Thermodynamics of the Sun. 305 



the surface of the earth — rigid, fluid, or gaseous. Suppose it 

 uninfluenced by external forces, take the temperature and 

 the volumes as independent parameters but suppose them to be 

 functions of the time. We write the known equation 



dQ_-dQ, dv dQ ^T 

 dt " ~dv ' dt + BT* dt ; * ' * ' ^ > 

 where Q, as usual, denotes the heat received from without, 

 „ v „ „ volume, 



„ T „ „ temperature of the body, 



» t 99 99 time. 



From (I.) we deduce 



dQ ~dQ dv 

 dT __ dt ~dv dt ,jj v 



*" so ( ' 



Daily experience tells us that the right member of (II.) has 



always the sign of -^, i. e. -j- has the sign of -=-• 



There is no doubt that mutual gravitation performs work 

 on the smallest body when it is changing its volume, hence 

 we can admit only two cases : — 



(1) The law that -^ has the sign of -j- is quite general 

 and applicable to the celestial bodies. 



(2) The law that >-=-* has the same sign as -j- holds only 



for small bodies, because the work of gravitation is so small 

 that the heat generated by these forces may be neglected. 



The first case suggests no discussion. For the second take 

 the converted heat into account. Instead of (I.) we have now 



dQ ,dV_(-dQ ,y[\dv, f3Q . 31^ ( ni\ 

 dt + dt -\-dv + -dvjdt + VdT ^-dTjdt' ' l J 



Y denotes the potential of gravitation. [The mechanical 

 equivalent of heat is supposed equal to unity.] But 



^-=0 

 dT u? 



since the potential of gravitation does not depend on tempe- 

 rature, and we see that if 



dN __ dV dv ' , TV v 



~dt~l)v"dt' {y ' } 



then the equation (III.) is reduced to (I.), and we have again 



