118 



Trans. Acad. Sci. of St. Louis. 



pated by impacts and radiations that the mass may never 

 become fused if the total mass of the planet is relatively 

 small. The possibilities in regard to the former temperature 

 of the earth are under consideration, but no final conclusion 

 can as yet be given. It does not at present seem necessary, 

 or even probable, that the material composing our earth was 

 ever in a state of fusion. 



In the case of the central mass left after the separation of 

 Mercury, it is of course easy to understand how this enor- 

 mous mass should finally fuse and vaporize. Its present con- 

 dition may be compared with what would result if it had 

 condensed to its present volume from a gaseous nebula filling 

 what might be called an equitable part of the vast space 

 whose radius is the distance to the nearest fixed star, which 

 is 3.06 X 10 18 cm. We may now compare the value of the 

 radius R of any spherical isothermal T with the radius R of 

 the zero isothermal forming the outer limit of the nebula. 



By (51) and (52) 



P_ 



n— 1 In n—\ 



JrJ (4-3n)n \+*( 1 _ |^p\^ 



( 



>,y2irk 



2(n-l) 



R 2 ~ n 



(56) 



Combining this equation with (55) by the elimination of 

 A and replacing R by xR in the resulting equation, the 

 value of x is 



x = 



, ^\ (2— n) 2 kM J _ 



2-n 

 2n 



(57) 



Hence 

 R = 



In 



R 2 ~ n 



. ^\ (2— n y kM ) J 



1—n 

 •2n 



(58) 



