Nipher — On Temperatures in Gaseous Nebulae. 277 



By substitution from equation (1) the last four equations 

 become 



VTR 



31 = 2 (I + h) -~l^ (14) 



5r=2(l + n)-^. (15) 



These are the equations which hold for any point within the 

 mass, 2 and H being related to each other in the manner 

 defined by (1). 



An examination of equation (10) shows that when T^R^ 

 (the temperature where R = \) is constant, n must be less 

 than unity, in order that the distribution may be physically 

 possible. If n is greater than unity, the value of the integral 

 at the lower limit increases, as the value of R determining 

 that limit approaches zero. The mass external to R is then 

 finite, while that internal to R is infinite. When ?i <; 1 the 

 reverse is true. This transition is accompanied by a change in 

 the sign of the indefinite integral. The mass is in one case 

 estimated from a zero where i? = go , and in the other, from a 

 zero at the center. 



By dividing the value M in (10) by the volume of the 



sphere, the resulting average density of the spherical mass is 



3 ' 



found to be .. times the density at the surface, as given 



by (9). The average density is then, 



CT^,R^^ 



^, = 3(l+n)2^^.^„^2- 



An n increases from zero and approaches unity, the aver- 

 age density of a spherical mass becomes more and more 

 nearly inversely as the cube of the radius, or R^d^ approaches 



