Jan. 27, 1887] 



NA TURE 



299 



cooled by radiation, falling down from the surface, and 

 hotter fluid rushing up to take its place. 



(2) The work done in an)- time by the mutual gravita- 

 tion of all the parts of the fluid, as it shrinks in virtue of 

 the lowering of its temperature, is but little less than (so 

 little less than, that we may regard it as practically equal 

 to') the dynamical equivalent of the heat that is radiated 

 from the sun in the same time. 



The rate of shrinkage corresponding to the present rate 

 of solar radiation has been proved to us, by the consider- 

 ation of our dynamical model, to be 35 metres on the 

 radius per year, or one ten-thousandth of its own length 

 on the radius per two thousand years Hence, if the 

 solar radiation has been about the same as at present 

 for two hundred thousand years, his radius must have 

 been greater by i per cent, two hundred thousand years 

 ago than at present. If we wish to carry our calculations 

 much farther back or forward than two hundred thousand 

 years, we must reckon by differences of the reciprocal of 

 the sun's radius, and not by differences simply of the 

 radius, to take into account the change of density (which, 

 for example, would be 3 per cent, for i per cent, change 

 of the radius). Thus the rule, easily worked out accord- 

 ing to the principles illustrated by our mechanical model, 

 is this : — 



Equal differences of the reciprocal of the radius corre- 

 spond to equal quantities of heat radiated away from 

 million of years to million of years. 



Take two examples : — 



(i) If in past time there has been as much as fifteen 

 mill, on times the heat radiated from the sun as is at 

 present radiated out in one year, the solar radius must 

 have been four limes as great as at present. 



(2) If the sun's effective thermal capacity can be main- 

 tained by shrinkage till twenty million times the present 

 year's amount of heat is radiated away, the sun's radius 

 must be half what it is now. But it is to be remar'^ced that 

 the density which this would imply, being i r2 times the 

 density of water, or just about the density of lead, is pro- 

 bably too great to allow the free shrinkage as of a cooling 

 gas to be still continued without obstruction through 

 overcrowding of the molecules. It seems, therefore, 

 most probable that we cannot for the future reckon on 

 more of solar radiation than, if so much as, twenty million 

 times the amount at present radiated out in a year. It is 

 also to be remarked that the greatly diminished radiating 

 surface, at a much lower temperature, would give out 

 annually much less heat than the sun in his present con- 

 dition gives. The same considerations led Newcomb to 

 the conclusion " that it is hardly likely that the sun can 

 continue to give sufiicient heat to support life on the earth 

 (such life as we now are acquainted with, at least) for ten 

 million years from the present time." 



In all our calculations hitherto we have for simplicity 

 taken the density as uniform throughout, and equal to the 

 true mean density of the sun, being about i '4 times the 

 density of water, or about a fourth of the earth's mean 

 density. In reality the density in the upper parts of the 

 sun's mass must be something less than this, and some- 

 thing considerably more than this in the central parts, 

 because of the pressure in the interior increasing to some- 

 thing enormously great at the centre. If we knew the 

 distribution of interior density we could easily modify our 

 calculations accordingly, but it does not seem prob.ible 

 that the correction could, with any probable assumption 

 as to the greatness of the density throughout a consider- 

 able proportion of the sun's interior, add more than a few 

 million years to the past of solar heat, and what could be 

 added to the past must be taken from the future. 



In our calculations we have taken Pouillet's number for 

 the total activity of solar radiation, which practically 



' "On the A^e of the Sun's Heat,- by Sir William Thomson (/l/.i^m//- 

 lans Magazine, March 1862); and Thomson and Tait's "Natural Philo- 

 sophy." andeditioni vol. i. part ii.. Appendix E- 



agrees with Herschel's. Forbes ' showed the necessity for 

 correcting the mode of allowing for atmospheric absorp- 

 tion used by his two predecessors in estimating the total 

 amount of solar radiation, and he was thus led to a 

 number r6 times theirs. Forty years later Langley,'^ in 

 an excellently worked out consideration of the whole 

 question of absorption by our atmosphere, of radiant heat 

 of all wave-lengths, accepts and confirms Forbes's reason- 

 ing, and by fresh observations in very favourable circum- 

 stances on Mount Whitney, 15,000 feet above the sea- 

 level, finds a number a little greater still than Forbes 

 (17, instead of Forbes's i'6, times Pouillet's number). 

 Thus Langley's number expressing the quantity of 

 heat radiated per second of time from each square 

 centimetre of the sun's surface corresponds to 133,000 

 horse-power per square metre, instead of the 78,000 

 horse-power which we have taken, and diminishes each 

 of our times in the ratio of i to 17. Thus, instead of 

 Helmholtz's twenty million years, which was founded on 

 Pouillet's estimate, we have only twelve millons, and 

 similarly with all our other time reckonings based on 

 Pouillet's results. In the circumstances, and taking fully 

 into account all possibilities of greater density in the sun's 

 interior, and of greater or less activity of radiation in past 

 ages, it would, I think, be exceedingly rash to assume as 

 probable anything more than twenty million years of the 

 sun's light in the past history of the earth, or to reckon 

 on more than five or six million years of sunlight for 

 time to come. 



But now we come to the most interesting part of our 

 subject — the early history of the sun. Five or ten million 

 years ago he may have been about double his present 

 diameter and an eighth of his present mean density, or 

 ■175 of the density of water; but we cannot, with any 

 probability of argument or speculation, go on continu- 

 ously much beyond that. We cannot, however, help asking 

 the question. What was the condition of the sun's matter 

 before it came together and became hot ? It may have 

 been two cool solid masses, which collided with the velo- 

 city due to their mutual gravitation ; or, but with enor- 

 mously less of probability, it may have been two masses 

 colliding with velocities considerably greater than the 

 velocities due to mutual gravitation. This last supposi- 

 tion implies that, calling the two bodies A and B for 

 brevity, the motion of the centre of inertia of B relatively 

 to A, must, when the distances between them was great, 

 have been directed with great exactness to pass through 

 the centre of inertia of A ; such great exactness that the 

 rotational momentum after collision was of proper amount 

 to let the sun have his present rotational period when 

 shrunk to his present dimensions. This exceedingly 

 exact aiming of the one body at the other, so to speak, is, 

 on the dry theory of probability, exceedingly improbable. 

 On the other hand, there is certainty that the two bodies 

 A and B at rest in space if left to themselves, undisturbed 

 by other bodies and only influenced by their mutual gravi- 

 tation, shall collide with direct impact, and therefore with 

 no motion of their centre of inertia, and no rotational 

 momentum of the compound body after the collision. 

 Thus we see that the dry probability of collision between 

 two of a vast number of mutually attracting bodies widely 

 scattered through space is much greater if the bodies be 

 all given at rest, than if they be given moving in any 

 random directions and with any velocities considerable 

 in comparison with the velocities which they would 

 acquire in falling from rest into collision. In this connec- 

 tion it is most interesting to know from stellar astronomy, 

 aided so splendidly as it has recently been by the spec- 

 troscope, that the relative motions of the visible stars and 

 our sun are generally very small in comparison with the 

 velocity (612 kilometres per second) a body would acquire 



' EJin. New Phil. Journal, xxxvi. 1844. 

 ^ " On the Selective Absorption of Solar Energy," An 

 \cicnce. vol. .xxv., March 1883. 



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