194 ON THE INTERACTION' OF NATURAL FORCES. 



NOTE TO PAGE 177. 



I must here explain the calculation of the heat which 

 must be produced by the assumed condensation of the 

 bodies of our system from scattered nebulous matter. 

 The other calculations, the results of which I have men- 

 tioned, are to be found partly in J. R. Mayer's papers, 

 partly in Joule's communications, and partly by aid of 

 the known facts and method of science : they are easily 

 performed. 



The measure of the work performed by the condensation 

 of the mass from a state of infinitely small density is the 

 potential of the condensed mass upon itself. For a sphere 

 of uniform density of the mass M, and the radius K, the 

 potential upon itself V — if we call the mass of the earth 

 772, its radius r, and the intensity of gravity at its 

 surface g — has the value 



,, 3 r^M^ 



Let us regard the bodies of our system as such spheres, 

 then the total work of condensation is equal to the sum 

 of all their potentials on themselves. As, however, these 

 potentials for different spheres are to each other as the 



M^ 



quantity -— , they all vanish in comparison with the sun ; 



even that of the greatest planet, Jupiter, is only about the 

 one himdred-thousandth part of that of the sun ; in the 

 calculation, therefore, it is only necessary to introduce the 

 latter. 



To elevate the temperature of a mass M of the specific 

 heat 0-, t degrees, we need a quantity of heat equal to 



