Yery — Stellar Revolutions loithin the Galaxy. 135 



whence " the average velocity in space of each star in the sys- 

 tem is 2XlT"05 = 34*10 km. per second."^ With this may be 

 compared Lord Kelvin's calcuilation that if 1,000,000,000 stars, 

 each of the sun's mass, started from a state of rest thousands 

 of millions of years ago (a considerably larger time allowance, 

 it will be noted, than has hitherto been admitted), and are now 

 uniformly distributed in a sphere whose radius is 30,900x10^* 

 km., the present mean velocity should be about 50 km. per 

 second. 



If we assume that the individual stellar motions at peri- 

 galacteum are controlled both in direction and speed by some 

 cluster, branch, or portion of a galactic ring, and that the gen- 

 eral stellar sphere has then but little influence, it must, never- 

 theless, be conceded that at the larger distances and throughout 

 the greater part of the stellar revolutions, if these are eccentric, 

 the general sphere exercises control, and that the subordinate 

 condensations or branches act only by the perturbations which 

 they produce. It seems probable that much greater stellar 

 velocities than those which have been measured, remain to be 

 discovered on the borders of the denser galactic aggregations. 

 Campbell finds that the velocity in the line of sight for stars 

 fainter than the 4'0 magnitude, is about 50 per cent greater 

 than for stars equal to, or brighter than, 3*0 magnitude. These 

 stars, however, were not classified galactically. 



Speaking only of observed stellar motions and, the effective 

 attractive mass which they indicate, it appears that a galactic 

 mass equivalent to 20,000,000 suns like ours, with a moderate 

 central condensation sufiicient to quicken the stellar motions 

 in our vicinity by one third of their amount with homogeneous 

 distribution, is a probable value. Stars, presumably belonging 

 to the galactic system, exist in numbers approaching or exceed- 

 ing hundreds of millions ; hence there are either a great many 

 stars of small mass, our sun being larger that the average, or 

 else much the larger number of stars is so situated that the 

 attractions are mutually annulled. 



The radius of the stellar sphere surrounding the main streams 

 of the Galaxy and under the control of their attraction, is 

 possibly 30,000 billion kilometers, as predicated by Lord Kel- 

 vin ; but the solar apogalactic recession does not seem to be 

 so great. The motion in a horpogeneous swarm is of the nature 

 of a simple oscillation; and between limits of ±6X10'" km. 

 with the total eflScient mass just given, the movement from one 

 extreme to the other will consume a little less than 30,000,000 

 years. Such an arrangement, however, can not endure, because 

 the intersecting paths entail numerous collisions near the cen- 



* Astropliysical Journal, xiii, 84, 1901. 



