THE RELATIONS OF INTERNAL PRESSURE, VOL- 

 UME, AND TEMPERATURE OF AN ISOLATED 

 MASS OF PERFECT GAS OF UNIFORM TEMPERA- 

 TURE AND IN EQUILIBRIUM UNDER THE ACTION 

 OF ITS OWN FORCES.* 



Calvin M. Woodward. 



I. 



Given an indpjinile sphere of gas at temperature T^, to find 

 the relation of p to r for any element, r being the distance 

 from the center of mass, and^ the pressure. 



Take for an element the gas inclosed between two con- 

 secutive concentric spheres and an indefinitely small cone 

 whose half-vertical angle is dd, and whose vertex is at O, the 

 center of the spheres and the center of mass. 



The volume of the element is irr'^dd'^dr, as seen in the 

 figure. If o be the density of the gas at the point, the mass 

 is 



irdr'^ddHr. 



The attraction between this element and the sphere, of 

 mass M, within the radius r, is 



kMirdrhWHr 



* Presented in abstract to The Academy of Science of St. Louis, March 

 20, 1899. 



(53) 



