ON THE INTERACTION OF NATURAL FORCES. 195 



Mat ; this corresponds, when Kg represents the mechanical 

 equivalent of the unit of heat, to the work A^Motf. To 

 find the elevation of temperature produced by the con- 

 densation of the mass of the sun, let us set 



we have then 



3 rM 



~5 A.K. m. a 



For a mass of water equal to the sun we have <r = 1 ; 

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

 and r, gives 



t = 2861 1000 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, 



738 

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



makes hardly a sensible alteration in the result. 



When a spherical mass of the radius R condenses more 

 and more to the radius R p the elevation of temperature 

 thereby produced is 



SA.wwlR, R 



or 



_3. r 2 M 



~5'~ 



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 the path of Neptune, which 

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



the magnitude 1 will then be equal to 600 o, and the above 



**o 



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

 derable amount. 



