1887. J on the Sun's Heat 7 



(2) The work done in any time by the mutual gravitation 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 consideration 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 one 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 dif- 

 ferences simply of the radius, to take into account the change of 

 density (which, for example, would be three per cent, for one per 

 cent, change of the radius). Thus the rule, easily worked out 

 according to the principles illustrated by our mechanical model, is 

 this : — 



Equal differences of the reciprocal of the radius correspond to 

 equal quantities of heat radiated away from million of years to 

 million of years. 



Take two examples — 



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

 times the heat radiated from the sun as is at present radiated out in 

 one year, the solar radius must have been four times as great as at 

 present. 



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

 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 remarked that the density which this would imply, 

 being 11*2 times the density of water, or just about the density 

 of lead, is probably too ^great to allow the free shrinkage as of a 

 cooling gas to be still continued without obstruction through over- 

 crowding 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 

 condition gives. The same considerations led Newcomb to the 

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

 give sufficient 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 



