RECENT ADVANCES IN SCIENCE 357 



The Laws of Statistical Astronomy. — An important review of 

 " The Determination of the Principal Laws of Statistical 

 Astronomy," by W. J. A. Schouten, being an Inaugural Dis- 

 sertation at Amsterdam, has been published by W. Kirchner 

 of Amsterdam. The chief statistical laws, which are required 

 to summarise our knowledge of the stellar system, are (1) the 

 law determining the variation of stellar distribution in different 

 parts of space, both in and out of the Milky Way ; (2) the law 

 of frequency of the luminosity in any part of space ; (3) the 

 law of distribution of the velocities. Various methods have 

 been employed in recent years to determine the nature and 

 form of these laws, the results which have been obtained being 

 in some instances markedly discrepant. Dr. Schouten 's dis- 

 sertation contains a critical examination of the principal methods. 

 The data upon which any determination of the fundamental 

 laws must be based are the same, viz. (1) the variation of mean 

 proper-motion with galactic latitude ; (2) the variation of 

 colour-index with galactic latitude ; (3) the distribution of 

 spectral types with respect to the galaxy ; (4) the galactic 

 condensation for stars of different magnitudes. 



An extensive account is given of the researches of Seeliger, 

 which are critically discussed, objections to the foundations of 

 his method being pointed out. Seeliger's work has been super- 

 seded by the later work of Schwarzschild, Kapteyn, and others, 

 but his critical summary will be found of value for purpose of 

 reference, the more so as Seeliger's researches are scattered 

 through many different publications. The methods used by 

 Schwarzschild and Kapteyn are compared : these methods differ 

 fundamentally in that whilst Schwarzschild expresses his data 

 empirically as mathematical functions, Kapteyn uses a method 

 which is more numerical. The former method possesses the 

 greater mathematical elegance, but the latter has the advan- 

 tages of being able readily to distinguish within what limits of 

 distance or luminosity the results are based on numerical data 

 and to what extent they are mere extrapolations. 



Dr. Schouten, as befits a pupil of Kapteyn, is in favour of 

 the latter's method, and the last portion of his dissertation 

 consists of a discussion of the best modern data on that method. 

 The results obtained, as might be expected, agree fairly well 

 with those obtained originally by Kapteyn ; it is known that 

 although the data available to Kapteyn were in places very 



