Nipher — Primitive Conditions in the Solar Nebula. 113 



gases from the interior escaping from such a nebula, since 

 molecular motion must cease at the outer limit. 

 The mass internal to any radius H is 



P 



M=i7r\ li^dJR 



Making B = xR^ where the extreme limits in x are 

 and i, and substituting S from the previous equation the 

 value of M is 



M=4.'TrA^- 



Cx 

 1_ 1. ^~3" I 1 / 





dx. 



(53) 



The value of f (»;) in this equation was platted for values 

 of X between 0.001 (where /(a;) = 4.720) and unity. The 

 integrals determined by means of the planimeter are given in 

 the following table. 



Mr. James of the mathematical department of Washington 

 University afterwards pointed out that the 

 above integral between the limits and 1 

 could be evaluated in terms of the Gamma 

 function. Putting 



2— n 



X = < "2^ we have 



X 



J f{x)dx 



I 



f[x)dx = 



2—71 I 



2-n 

 t 2n 



4— 3« 

 t 2« 



— 1 



l+n 



(1-0 



— 1 



df 



Since rt = 1.101, the function is transcendental and its 

 value is finite. Its value is * 



♦ De Haan. Table 1, No. 8. 



