5S4 



NA TURE 



[April 18, 1895 



shown what is the rate of increase of the melting tem- 

 perature with increase of pressure of this rock : Laplace's 

 hypothetical l?.w of increase of density downwards in the 

 earth cannot be ver>' wrong, and from this a law of in- 

 crease of pressure downwards may be formulated. From 

 these data Mr. King finds what are the temperatures at 

 various depths, which if exceeded would mean liquidity. 

 A liquid layer inside the earth's crust being assumed to 

 be impossible, Mr. King, trying all sorts of Kelvin solu- 

 tions of a solid earth of uniform conductivity and 

 uniform temperature, initially finds a maximum age of 25 

 million years, the initial temperature being not greater 

 than 2000" C. ! Furthermore, higher initial temperatures 

 are not possible ! 



Now it is evident that if we take any probable law of 

 temperature of convective equilibrium at the beginning 

 and assume that there may be greater conductivity 

 inside than on the surface rocks, Mr. King's ingenious 

 test for liquidity will not bar us from almost any 

 great age. 



(4) There remain, lastly, considerations drawn from 

 the age of the sun. On the assumption that all the 

 energ)' possessed by the sun was that due to the mutual 

 gravitation of its parts, and that the sun is now of uni- 

 form density, Helmholtz found that the sun may have in 

 the past radiated as much as 22 million times his present 

 annual loss. Langley found that the sun's present rate 

 of radiation was under-estimated, and the statement of 

 Prof. Newcomb may be taken as that of Helmholtz, 

 corrected. Newcomb says (" Popular Astronomy," p. 523): 

 " If we take the doctrine of the sun's contraction as fur- 

 nishing the complete explanation of the solar heat during 

 the whole period of the sun's existence, we can readily 

 compute ... It is thus found that if the sun had, in the 

 beginning, filled all space, the amount of heat generated 

 by his contraction to his present volume would have been 

 sufficient to last iS million years at his present rate of 

 radiation." 



Lord Kelvin pointed out (pp. 364-65, vol. i. " Pop. 

 Lectures") that Helmholtz had assumed a sun of uniform 

 density, whereas the sun's density must increase very 

 much towards his centre, and as a result of cal- 

 culation on the assumption that only half of the 

 original energy was available (p. 374), that the 

 radiation was greater in the past, and that the 

 original collisions occurred practically simultaneously, 

 he says : " We may therefore accept as the lowest esti- 

 mate for the sun's initial heat 10,000,000 times a year's 

 supply at present rate, but 50,000,000 or 100,000,000 as 

 possible, in consequence of the sun's greater density in 

 his central parts." And again (p. 375) : " It seems there- 

 fore, on the whole, most probable that the sun has not 

 illuminated the earth for 100,000,000 years, and almost 

 certain that he has not done so for 500,000,000 years. 

 This last number, then, is Lord Kelvin's higher limit. 

 After six years, in 1868, Lord Kelvin returned to the 

 question, and he says (p. 53, vol. ii. " Pop. Lect. and 

 Addresses ") : " The estimates here are necessarily very 

 vague, but yet vague as they are, I do not know that it 

 is possible, upon any reasonable estimate, founded on 

 known properties of matter, to say that we can believe 

 the sun has really illuminated the earth for five hundred 

 million years." 



In his R.I. address of 1887 Lord Kelvin gave no 

 higher limit. I think that, on his specified assump- 

 tions in giving these large numbers, he has been 

 very generous ; for, taking Mr. Homer Lane's deter- 

 mination of the internal density of the sun, 1 find that the 

 Helmholtz total energy need only be nmhipUed by 

 about aA. If, however, instead of taking, as Mr. II. Lane 

 did, v\ as the ratio of specific heat, we take a less 

 number, and there is no reason why we should not, we 

 find much greater densities towards the centre, and a 

 much greater total energy and age. Still, I think ili.it it 



NO. 1329. VOL. 51] 



is only when we escape from the above assumptions that 

 we can see our way to increase the higher limits which 

 have been quoted. 



To justify the Helmholtz hypothesis of mere mutual 

 attraction, initially, between the portions of matter which 

 form the sun. Lord Kelvin (" Pop. Lect.," vol. i., pp. 

 41 1-3) dwells upon the great improbability that any parts 

 of the sun possessed much initial velocity. He shows 

 that if two bodies, A and B, came together to form the 

 sun, when the bodies were still far apart before collision, 

 the motion of the centre of B relatively to A, must have 

 been directed with great exactness to pass nearly through 

 the centre of A (as the sun has a comparatively small 

 moment of momentum), and this was very improbable 

 if the bodies had initial velocities. But this argument is 

 only satisfactory when the bodies coming together are 

 two in number. For example, let us imagine in early 

 times a sun of half the mass of the present one, but of 

 many times its diameter. It is possible that its radiant 

 energy was supplied by meteors. If the meteor feeding 

 was in excess, the sun- became larger in volume. If 

 there was too little meteor feeding, the sun became 

 smaller. Even if there was a very excessive supply for 

 a short time, say by the incoming of a huge meteor, we 

 need not assume excessive radiation in consequence. 

 Such meteors may have come from stellar space with 

 great initial velocities, and may have possessed before 

 collision many times the kinetic energy which a 

 mere solar system meteor of the same mass would 

 possess.' If there were many such meteors, their paths 

 might be enormously out of line with one another and 

 with the centre of the sun, and yet we need not imagine 

 them to alter much the moment of momentum of the 

 sun about its axis. If we look for the prolntble age of ] 

 the sun as deduced frotn mere physics, we ought to take 

 Helmholtz' condition of mere mutual attraction, the 

 Helmholtz calculation being corrected of course for 

 greater internal density ; but if we look for a higher limit 

 to the age of the sun, it is difficult to see why we may 

 not multiply Lord Kelvin's total energy and age of 500 

 million years. 



Again, the ages determined by Von Helmholtz, Prof. 

 Newcomb, and Lord Kelvin, are given on the uniformi- 

 tarian assumption that the sun has been radiating energy 

 always at his present rate. If we may imagine that for 

 long periods the sun radiated at a smaller rate, 

 whether because his mass was smaller, or because 

 of his atmosphere, we again have an increase 

 to the calculated .age. Prof. Newcomb seems to 

 have noticed this, and to meet the objection 

 (p. 525, "Popular Astronomy") he says, "that a 

 diminution of the solar heat by less than one-fourth of 

 its amount would probably make our earth so cold, that 

 all the water on its surface would freeze, while an increase 

 by much more than one-half would probably boil the 

 water all away." On account of this exigency, indeed, 

 he reduces his previous estimate in the ratio of nine to 

 five. This statement ought to have the careful consider- 

 ation of men who know more about astronomical physics 

 than I do. It means that if the earth were now isi per 

 cent, further away from the sun, there would be no w.ater 

 and no life, only ice ; and if we were 184 per cent, nearer 

 the sun, there would be again no water and no life, only 

 steam. It becomes an important question, is there no 

 life, is there no water on the planet Venus which has 

 twice our solar radiation.' Is all its water in its .atmo- 

 sphere as steam? Again, Mars has only 40 per cent, 

 of our solar r.adiation ; is there no life, no water, 

 only ice upon Mars? I have no right to speak 

 on such a subject, but I understood that the atmo- 

 sphere of Venus was much like that of our own planet, 

 and that the water of Mars is not all ice, for his pol.ar 



' The velocUici of «l.-irs are probubly much less than the possible velo- 

 cities of smaller bodies. 



