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 dr by — dp^ and 

 equating the two forces, we have 



.2 7d2 7 — kMirdr'^'dd^dr 



M^-'^. (1) 



kod7' 



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

 both ilif and 3 change. 



Let the equation of the gas be 



pv 



= ^ = CT, ^^^ 







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

 T = T;, we have 



P 

 and (1) becomes 



i)i = _£T..':!^. (3) 



k pdr 



Now 3/ itself is a function of p and r; its differential from 

 geometrical considerations is 



whence 



w 



M can therefore be eliminated by differentiating (3) with 

 respect to r and equating the two values of the differential 



a, • , dM 

 coeiBcient — — -. 

 dr 



