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 R is 



M 



1 



R 2 8dR 



Making; R = xR n where the extreme limits in x are 

 and 1, and substituting & from the previous equation the 

 value of M is 



1 J_ 4— 3n 



M = 4TrA i - n B n R ( ?- n 



x i- n 



In \ 



dx. 



(53) 



The value of / (x) 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 I C x ,. . , 



above integral between the limits and 1 K 



O — ■ 



could be evaluated in terms of the Gamma 0*1 



0.2 

 0.3 

 0.4 

 0.5 

 0.6 



J 2 — n I "t^L-i 1 ±^_i 0.7 



f{x)dx = -^- I t » (1—t) « dt 0.8 



^° i!o 



function. 



Putting 



1—n 



x = t~ 1 in~ we have 



■2—n 



0.2167 

 0.3685 

 0.5008 

 0.6188 

 0.7223 

 0.8122 

 0.8870 

 0.9450 

 0.9835 

 0.9976 



Since n = 1.101, the function is transcendental and its 

 value is finite. Its value is * 



* DeHaan. Table 1, No. 8. 



