NO. 8.] REMARKS ON THE EARTH'S CRUST. 71 



_ =crc . 



Ci -"o 



if, as previously, we assume that h l = 0'02# , and fe 2 =3'5 km.; for every 

 additional 1000 m. in the height of the plateau, the thickness of the added 

 mass must consequently be increased by 20 m. 



In the following pages we shall assume, for the sake of simplicity, that 

 there is on an average the same quantity of matter over every surface unit 

 of the inner nucleus. If we then imagine all the deficiencies of matter in the 

 depths compensated by filling up from the corresponding accumulations above 

 sea-level, the surface of all continents would in the main coincide with the 

 spherical surface through sea-level. 



I have above taken the thickness of the earth's crust to be 0'02 of the 

 earth's radius. How far down we must go before we reach a depth where 

 we may assume that the density is constant all over the earth, will depend 

 upon the manner in which the density on an average alters downwards from 

 the surface of the continents and from the bottom of the oceans. By the 

 inequality in the moon's motion, dependent on the ellipticity of the 

 earth, we may now infer how the density on the whole ought to change 

 inwards towards the interior of the earth. Helmert gives the following 

 formula: 1 



where 6 is the density, a c the equatorial radius of the earth, and a the 

 equatorial radius of the equipotential surface through the point under con- 

 sideration. When a = a c , *. e. at the surface of the earth, the density becomes 

 2'66. If s denotes the density at the surface of the inner nucleus, and the 

 same symbols are employed as before, we obtain for the density, g t , h km. 

 above this surface, since a = -R h l + h, and a = ,R , 



? = s 0-00177 h. 



This gives a very trifling change of density in the external strata of the 

 earth. In the earth's crust, however, which has been subject to a more 

 rapid cooling and less pressure than the interior of the earth, we may possibly 



F. R. HELMERT. ffihere Oeoddsie. Bd. 11, p. 487. 



