j^ipher — Gaseous Nebulae in Gravitational Contraction. 65 



^j,l£^{p-l). (7) 



By equating (6) and (7) the specific heat during this opera- 

 tion in which pressure, volume and temperature all change is 



C 



s = 



(8) 



This result is the well-known expression for the difference 

 between the specific heat at constant pressure and the specific 

 heat at constant volume. 



The value of J in C. G. S. units and Centigrade degrees 

 is 4.19X10^ 



The annexed table gives for a few of the '* permanent" 

 gases, the values of C, and of the specific heat s of such 

 gases when forming this gravitating cosmical mass in isen- 

 tropic compression. 



The values of C are computed from Regnault's determina- 

 tions of 6. 



SUBSTANCE. 



Hydrogen 



Air 



Oxygen 



4.140X10^ 

 2.868X10« 

 2.594X10« 



0.988 



0.0685 



0.0619 



In the cylinder of the Carnot engine where gravitation is not 

 involved, and where the pressures are uniform, the specific 

 heat of isentropic compression, computed as has been done 

 for this nebula, is the specific heat of constant volume. 



During this operation the average condition of the gas 

 within radius H changes, and this change may be represented 



