NO. 8.] REMARKS ON THE EARTH'S CRUST. 67 



If the integration in this equation is effected in the same way, we obtain: 



_, _ a _ l _ a -- , 



** jt 



where Q" is the difference between two densities, which may be considered 

 as a kind of mean value of p, and Q, between h = and h = h t fo 2 , 

 differing from $', although the difference cannot be great, as in any case 

 gj e is only very small. (/ may be straightway put down as equal to ,' 

 in equation III. According to this equation, 



(^'-i)h,=d- Q '(h,-h t ), 

 which, substituted in the previous equation, gives 



AM 2 i _ tii ti \ r -.""! ~r~ ""i -f_*Ll 



__] (fci _ kj [9 __ -- ? __j. 



As already mentioned, there can only be a slight difference between q" 

 and p'. The numerical value of Q" is probably less than that of p', as the 

 difference in density is least, and the densities themselves greatest, in the 

 lowest strata, where the factor (h h^} in the first integral IV. has its 

 greatest value. Recollecting that S, Q" and g' are negative, we may write, 

 if we substitute Q' for q" 



-*(1--5 L )^ -(fri-Mf'-S 1 -. 



/1 . 



If now equation III. is employed for the elimination of Q' (h t fc 2 ) ,we 

 finally obtain 



or 



A << / ' 1 \ i. "i / 1 _i_ i T~ 2 'i V 



O<?,(QI IJrtj-p-llH -- p -- ) v. 



Kfl ** 



If, as previously stated, we assume that fe 2 equals 3'5 km., and that the 

 average density in the uppermost 3'5 km. of the continents is 2'7, then, with 

 a sufficient degree of accuracy, 



3 <, 6 ^- km. of density one. V b. 



^o 



Even if the exterior spherical shell has a thickness corresponding to 0'02 

 of the earth's radius, or h^ = circ. 126 km., 



- d 5^ 120 m. of density one. 



