54 Trans. Acad. Sei. 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 ^9 for the distance dr by — dp, and 

 equating the two forces, we have 



2 7fl2 7 kMirdr'^ddHr 

 TTv^du^dp = — ; , 



or M= — '^. (1) 



kddr 



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

 both 3/ and d change. 



Let the equation of the gas be 



pv=]L = CT, ^2> 







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

 T = Tq, we have 



and (1) becomes 



M=-£Ik^^. (3) 



k pdr 



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

 geometrical considerations is 



dM = 47rr2t?(Zr, 

 whence 



dM _ 47r?-^p ,^> 



dr - Cl\ 



M can therefore be eliminated by differentiating (3) with 

 respect to r and equating the two values of the differential 



„ . , dM 

 coetEcient -— — 

 (tr 



