386 POPULAR LECTURES AND ADDRESSES, 



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 differences 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 



(i) 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 



