24 Trans. Acad. Sci. of St. Louis. 



By the law of Mariotte, the volume and pressure of any 

 mass of gas are defined by the equation, 



PV=NT (24) 



where uVis a constant, and 2Ms a fixed absolute temperature. 

 By the law of Gay Lussac, the volume of the same mass of 

 gas under constant pressure is proportional to the absolute 

 temperature, and defined by the equation 



PV = ]SrT (25) 



We shall assume that these laws, derived from terrestrial 

 experiments on many single and compound gases under 

 varied conditions, hold true also in the body of the Sun. A 

 quantity of heat dQ applied to any element of the Sun's mass 

 will do external work by expanding the volume (under con- 

 stant pressure) and internal work against resisting molecular 

 forces. Suppose A to be a constant, and let ^ and '/^ be 

 unknown functions of the volume and internal pressure re- 

 spectively. Then we shall evidently have the differential 

 equation, 



dQ^A{^dP^- >FdV) (26) 



If now we apply the heat to a unit volume of the gas under 

 constant pressure, we shall have 



dQ^A¥dV=-^dT (27) 



where 'Cp is the specific heat of the gas. Thus, under con- 

 stant pressure, 



AdV 



(28) 



dT P 

 By the law of Gay Lussac in ( 25 ) we have rr/ = tt, and 



hence 



^.P 



If now we suppose V constant, and apply the heat dQ to 

 the gas under constant volume, we shall have 



dQ = A^dP = :,dT (30) 



where C^ is the specific heat under constant volume. 



