ETHER AND GRAVITATIONAL MATTER. 227 



is destined to travel through it in the course of perhaps two or three 

 million years and to pass away into space never to return to us. 



Sec. 18. Many of our supposed 1,000,000,000 stars, perhaps a great 

 majority of them, may be dark bodies; but let us suppose for a 

 moment each of them to be bright, and of the same size and bright- 

 ness, as our sun; and on this supposition and on the further supposi- 

 tions that they are uniformly scattered through a sphere (5) of radius 

 3'09 . 10 16 kms., and that there are no stars outside this sphere, let us 

 find what the total amount of starlight would be in comparison with 

 sunlight. Let n be the number per unit of volume of an assemblage 

 of globes of radius a scattered uniformly through a vast space. The 

 number in a shell of radius <j and thickness dq will be nA7t<fdq, and 

 the sum of their apparent areas as seen from the center will be 



— 2" n . ±7i<fd<j or n . ^(fdq. 



Hence, by integrating from y = to q=r, we find 



n.4c7t*a 2 r (8). 



for the sum of their apparent areas. Now if N be the total number 

 in the sphere of radius r we have 



n=N/(jjp) (9). 



Hence (8) becomes N . ?>7t( - ) ; and if we denote by a the ratio of 

 the sum of the apparent areas of all the globes to ±it we have 



a = t00 (10) - 



(1 — a) <*, very approximately equal to l/a, is the ratio of the apparent 

 area not occupied by stars to the sum of the apparent areas of all their 

 disks. Hence alpha is the ratio of the apparent brightness of our star- 

 lit sky to the brightness of our sun's disk. Cases of two stars eclips- 

 ing one another wholly or partially would, with our supposed values 

 of r and a, be so extremely rare that they would cause a merely negli- 

 gible deduction from the total of (10), even if calculated according to 

 pure geometrical optics. This negligible deduction would be almost 

 wholly annulled by diffraction, which makes the total light from two 

 stars, of which one is eclipsed by the other, very nearly the same as 

 if the distant one were seen clear of the nearer. 



Sec. 19. According to our supposition of section 18 we have N=10 9 , 

 « = 7.10 5 krns., and therefore rla=4: , 4:.10 i0 . Hence by (10) 



«=3-87.10- 13 (11). 



