( 145 ) 



data, namely by those derived from the double stars. The optically 

 double stars cannot however teach ns anything about the masses of 

 the stars themselves as will appear from the following consideration 

 (also occurring in "The Stars" by Newcomb). Let us suppose that a 

 binary system is 7^ times as near to us, while all its dimensions 

 become n times as small, but that the density and the radiation 

 remain the same. Then the mass will diminish in the propor- 

 tion of 7i' to 1, the major axis of the orbit a in the proportion 

 of n to 1 and hence the time of revolution remains the same ; 

 the luminosity becomes ii^ times as small, therefore the apparent 

 brightness remains the same as well as the apparent dimensions of 

 the orbit, in other words: it will appear to us exactly as it was 

 before. Hence the mass cannot be found independently of the 

 distance. Let a be the angular semi-major axis, M the mass, P 

 the time of revolution, d' the density, ). the radiating power, ti the 

 parallax and q the radius of the spherical volume of the star, then 



we shall have: rrM/^ — : the mass M is a constant value X o'd, 



the apparent brightness H is sx constant X ^^Q^^» Eliminating from 

 this the parallax and the radius, we find 



a' d^ 



Thus from the known quantities : elements of orbit and brightness, 

 we derive a relation between the physical quantities: density 

 and radiating power, independently of the mathematical dimen- 

 sions. This relation has been derived repeatedly. In the paper 



. ■;. \U a' 

 cited before Maunder gives values for the density tf = c 



HJ P* 



in the supposition of equal values of ). ; he found for the Sirius stars 

 (l«t type) 0,0211, for the solar stars (all of the 2"^ type) 0,3026, 

 hence 14 times as large on an average ; we can also say that 

 when we assume the same density the radiating power of the 

 Sirius stars would be 6 times as large ; the exact expression would 

 be that the quotient X^I(P is 200 times as large for the Sirius stars 

 as for the solar stars. 



In a different form the same calculation has been made by 

 Hertzsprung by means of Aitken's list of binary system elements ^). 

 By means of — 2,5 log II—= m he introduces into his formula the 

 stellar magnitudes; if we put in the logarithmical form 



1) Lick Observatory Bulletin Nr. 84. 



10 

 Proceedings Royal Acad. Amsterdam. Vol. IX. 



