But what we may hope to attain and for which I think we possess 



