Nipher — Gaseous Nebulae in Gravitational Contraction. 69 



the centre. The real conditions will then be determined by 

 the rate at which heat can be taken from the mass. The loss 

 of heat will still result in a rise of temperature of the radiat- 

 ing mass and a contraction in volume. At the same time this 

 loss of heat from the mass at a greater or less rate will deter- 

 mine the time required for the nebula to pass through its 

 history of gravitational contraction. 



In this discussion the conditions are somewhat special in 

 their character, and the equations are not in a form adapted 

 to other and general conditions. If any initial condition be 

 assumed in which the temperature of the mass is T , and if 

 the mass contract so that the ratio of contraction is every- 



r 

 where p = -°» then equations (4) and (5) may be written 



c 2 T y 



P ~ 2irkR* ' (15) 



These equations give the pressure and density at any point 

 distant R from the centre, after any contraction p has taken 

 place. 



The value of g at any point within the mass will be 



2CTj> 



? = T < 16 > 



and the mass internal to any point distant R will be 



*_!££*. (17) 



The final temperature throughout the mass will be 



T= P T . (18) 



If, for example, the ratio of contraction p, be made 4, then 

 at any fixed point in space distant i?, the values of g, 8 and 

 M will be made four times as great, while the pressure will 

 become sixteen times as great. 



