ox THE INTEEACTION OF NATURAL FORCES. 195 



Mat ; this corresponds, when A^ represents the mechanical 

 equivalent of the unit of heat, to the work kgM.aL To 

 find the elevation of temperature produced by the con- 

 densation of the mass of the sun, let us set 



we have then 





5 A.K 



For a mass of water equal to the sun we have o- = 1 ; 

 then the calculation with the known values of A, M, R, w, 

 and r, gives 



< = 28611000° Cent. 



The mass of the sun is 738 times greater than that of 

 all the planets taken together ; if, therefore, we desire to 

 make the water mass equal to that of the entire system, 



we must multiply the value of t by the fraction . which 



739 



makes hardly a sensible alteration in the result. 



When a spherical mass of the radius R condenses more 



and more to the radius E^, the elevation of temperature 



thereby produced is 



5*A . mcr 1 R, Rq J 



or 



3, rm r . R 



5 ARim< 



Supposing, then, the mass of the planetary system to be 

 at the commencement, not a sphere of infinite radius, but 

 limited, say of the radius of tlje path of Neptune, which 

 is six thousand times greater than the radius of the sun, 



T> 



the magnitude — ^ will then be equal to gQoo, and the above 



value of t would have to be diminished by this inconsi- 

 derable amount. 



