Nipher — On Gravitation in Gaseous Nebulae. 63 



when applied to the entire sphere by (3) and (2) the equa- 

 tion becomes 



3^27-2 4 

 3A^o=2^^.3-^»'=^^o^o- (13) 



This result agrees perfectly with (12), that equation apply- 

 ing to volume of unit mass, and (13) to the volume corre- 

 sponding to the average density of mass M^. 



The same equation applied to the mass M^ when contracted 



4 

 to volume F = o ^ri?^ gives 



3PF = PX 4 7rP3 = CT^M^. (14) 



Hence the pressure which must be applied to the contracted 

 sphere, in order to hold it in equilibrium, is, by solving (14) 

 and replacing M^ from (3), 



The pressure at this surface after contraction has taken 

 place, is therefore p times as great as was required in the 

 initial state, as will be seen from (6). 



The weight of unit mass at the surface after contraction is. 



This value is also p times as great as the value given by (8). 



It is evident therefore that the weight of a gramme at any 

 fixed point within the entire mass has, by reason of this 

 shrinkage, been multiplied by p. 



It follows that the density of the gas at the surface R, 

 where the pressure is now given by (15), must be 



GT,p^ 



VT^~ -ZirkR' 



(17) 



The effect of this shrinkage upon the pressure which the 



