300 CELESTIAL DYNAMICS. 



VIII. THE EARTH'S INTERIOR HEAT. 



WITHOUT doubt there was once a time when our globe 

 had not assumed its present magnitude. According to this, 

 by aid of this simple assumption, the origin of our planet may 

 be reduced to the union of once separated masses. 



To the mechanical combinations of masses of the second 

 order, with masses of the second and third order, &c., the 

 same laws as those enunciated for the sun apply. The collis- 

 ion of such masses must always generate an amount of heat 

 proportional to the squares of their velocities, or to their me- 

 chanical effect. 



Although we are not in a position to affirm anything cer- 

 tain respecting the primordial conditions under which the 

 constituent parts of the earth existed, it is nevertheless of the 

 greatest interest to estimate the quantities of heat generated by 

 the collision and combination of these parts by a standard 

 based on the simplest assumptions. 



Accordingly we shall consider for the present the earth to 

 have been formed by the union of two parts, which obtained 

 their relative motions by their mutual attraction only. Let 

 the whole mass of the present earth, expressed in kilo- 

 grammes, be T, and the masses of the two portions T x and 

 x. The ratio of these two quantities may be imagined to 

 assume various values. The two extreme cases are, when a; 

 is considered infinitely small in comparison with T, and when 

 x = T x = % T. These form the limits of all imaginable 

 ratios of the parts T a and x, and will now be more closely 

 examined. 



Terrestrial heights are of course excluded from the fol- 

 lowing consideration. In the first place, let x, in comparison 

 with T a;, be infinitely small. The final velocity with 

 which x arrives on the surface of the large mass, after having 



