See — Temperature of the Sun and Ages of Stars and Nebulae. 25 



dT V 

 Since by (24) -rp = -^-, we nave 



<l> = AdP = AN> < 31) 



and thus (26) becomes 



dQ = ^^ VdP+^PdV I (32) 



It is found by experiment that the ratio k = f- — 1.4, in 



common air and most terrestrial gases; but in monatomic 

 gases the value rises to 1.66, and in gases of very complex 

 molecular structure falls to 1.03, as in vapor of oil-of -turpen- 

 tine. Now suppose that the element of solar gas expands or 

 contracts adiabatically, so that no heat is gained or lost by it ; 

 then dQ = 0, and (32) becomes 



dP d V 



- F + k-y = (33) 



which is the differential equation for the pressure and volume 

 of an element of the Sun's mass in convective equilibrium. 

 Integrating this equation for the changes undergone by the 

 element in passing from the states P lt V v to P, V, we have 



,P „V 



dV 



^p, Jv x 



= (34) 



Equation (34) thus gives 



log P + k log V = log P x + h log V v or 



PV k = P 1 V l l (35) 



But since ^r — - , we may write, 



= '. (:-)' 



(36) 



