56 ILLINOIS STATE ACADEMY OF SCIENCE 



shape with a decreasing stellar density as one recedes 

 from the center of the cluster. For every star that ap- 

 proaches the center of the cluster another star recedes, 

 so that the general appearance of the cluster remains 

 unaltered throughout the ages. If such a cluster has a 

 radius of ten parsecs (33 light years) and contains one 

 hundred thousand stars of the same mass as our sun, and 

 these are conservative estimates, it would require ten mil- 

 lions of years for a complete oscillation of a star, forward 

 and backward, across the cluster; and many thousands of 

 such oscillations would have occurred before the exquisite 

 symmetry of these clusters would have been attained. 

 As we have no reason for supposing that they were all 

 started upon their careers simultaneously, nor that they 

 have just arrived at the state of equilibrium, it is hard 

 to escape the conclusion that some of them, at least, are 

 hundreds of billions of years old. Yet, notwithstanding 

 this great age, none of them exhibits signs of decadence. 

 They seem to be neither youthful nor senile; their state 

 is one of vigorous maturity. 



As for the galaxy as a whole, it has been remarked by 

 Jeans that if the gravitation between the stars were sud- 

 denly annihilated the effect of this annihilation upon the 

 motions of the stars would be imperceptible even after 

 the lapse of ten millions of years, so slowly does the 

 gravitational attraction of the galaxy affect the motions 

 of its individual members. Assuming that the radius of 

 the galaxy is two thousand parsecs (6,600 light years) 

 and that the average velocity of the stars is 40 kilometers 

 per second, and these are the ordinary assumptions of 

 the astronomers; assuming further that the galaxy is 

 neither expanding nor contracting, and this is a pure 

 assumption, as we have no definite knowledge on the 

 subject, then the total mass of the galaxy is slightly 

 greater than nine hundred million times the mass of the 

 sun. Assuming that there are this many stars (some of 

 this matter, at least, is in the form of nebulae) within the 

 boundaries of the galaxy, then some other star will ap- 

 proach our sun as close as the orbit of the earth on an 

 average of once in a million billion years. These close 



