Gravitational Matter through Infinite Space. 175 



ratio of the sum of the apparent areas of all the globes to 4*7r 

 \ve have 



-¥©" •"»>• 



(l_ a )/ a? very approximately equal to 1/a, is the ratio of the 

 apparent area not occupied by stars to the sum of the apparent 

 areas of all their discs. Hence a is the ratio of the apparent 

 brightness of our star- lit sky to the brightness of our sun's 

 disc. Gases of two stars eclipsing one another wholly or 

 partially would, with our supposed values of r and a, be so 

 extremely rare that they would cause a merely negligible 

 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. 



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

 a = 7.10 5 kilometres, and therefore r/a — ±'-±.10 l °. Hence 

 by (10) 



* = 3-87.10- 13 (11). 



This exceedingly small ratio will help us to test an old and 

 celebrated hypothesis that if we could see far enough into 

 space the whole sky would be seen occupied with discs of 

 stars all of perhaps the same brightness as our own sun, and that 

 the reason why the whole of the night-sky and day-sky is not 

 as bright as the sun's disc, is that light suffers absorption 

 in travelling through space. Remark that if we vary r 

 keeping the density of the matter the same, N varies as the 

 cube of r. Hence by (10) a varies simply as r; and therefore to 

 make a. even as great as 3*87/100, or, say, the sum of the 

 apparent areas of discs 4 per cent, of the whole sky, the radius 

 must be 10 ll .r or 3'OD.IO 27 kilometres. Now light travels at 

 the rate of 300,000 kilometres per second or 9"45.10 12 kilo- 

 metres per year. Hence it would take 327.10 14 or about 

 3J.10 14 years to travel from the outlying suns of our great 

 sphere to the centre. Now we have irrefragable dynamics 

 proving that the whole life of our sun as a luminary is a 

 very moderate number of million years, probably less than 

 50 million, possibly between 50 and 100. To be very liberal, 

 let us give each of our stars a life of a hundred million years 

 as a luminary. Thus the time taken by light to travel from 

 the outlying stars of our sphere to the centre would be about 

 three and a quarter million times the life of a star. Hence, 

 if all the stars through our vast sphere commenced shining 



