26 Trans. Acad. Sci. of St. Louis. 



P T P T 



With unit mass -w = -f^ , = W = W, and we have 



T 





If now the density of the Sun at the point a x be taken as 

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

 the important equation 



T= T x a k -\ (37) 



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

 the law of density is known. 



4. Determination 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 R, and 

 by a the ratio of acceleration of gravity at the distances 

 r and R from the center respectively, we shall have 



a = 



mR 2 



1*M 



(38) 



Differentiating this equation with respect to r, we get 



da R 2 dm 2mR 2 



dr ~~ M? ~dr ~~ Mr* ' or 



da R 2 dm 2a 



dr " Mr 2 dr r ' 



If now we designate the mean density of the sphere of 

 radius R by a we shall have 



M=^dR i (40) 



The element of mass between the two sphere surfaces r and 

 r-\-dr is given by 



dm = irar 2 dr (41) 



Then by (40) 



dm ZMor 2 



dr ~ R 6 d 



