Nipher — On Temperatures in Gaseous Nebulae. 277 



By substitution from equation (1) the hist four equations 

 become 



CTB 



Ji = 2(14-n)-y- (14) 



g = 2{l-^n)-j^' (15) 



These are the equations which hold for any point within the 

 mass, 2 and R 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 71 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 n < 1 the 

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

 the sign of the indefinite intei^ral. The mass is iu one case 

 estimated from a zero where R = cfj , and in the other, from a 

 zero at the center. 



By dividing the value ill/ in (10) by the volume of the 

 sphere, the resulting average density of the spherical mass is 



o 

 O 



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



by (9). The average density is then, 



CT^,R^^ 

 d„= 3(l+n) 2^^^^r^^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 



