Nipher — Gaseous Nebulae in Gravitational Contraction. 67 



on the co-ordinate plane T, V, in a curve of which (11) is 

 the equation. 



Eliminating Fin (10) and (11) 



2(7* 



In like manner by the elimination of T in the same equa- 

 tions 



PF* = (*)*** (13) 



These equations represent projections of the path on the 

 other co-ordinate planes. 



The relations involved in (11), (12) and (13) were pub- 

 lished by Kitter* in 1878, in the form 



* jl T* ™ . 



p v * = const., TV = const., —p = const. The equations 



which precede determine the value of these three constants in 

 terms of the mass M of the gas, the constant O for the gas, 

 and the gravitation constant k. 



The preceding equations may be used in determining the 

 total heat produced in the shrinkage of a given mass M, from 

 infinite dimensions to a sphere of radius R, the distribution 

 of pressure throughout the mass being as previously assumed. 

 If the value CTbe eliminated in the general equations for P 

 and My the pressure at the surface of the mass M whose 

 radius is R, is found to be, 



M 2 k 



The work done on this mass by superposed layers while the 

 radius shortens by dR is 



dW^ — AirlPPdR. 



Hence 





*R 



M*k II dR _ Wk 

 T ' R 2 ~ 2R' 



oo 



* Annalen der Physik und Chimie. Bd. V. S. 560. 



