54 Trans. Acad. Sci. of St. Louis. 



in which k is the attraction between two units of mass at a 

 unit's distance from each other. This force of attraction is 

 balanced by an excess of pressure on its inner surface. De- 

 noting the variation in p for the distance cZr by — dp^ and 

 equating the two forces, we have 



irr^doMp = — , 



M=-;^. (1) 



It is evident that in the above expression as r changes, 

 both Maud 3 change. 



Let the equation of the gas be 



,in which v is the volume of a unit of mass; hence since 

 T= T,, we have 



nnd (1) becomes 



i,f=_^«/_!^. (3) 



k pdr 



Now ikf itself is a function of p and r; its differential from 

 geometrical considerations is 



whence 



M can therefore be eliminated by differentiating (3) with 

 respect to r and equating the two values of the differential 



coefficient — - — 

 dr 



