2^ipher — The Law of Contraction of Gaseous Nebulae. 159 



4 

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



o 



The average pressure within radius B may be found by 

 substituting P from eq. (10) in the equation 



r 



P' = ^^. =3|^P. (37) 



6 — 5?! 

 47r I RHR 



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

 age pressure within the mass i¥" would be infinite. Making 

 71 = 1.1 the average pressure is found to be 5.4 P . 



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

 mass 



If n = 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 

 w = 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 



^a = ^^^^T=1.0S T, (39) 



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

 perature is 



