196 SEE— TEMPERATURE, SECULAR COOLING [April 20, 



we approach the surface the fall of temperature would be slow in 

 all the inner shells of the nucleus. In fact a considerable sphere at 

 the centre would have nearly uniform temperature. But the central 

 temperature could not be lower than that of the enclosing shells ; 

 for, if so, the heat would flow towards the centre, and when uni- 

 formity was established throughout the nucleus, the flow would start 

 again towards the surface, still leaving the nucleus the hottest part 

 of the sphere. 



If some such process be the way in which our globe condensed, 

 it will follow that the temperature is nearly uniform in a central 

 nucleus of considerable size; but towards the surface the fall of 

 temperature would become much more rapid. The curve of tem- 

 perature thus inferred for the epoch of consolidation corresponds 

 closely to that of an ellipse, in which the semi-axis major represents 

 the radius of the earth, and the semi-axis minor the temperature at 

 the centre. We cannot, to be sure, feel entirely confident that this 

 is the exact distribution of temperature within the earth; but it is 

 quite clear that the curve is of this general form, and no doubt an 

 elliptical distribution of temperature will give a close approximation 

 to the truth, which probably is all we can hope for at present. Thus 

 we have established one approximate criterion for the internal dis- 

 tribution of the terrestrial temperature. 



The other important criterion is quantitative in character, and 

 is to the effect that one half of the primordial heat of condensation 

 still remains stored up in the globe. This is shown by the follow- 

 ing general formula : 



Q k-e 



W k-^V 



(0 



where Q is the quantity of heat radiated away, W the total amount 

 of work done by gravity, k the ratio of the specific heat of a gas 

 under constant pressure to that under constant volume, and € is the 

 exponent 4/3, in the adiabatic formula pv^ =C (cf. A. N., 4053, 

 or Ritter's '' Auwendungen der Mechanischen Warmetheorie auf 

 Kosmologische Probleme," Leipzig, 1882). 



The temperature attained in the development of the earth must 

 have been very great for all the inner portions, and hence we need 

 not hesitate to adopt the monatomic theory as being most nearly 



