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 = TT TT i?% the same equation gives 



F' X -y^— TV B^ =2 (1 + n) 7 " 

 1 — n k 



Hence solving for P', 



P' — (\ n^ \ 0^0 — M n^\ ^ o" 



lirkB? ^ ^ 2iTkB? 



(20) 



The pressure at this surface of radius 72, before contraction 

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

 of contraction, been multiplied by p^~'^'\ 



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

 tion, 



d'= (l — n^\ ^^"^0= d-n-'^ ^^'^ . (21) 

 "^ ^^ ^^^27rkB' ^^ '' > 2'7rkB^ ^ ^ 



This density is determined by dividing (20) by CTg, or, 



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



4 . 3 



volume - 7ri?^, by this volume and by the factor Equa- 



3 1 — n 



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



contraction took place. This density has by the contraction 



been multiplied by />^~". 



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

 It is the mass initially within radius i?^. The mass within 

 the same volume, of radius B, before contraction, is given in 

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



The weight of a gramme at this surface after contraction 

 has taken place is 



y' = 2(l + «)-i^=2(l+«)-^. (22) 

 This value has been multiplied by ,0^"". 



