^ 



216 IL Hehnhohz on the Interaction of Natural Forces. 



To elevate tlie temperature of a mass M of the specific heat o-, t degrees, 

 we need a quantity of heat equal to Ma/; this corresponds, when A^ rep- 

 resents the mechanical equivalent of the unit of heat, to the work AffM(Jt, 

 To find the elevation of temperature produced by the condensation of the 

 mass of the sun, let us set AoMrrt — V ' 



3 r^M 



we have then t 



5 ' A .R .m. cr " 



For a mass of water equal to the sun we have 0" = ! ; then the calcula- 

 tion Avith the tnown values of A, M, R, m^ and r, gives 



^ = 28011000^ 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, Ave 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^, the elevation of temperature thereby produced is 



^ 3 r^M / 1 1 \ 3 rsM 



5 A.ma\^R^ Rq/' 5 AR,m<y 



Supposing, then, the mass of the planetary system to be at the com- 

 mencement, 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 ^^ will then be equal to -s-^Vxtj ^"^ ^^^^ above 



Ro 



value of t would have to be diminished by this inconsiderable amount. 



Frojn the same formula, we can deduce that a diminution of yjy^^u ^f 

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

 sun, equivalent to 28G1 degrees Centigrade. And as, according 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 density, 

 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 rotation 

 of the heavenly bodies round their own axes is^ in comparison with the 

 other quantities, very small, and may be neglected. The vis viva of the 

 motion of revolution round the sun, if (^ be the mass of a planet, g its 



distance from the sun, is 



m \ R 



1 ,. , ., 1 



Omitting tlie (quantity — as very small coraiiared witli ^, and dividing 

 by tlie above value of V, we obtain ^ = ^ fi . 



The mass of all the planets together is ^.^ of the mass of the sun, 



t 



tence the value of L for the entire system is L = t^ . V. 



ft 



