I9I2.] OF THE GLOBULAR CLUSTERS. 125 



the part of I I U-^dS due to the surface of the sphere is in- 

 finitely small of the order of the radius a, which is of the first order of 

 small quantities, and may therefore be neglected. It only remains, 



then, to consider the part of I I V ^-dS due to the spherical 



surface. 



As F is supposed to vary continuously, we may take for it the 

 value V which is that attained at the point P. Then, since 



■(;) 



dU dU ^\r ) I I 



(•7) 



dn dr dr r^ «"' 



the integral over the sphere 6'^47ra- will become 



Accordingly, the equation (15) becomes 

 r r Cf^U^V dUdV dUdV\ , , , 



(20) 



47rF 



In these formulae, as before, the triple integrals extend through the 

 whole space, and the double integrals over the whole surface. If F 

 had become infinite, instead oi U, there would have been the corre- 

 sponding term — ^ttU' to be added to the right member of (19). 



Now in a globular cluster of stars subjected to the mutual gravi- 

 tation of its components over long ages, many close approaches will 

 eventually develop: and they may depend on the wandering of stars 

 within either the outer shell or the central sphere, or from the shell 



