Original and Actual Fluidity of the Earth and I'lanets. 2C7 



from the domain of positive science, and to possess an interest for the mathe- 

 matician alone. 



I shall conclude this investigation by examining the structure of the Earth 

 on the simple but improbable hypothesis of homogeneity, and by determining 

 how far the density belonging to the rocks of the surface may extend to the 

 materials composing the interior of the Earth. 



If the Eiirth be supposed to be composed of a solid shell, having the density 

 of the I'ocks at its surface, and of a fluid homogeneous nucleus, equations (14) 

 and (15) will become 



Tp^i-rPoC^-fO^A-, (19) 



and ^ ^ ^ 



a 



- \p,ea:-+(p-rJ e.an = (2e-m) Aa=; (20) 



in which />„ signifies the density of the rocks of the shell, p the density of the 

 nucleus, and A the mean density of the whole Earth. To equations (19) and 

 (20) must be added the following, which expresses that the mass of the Earth 

 is equal to the sum of the masses of its shell and nucleus. 



a 



Eliminating p from (19) and (20) by means of (21), they become respectively 



p-po = (^-Po)%- i-n) 



5 



and 



•2 f , , aM 3 , , m 



- { P„ + (A - p„) ^3 j ., - - p, {e - e,) = A -, (22) 



(i r a^ 1 a^ 1 



5 K"' a^ + (^ - P'>^ '■ J = ^-' - "'^ "^ a? ^^^^ 



In the case of the Earth A = 'p,, ; substituting this value of the mean den- 

 sity, and solving equations (22) and (23) with respect to e,, we find 



7e — 5m , . , 



^. = — 3 — 4>'; (25) 



a 



<f> being used to denote the fraction — . 



a, 



VOL. XXII. 2 N 



