228 ETHER AND GRAVITATIONAL MATTER. 



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 disks 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 disk is that light 

 suffers absorption in traveling 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 oc 

 even as great as 3'87 LOO, or, say. the sum of the apparent areas of 

 disks 4 per cent of the whole sky, the radius must be 10". r, or 

 3-09.10 27 kms. Now, light travels at the rate of 300,000 kins, per 

 second, or 9"45.10 12 kms. per year. Hence it would take 3 # 27.10 u , or 

 about 3i-10 u , years to travel from the outlying suns of our great 

 sphere to the center. Now we have irrefragable dynamics proving 

 that the whole life of our sun as a luminary is a very moderate num- 

 ber of million years, probably less than fifty million, possibly between 

 fifty and one hundred. 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 

 center 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 at the same time, three and a quarter million times the life of 

 a star would pass before the commencement of light reaching the 

 earth from the outlying stars, and at no one instant would light be 

 reaching the earth from more than an excessively small proportion of 

 all tin 1 stars. To make the whole sky aglow with the light of all the 

 stars ai the same time the commencements of the different stars must 

 be timed earlier and earlier for the more and more distant ones, so 

 that the time of the arrival of the light of every one of them at the 

 earth may fall within the durations of the lights at the earth of all 

 the others! Our supposition of uniform density of distribution is, of 

 course, quite arbitrary, and (sections 13, 15, above) we ought in the 

 greater sphere to assume the density much smaller than in the smaller 

 sphere (5); and. in fact, it seems that there is no possibility of having 

 enough of stars (bright or dark) to make a total of star-disk area 

 more than 10 '' or L0 _n of the whole sky. 



Sec. 20. To understand the sparseness of our ideal distribution of 

 1,000,000,000 suns divide the total volume of the supposed sphere of 

 radius /• (.">) by LO 9 , and we find L23*5.10 39 cu. kms. as the volume per 

 sun. Taking the cube root of this, we find 4*98.10 13 kms. as the edge 

 of the corresponding cube. Hence if the stars were arranged exactly 

 in cubic order, with our sun at one of the eight corners belonging to 

 eight neighboring cubes, his six nearest neighbors would be each at 

 distance 4*98.10 13 kms.. which is the distance corresponding to paral- 

 lax 0"'62. Our sun, seen at so great a distance, would probably be 



