74 0. E. SCHIOTZ. [NORW. POL. EXP. 
Fen SA ON hl aes 
(e, — 1), and under it a base of thickness (#, — h.) and density (0, — @), which 
on the whole is negative. Along the coast margin, we must imagine this 
covering with density (e, — 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, — h,), 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 0 
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 g 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, and R,, and half the aperture of the 
cone @, the attraction will be F¢ 
F 
red 5 — 3 : et wacees |e 
Ong OT aa 8 R? [28s @ + cos 6 — sin @) sin 5 
— (Ri +Ri+ Ki Bs cos 6 —3 Ri sin? 6) VR? ae On, R, cos a| a Vil. 
QR, (1—sin 5) sin § 
VR? + R2 —2R, R, cos 6 — (R, — R, cos 8), 
+22 of. R, sin? 6 cos 6 log. nat. 
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 
