October 24, 1901] 



NA TUBE 



627 



more consistent with the analogies of the known 

 properties of molar matter, which should be their guides, 

 to suppose that ether had not the quality of exerting an 

 infinitely great force against compressing action of 

 gravitation. Hence if they assume that it extended 

 through all space, ether must be outside the law 

 of gravitation, that is to say, truly imponderable. 

 He remembered the contempt and self-complacent com- 

 passion with which sixty years ago he himself, he was 

 afraid and most of the teachers of that time looked 

 upon the ideas of the elderly people who went before 

 them, who spoke of " the imponderables." He feared 

 that in this, as in a great many other things in science, 

 they had to hark back to the dark ages of fifty, sixty or 

 a hundred years ago, and that they must admit there was 

 something which they could not refuse to call matter, 

 but which was not subject to the Newtonian law of 

 gravitation. That the sun, stars, planets, and meteoric 

 stones were all of them ponderable matter was true, but 

 the title of his paper implied that there was something 

 else. Ether was not any part of the subject of his paper ; 

 what he dealt with was gravitational matter, ponderable 

 matter. Ether they relegated, not to a limbo of imponder- 

 ables, but to distinct species of matter which had inertia, 

 rigidity, elasticity, compressibility, but not heaviness. In 

 a paper he had already published he had given strong 

 reasons for limiting to a definite amount the quantity of 

 matter in space known to astronomers. He could scarcely 

 avoid using the word "universe," but be meant our 

 universe, which might be a very small affair after all, 

 occupying a very small portion of all the space in which 

 there is ponderable matter. 



Supposing a sphere of radius 3'09.io"' kilometres (being 

 the distance at which a star must be to have parallax 

 o' 'ooi) to have within it, uniformly distributed through 

 it, a quantity of matter equal to one thousand million 

 times the sun's mass, the velocity acquired by a body 

 placed originally at rest at the surface would, in five 

 million years, be about 20 kilometres per second, and in 

 twenty-five million years would be 108 kilometres per 

 second (if the acceleration remained sensibly constant 

 for so long a time). Hence if the thousand million suns 

 had been given at rest twenty-five million years ago, 

 uniformly distributed throughout the supposed sphere, 

 many of them would now have velocities of twenty or 

 thirty kilometres per second, while some would have less 

 and some probably greater velocities than 108 kilometres 

 per second ; or, if they had been given thousands of 

 million years ago at rest so distributed that now they 

 were equably spaced throughout the supposed sphere, 

 their mean velocity would now be about 50 kilometres per 

 second {P/ii'L Mai^^-, August igot, pp. 169, 170). This is 

 not unlike the measured velocities of stars, and hence it 

 seems probable that there might be as much matter as 

 one thousand million suns within the distance 309. 10"' 

 kilometres. The same reasoning shows that ten thousand 

 million suns in the same sphere would produce velocities 

 far greater than the known star velocities, and hence 

 there is probably much less than ten thousand million 

 times the sun's mass in the sphere considered. A general 

 theorem discovered by Green seventy-three years ago 

 regarding force at a surface of any shape, due to matter 

 (gravitational, or ideal electric, or ideal magnetic) acting 

 according to the Newtonian law of the inverse square of 

 the distance, shows that a non-uniform distribution of the 

 same total quantity of matter would give greater veloci- 

 ties than would the uniform distribution. Hence we 

 cannot, by any non-uniform distribution of matter within 

 the supposed sphere of 3'09. 10"' kilometres radius, escape 

 from the conclusion limiting the total amount of the 

 matter within it to something like one thousand million 

 times the sun's mass. 



Lord Kelvin then went on to compare the sunlight with 

 the light from the thousand million stars, each being 



NO. 1669, VOL. 64] 



supposed to be of the same size and brightness as our 

 sun ; and stated that the ratio of the apparent brightness 

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

 would be 3-87.10"'^. This ratio {P/iil. Mtti^^., August 1901, 

 p. 175) varies directly with the radius of the containing 

 sphere, the number of equal globes per equal volume 

 bemg supposed constant ; and hence to make the sum of 

 the apparent area of discs 3'87 per cent, of the whole sky, 

 the radius must be 3*09. 10-' kilometres. With this radius 

 light would take 31.10'* years to travel from the outlying 

 stars to the centre. Irrefragable dynamics proves that 

 the life of our sun as a luminary is probably between 50 

 and 100 million years ; but to be liberal, suppose each of 

 our stars to have a life of 100 million years as a luminary, 

 and it is found that the time taken by light to travel from 

 the outlying stars to the centre of the sphere is three and 

 a quarter million times the life of a star. Hence it follows 

 that to make the whole sky aglow with the light of all the 

 stars at the same time the commencements of the 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 dura- 

 tions of the lights of all the others at the earth. His 

 supposition as to uniform density is quite arbitrary ; but 

 nevertheless he thought it highly improbable that there 

 could be enough stars (bright or dark) to make a total of 

 star-disc-area more than lo"'- or 10-" of the whole sky. 

 To help to understand the density of the supposed 

 distribution of 1000 million suns in a sphere of 3'09. 10'" 

 kilometres radius, imagine them arranged exactly in cubic 

 order, and the volume per sun is found to be i23'5.io'''-' 

 cubic kilometres, and the distance from one star to any 

 one of its six nearest neighbours would be 4^98. 10'' 

 kilometres. The sun seen at this distance would pro- 

 bably be seen as a star of between the first and second 

 magnitude ; but supposing our 1000 million suns to be 

 all of such brightness as to be stars of the first magnitude 

 at distance corresponding to parallax i"'o, the brightness 

 at distance 3'09. to'" kilometres would be one one-mil- 

 lionth of this ; and the most distant of our stars would 

 be seen through powerful telescopes as stars of the 

 sixteenth magnitude. Newcomb estimated from 30 to 

 50 million as the number of stars visible in modern tele- 

 scopes. Young estimated at 100 million the number 

 j visible through the Lick telescope. This larger estimate 

 is only one-tenth of our assumed thousand million masses 

 , equal to the sun, of which, however, nine hundred million 

 ' might be either non-luminous, or, though luminous, too 

 distant to be seen by us at their actual distances from 

 the earth. Remark also that it is only for facility of 

 counting that we have reckoned our universe as a thou- 

 sand million suns ; and that the meaning of our reckoning 

 j is that the total amount of matter within a sphere of 

 j 3"09. lo'" kilometres radius is a thousand million times 

 j the sun's mass. The sun's mass is rgg. 10'-^ metric tons, 

 or rgg.io^-* grammes. Hence our reckoning of our sup- 

 posed spherical universe is that the ponderable part of it 

 amounts to i '99. 10*'- grammes, or that its average density 

 is r6i.io~'-'^ of the density of water. 



Lord Kelvin returned to the question of sum of 

 apparent areas, the ratio of which to 4^-, the total 

 apparent area of the sky viewed in all directions, is given 

 by the formula {P/iil. Maff., August 1901, p. 175) 



a = — ( -' ) ; provided its amount is so small a fraction 



of unity that its diminution by eclipses, total or partial, 

 may be neglected. In this formula, N is a number of 

 globes of radius <j uniformly distributed within a spherical 

 surface of radius r. For the same quantity of matter in 

 N' globes of the same density, uniformly distributed 



through the same sphere of radius r, we have 



(;;.)■ 



and therefore 



With N = io'', r=309 10'" kms. ; 



