74 0. E. SCHI0TZ. [NORW. POL. EXP. 



(0, 1), and under it a base of thickness (h l h z ) and density (^i Q), which 

 on the whole is negative. Along the coast margin, we must imagine this 

 covering with density (Q } 1), decreasing in thickness outwards towards the 

 bottom of the ocean, following the slope of the continents down to the depths 

 the covering here too, resting upon a substratum of thickness (h^ fe 2 )> whose 

 density, however, is not constant at the same depth, but decreases in an 

 outward direction as the thickness of the covering diminishes, and becomes 

 where the covering ceases. We thus suppose that the sum of the added masses 

 above every element of the surface of the inner nucleus, everywhere equals 0. 

 If we now consider a point on the surface of a continent, we shall find 

 that the attraction exerted upon it will depend not only upon the masses 

 that determine the attraction out on the ocean, but also upon the above- 

 mentioned added masses. If the point is sufficiently far from the coast, 

 these will very nearly neutralise one another's effect, as their sum is zero. 

 If the point approaches the coast, the effect arising from the fact that the 

 added masses do not form a continuous shell all round the earth, will become 

 more and more apparent ; and as the positive masses lie nearer to the point 

 acted upon than the negative, the result will be, as we shall see, a slight increase 

 of attraction towards the coast-margin. In order to have a clearer view of 

 this, we will first calculate the effect of a conical section of a spherical shell 

 with constant density Q at a point situated at the pole of the zone; the vertex 

 of the cone must be imagined in the centre of the sphere. If the external 

 and internal radii of the shell are R 9 and R 2 , and half the aperture of the 

 cone 8, the attraction will be F 



- (B\ + R\ + R R z cos 6 - 3 Rl sin 2 0) V^ + R\ - 2fl R t cos 01 + 



2E (l-sin)sin 

 2 n % f. RQ sin 2 9 cos 6 log. nat. 



V.RO + R\ 2.R .R 2 cos 6 (R 2 B cos 0), 

 where f, as before, indicates the constant of gravity. 



The first term is independent of the aperture, and represents half the 

 attraction of the entire shell at the point under consideration. The two other 



VII. 



