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



P T P. T x 



With unit mass -r^ = -y , = -^ = 17 ' anc * we nave 



2 7 





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= Zy- 1 , (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 

 in 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 



(38) 



Differentiating this equation with respect to r, we get 



da _ R 2 dm 2mR 2 

 dr ~ M?~dr ~ Hfo* ' 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 



Jf=-gTffi? 3 (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 3Mar 2 



dr ~ R s 5 V ' 



