146 Trans. Acad. Sci. of St. Louis. 



» 

 and heat is being taken from the gas. For isothermal com- 

 pression, the specific heat is of course infinite. In the cases 

 lying in the angle t^ m, p^ compression is still going on, but 

 the temperature is falling, while heat is being removed from 

 the gas. In the angle ^. m, v\ both temperature and pres- 

 sure are falling, and the specific heat is still negative. It is 

 evident that the gas at any point in a gravitating nebula, 

 must be going through an operation which would be repre- 

 sented by a line in the figure lying within the angle /c, m^p. 

 We shall make an attempt to locate this path. 



At a distance R from the center or nucleus of a cosmical 



*' gaskugel," where the density of the gas isS=-, the 



mass internal to B being M, the law of gravitation gives the 

 equation ^ 



dP M ^ 



^ = _^— g, (8). 



where h is the gravitation constant. 



By eq. (3) this becomes 



dP , MfPy 



dR 

 Hence 



(A.\n R2 dP 



^=-\p) TdR' 



By differentiation. 



dM _ An 

 dR~~lc 



By Geometry 



Lzi!: dP. n 



m d'^P dP( 2P^R ^^^ " dR\ 



p\ dm + dR\ pi ^pi ) 



^ = ^7rR^8 = 4.7rR2~, 



dR A- 



An 



