112 



Trans. Acad. Sci. of St. Louis. 



distance from the center. The pressure in atmospheres is 

 found to be 1.74 X 10 -7 , and the density in grammes per cc. is 

 found to be 1.40 X 10~ 12 . These values remind one of the 

 conditions in a highly exhausted Crookes tube. It is at once 

 evident that we can hardly conceive planetary masses being 

 separated from a nebula having such a high degree of atten- 

 uation. 



Of course the assumption made implies that the mass ex- 

 ternal to Neptune's orbit is infinite. The pressure at Saturn's 

 distance from the center would be 2.85 X 10 -6 atmosphere, 

 and nevertheless more than half of the entire mass of the 

 solar system would lie in the spherical shell between the 

 orbits of Saturn and Neptune. 



In order to examine the case of a nebula having a finite 

 mass we may introduce into eq. (10) of the former paper a 

 constant of integration. This constant is so chosen that the 

 pressure becomes zero at any radius R . Eq. (10) then becomes 



P = A 2 ~ n B 



n n 



\RV \1Q) 



(51) 



where B 



4c7i — dn 2 \2-?i 



/ 4?i — 6n e \ 

 = \(2 — ny2irk) 



In this equation, h is the gravitation constant = i » l9 v irt 7* 

 Since P = A$ n , the density at any distance R will then be 



— L 1 

 8 = A 2 - n B n — 



2 

 Bi-n 



-d) 



'in ~ 

 B\2= 



(52) 



Since -r = Pv = O T it will be observed that pressure, 



density and temperature all approach zero, as R approaches 

 R . This of course means that the law of a perfect gas does 

 not hold for the outer layers of the nebula. It also seems 

 to indicate that there is no very serious danger of the heated 



