THE SUN'S HEAT. z 5 



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 proba- 

 bly 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 can not for the future reck- 

 on 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 temper- 

 ature, would give out annually much less heat than the sun in his pres- 

 ent 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 density of 

 the sun, being about 1*4 time 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 something con- 

 siderably more than this in the central parts, because of the pressure 

 in the interior increasing to something enormously great at the center. 

 If we knew the distribution of interior density, we could easily modify 

 our calculations accordingly ; but it does not seem probable that the 

 correction could, with any probable assumption as to the greatness of 

 the density throughout a considerable 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 agrees with Herschel's. 

 Forbes* showed the necessity for correcting the mode of allowing for 

 atmospheric absorption used by his two predecessors in estimating the 

 total amount of solar radiation, and he was thus led to a number 1*6 

 * "Edinburgh New Philosophical Journal," vol. xxxvi, 1S44. 



