68 Trans. Acad. Sci. of St. Louis. 



Here M\/k is the mass in astronomical units. The initial 



temperature, when i? = co must be assumed to be zero. In 



its final condition the temperature of the mass has risen to T. 



C 

 The specific heat has been shown to be -y. Hence the total 



heat produced within the mass M during the operation was 



MCT 



J—. The work-equivalent of this heat is 



W=MCT. 



Equating the two values of W, and solving for T, 



Mk 



T 



2CR 



This equation is identical with (3) and the result merely 

 shows the nature of the conditions which are involved in the 

 equations which precede. 



The last equation was originally deduced by C. M. Wood- 

 ward in the paper previously cited. It was deduced as a 

 condition of statical equilibrium in a cosmical mass of gas of 

 uniform temperature T, Woodward denied that it could 

 apply in gravitational contraction, or even that gravitational 

 contraction was possible. 



It is certainly true that the equations given in this discus- 

 sion involve at each point in the gaseous m.ass, a condition of 

 balanced forces. It is as though a weight on a piston rod is 

 continually and automatically increased as isentropic com- 

 pression proceeds, and at the precise rate which continuous 

 isentropic compression demands. 



If the infinite space occupied by this cosmical mass of gas, 

 may be considered the first of an infinite series of infinite 

 spaces having perhaps increasingly higher orders of mag- 

 nitude, we might suppose that heat developed in the nebula 

 by compression may dissipate by radiation, into the realms 

 beyond. If heat could thus be abstracted from all parts of 

 the mass with equal facility, the conditions resulting would 

 certainly be different from those which would result if the 

 radiation were greatest from those parts most remote from 



