Prof. Helmholtz on the Interaction of Natural Forces. 517 



To elevate the temperature of a mass M of the specific heat a, 

 t degrees, we need a quantity of heat equal to Mrrt ; this corresponds, 

 when Ag represents the mechanical equivalent of the unit of heat, 

 to the work AgMat. To find the elevation of temperature produced 

 by the condensation of the mass of the sun. let us set 



AgMat=Y; 



we have then 



3 r^M 



5 A . R .»i . o- 



For a mass of water equal to the sun we have (t= 1 ; then the cal- 

 culation with the known values of A, M, R, m, and r, gives 



f=2861 1000° Cent. 



The mass of the sun is 738 times greater than that of all the pla- 

 nets 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 makes hardly a sensible alteration in 



7 oy 



the result. 



When a spherical mass of the radius R condenses more and more 

 to the radius R,, the elevation of temperature thereby produced is 



"~5'A 



r'-M 



IR, RoJ 



5 AR,»z(7 



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 — i will then be equal to 



Kg 



-^. and the above value of t would have to be diminished by this 



6«00 



inconsiderable amount. 



From the same formula, we can deduce that a diminution of -^^ 

 of the radius of the sun would generate work in a water mass equal 

 to the sun, equivalent to 2861 degrees Centigrade. And as, accord- 

 ing to Pouillet, a quantity of heat corresponding to 1;^ degree is lost 

 annually in such a mass, the condensation referred to would cover 

 the loss for 2289 years. 



If the sun, as seems probable, be not everywhere of the same den- 

 sity, but is denser at the centre than near the surface, the potential 

 of its mass and the corresponding quantity of heat will be still 

 greater. 



Of the now remaining mechanical forces, the vis viva of the rota- 

 tion of the heavenly bodies round their own axes is, in comparison 



