NipUer — Oaseoua Nebulae in Gravitational Contraction, 67 



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

 the equation. 



Eliminating Fin (10) and (11) 



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

 tions 



PV^ = (rf^. (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 Ritter* in 1878, in the form 



Pv^ = 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 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 B, the distribution 

 of pressure throughout the mass being as previously assumed. 

 If the value CT be eliminated in the general equations for P 

 and M, the pressure at the surface of the mass iJf whose 

 radius is B, is found to be, 



__ M'^k 



The work done on this mass by superposed layers while the 

 radius shortens by dB is 



dW=—^7rB''FdB. 

 Hence 



rB 



Vc I dB 



f j B' 



M^: I dB_Wk 

 W o I JD2 - 2B' 



AnnaJen der Physik tind Chimie. Bd. V. S. 550. 



