26 Trayis. Acad. Sci. of St, Louis, 



P T P T 



With unit mass -^ = ^ , = ^^ = ^\ and we have 



(a \^— 1 



If now the densit}^ of the Sun at the point a^ be taken as 

 unity, T^ being the temperature of this point, we shall have 

 the important equation 



T= T^a'-\ (37) 



by which the law of temperature can be determined as soon as 

 the law of density is known. 



4. Determinalion of the law of density. If we denote by 

 m the mass included in the sphere of variable radius r, and 

 by M the total mass included in the sphere of radius i?, and 

 by a the ratio of acceleration of gravity at the distances 

 r and R from the center respectively, we shall have 



^-^^ 

 «=^;W (38) 



Differentiating this equation with respect to r, we get 



da _ i?2 dm 2mB^ 

 dr ~ M?~dr~~~M7^' ^^ 



da P^ dm 2a 



dr "~ Mi-"^ dr r ^ ^ 



If now we designate the mean density of the sphere of 

 radius Rhy a we shall have 



4 



il/zr-TT^ri?^ (40) 



The element of mass between the two sphere surfaces r and 

 T-\-dr is given by 



dm — irar'^dr (41) 



Then by (40) 



dm ^Mffr^ 

 dr R'd ^ ^ 



