Nipher — On Temperatures in Gaseous Nebulae. 279 



Let it be assumed that the temperature of each element of 



mass remains unchanged. After the mass has contracted to 



4 

 volume F = TV TT R^, the same equation gives 



P' X .p^— TT i?3 = 2 (1 + n) ^ 7 ' ^ 

 1 — n ' k 



Hence solving for P', 



^'=(^-''^)2'S§3 = (l-»^)2?S. (20) 



The pressure at this surface of radius i?, before contraction 

 took place, is given by (8). The pressure here has by reason 

 of contraction, been multiplied by ^^"^n 



The density at the same surface is therefore, after contrac- 

 tion, 



This density is determined by dividing (20) by GT^^ or, 

 by dividing the mass M^ of (18) which now fills a sphere of 



A ^ 



volume - ttR^, by this volume and by the factor . Equa- 



tion (9) gives the density at this surface of radius R before 

 contraction took place. This density has by the contraction 

 been multiplied by p^~^. 



The mass within radius R after contraction is given in (18). 

 It is the mass initially within radius R^, The mass within 

 the same volume, of radius i?, before contraction, is given in 

 (10). This mass has also been multiplied by ^^~". 



The weight of a gramme at this surface after contraction 

 has taken place is 



^' = 2(l + n)-^^=2(l+n)-^. (22) 

 This value has been multiplied by ^o^-^. 



