176 Lord Kelvin on Ether and 



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 the stars. To make the 

 whole sky aglow with the light of all the stars at 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 densitv 

 of distribution is, of course, quite arbitrary; and (§§ 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-disc-area more 

 than 10" 12 or 10" 11 of the whole sky. 



§ 20. To understand the sparseness of our ideal distribution 

 of 1000 million suns, divide the total volume of the supposed 

 sphere of radius r (5) by 10 9 , and we find 123*5. 10 39 cubic 

 kilometres as the volume per sun. Taking the cube root of 

 this we find 4'98.10 la " kilometres as the edge of the corre- 

 sponding cube. Hence if the stars were arranged exactly in 

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

 to eight neighbouring cubes, his six nearest neighbours would 

 be each at distance 4*98. 10 13 kilometres ; which is the distance 

 corresponding to parallax 0"*62. Our sun seen at so great a 

 distance would probably be seen as a star of something between 

 the first and second magnitude. For a moment suppose each 

 of our 1000 million suns, while of the same mass as our own 

 sun, to have just such brightness as to make it a star of the first 

 magnitude at distance corresponding to parallax 1"*0. The 

 brightness at distance r (5) corresponding to parallax 0"*001 

 would be one one-millionth of this, and the most distant of 

 our assumed stars would be visible through powerful telescopes 

 as stars of the sixteenth magnitude. Newcomb (Popular 

 Astronomy, 1883, p. 424) estimated between 30 and 50 

 million as the number of stars visible in modern telescopes. 

 Young (General Astronomy, p. 448) goes beyond this 

 reckoning and estimates at 100 million the total number of 

 stars visible through the Lick telescope. This is only the 

 tenth of our assumed number. It is nevertheless probable 

 enough that there may be as many as 1000 million stars 

 within the distance r (o) ; but many of them may be extinct 

 and dark, and nine-tenths of them though not all dark may be 

 not bright enough to be seen by us at their actual distances. 



