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 = 77 TT E^, the same equation gives 



P' X ^^— TT 7^3 = 2 ( 1 + n) 7 Q 

 1 — n k 



Hence solving for P', 



^ hirkB' ^^ '' ^2 7^^•P2 (^^) 



The pressure at this surface of radius P, before contraction 

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

 of contraction, been multiplied by />^~2". 



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

 tion , 



8' = (1 — n"^) ^"^Q ^"= n — 7i2^ ^^<^^ . (21) 



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 -ttP^, by this volume and by the factor Equa- 



3 1 — 71 



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

 contraction took place. This density has by the contraction 

 been multiplied by p^~^. 



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

 It is the mass initially within radius Pg. The mass within 

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

 (10). This mass has also been multiplied by /9^~". 



The weight of a gramme at this surface after contraction 

 has taken place is 



<,' = 2(l + «)i^=2(l + „)-^'. (22) 

 This value has been multiplied by p^"^ . 



