'9I5-] OF THE GLOBULAR CLUSTERS. 157 



XVI. The Projectile Forces which Set the Double and Mul- 



TIPPLE Stars Revolving in Their Orbits, Point to 



Origin in the Distance. 



If we have a stellar system made up of several components, we 

 may designate the masses of the individual stars by M^, M,, M^ . . ., 

 Mn. We shall first consider a binary star with masses M^ and M,. 

 Then the moment of momentum of the components about the com- 

 mon center of gravity of the system will be 



m^ + mXm^ + m/'-^^' 



)■ 



(50j 



( ^^P \r^ / 2 ^^1^2 2n / -2 



where c is the eccentricity of the orbit, and p the radius vector, and 

 n the mean angular velocity in the orbit (cf. inaugural dissertation, 

 "Die Entwickelung der Doppel-Stern Systeme," Berlin, 1892, p. 16). 

 When the other elements are unchanged, we find that the moment 

 of momentum of the binary system decreases with the increase of the 

 eccentricity. In case of a circular orbit, e vanishes, and O is con- 

 stant. In the general equation of the planetary theory the unit of 

 time may be so chosen that the constant of attraction (cf. Gauss, 

 " Theoria Alotus," Lib. I., § i ) becomes 



and we may therefore put Vt for n and p for a, and the second mem- 

 ber of (50) becomes 



p-Q.Vi-e' = -,r^,^-^.^.p^V\-c-, (52) 



the radical involving e to be unity in circular orbits. 



From this equation (52) it appears that with constant mass the 

 moment of momentum of a system of double stars depends on the 

 square root of the mean radius vector, and therefore increases rap- 

 idly with the distance. 



