172 ON THE INTERACTION OF NATURAL FORCES. 



NOTE TO PAGE 157. 



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 mentioned, are to be found partly 

 in J. K. 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 R, the potential upon 

 itself V if we call the mass of the earth m, its radius r, and 

 the intensity of gravity at its surface g has the value 



V- 3 



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 quantity -' they all 



Jfcl 



vanish in comparison with the sun ; even that of the greatest 

 planet, Jupiter, is only about the one hundred- 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 

 IT, t degrees, we need a quantity of heat equal to Mer ; this 

 corresponds, when A.g represents the mechanical equivalent of 

 the unit of heat, to the work A^Mo-i. To find the elevation of 



