Nipher — The Law of Contraction of Gaseoxis Nebulae. 159 



4 



If n were ^ the average density would be at the center. 



The average pressure within radius R may be found by 

 substituting P from eq. (10) in the equation 



t 



pR 



X 



47r I i?2 PdH 

 ^» = h =3«-T7P- (87) 



6 — hn 

 47r I RHR 



It is to be observed that if n were as large as 1.2 the aver- 

 age pressure within the mass ilf would be infinite. Making 

 w = 1.1 the average pressure is found to be 5.4 P . 



By (10) the average pressure is distant from the center of 

 mass 



2 — n 

 _ ,1 6 hn\ 'in 



R 



"a 



(-sSV" ^ = «-*»^^- (38)- 



If ?i ^ 1.2 the average pressure would be at the center. 

 It is therefore clear that n must be less than 1.2 in order that 

 the distribution may be physically possible. The value with 

 n = 1.1 is given above. It locates the gas of average pres- 

 sure almost exactly midway between the center and the spher- 

 ical surface of radius R. 



The average temperature, deduced in the same way from 

 (12), is 



^« = 3^=^i r=1.08 T. (39) 



The distance from the center to the surface having this tern- 

 perature is 



