NO. 8.] REMARKS ON THE EARTH’S CRUST. 75 
terms, on the other hand, vary with 6; for a certain value of the latter, their 
sum equals 0. For smaller values their sum is negative, and its numerical 
value becomes greater and greater the nearer @ approaches 0, in which case 
the numerical value becomes equal to the first term. For greater values of 
6, the sum becomes positive, and increases continually with 6, until for @ = zz 
it becomes equal to the first term. An idea of the value of 6 for which the 
sum of the two terms equals 0 may be obtained by the aid of the following 
proposition, which is easily proved. Ifa point Pis situated outside a spherical 
shell with constant density and its centre at O, a spherical surface with the 
line OP as its diameter will divide the shell into two parts, which will each 
exert an equal influence upon P, and thus an influence equal to half that 
of the entire shell. Thus the thinner the shell, the smaller will be the angular 
radius, @, of the conical section, which will exert an influence equal to half 
that of the entire shell upon a point in the centre of the limiting zone. 
By the aid of the above expression, we will try to determine the influence 
of a similar conical section of the above-mentioned continental added masses 
upon a point on the earth’s surface in the centre of the limiting zone. We will, 
as before, assume the thickness of the earth’s crust to be h, = 0°02 Ry, and 
the depth of the sea, h, = 3°5 km. = aS R,. 1 For the sake of simplicity 
we will assume the densities, (0, — 1) and (g, — 9), to be constant in both 
layers. This will make no perceptible change, as the numerical value of 
(0, — @), according to what we have said above with regard to the con- 
stitution of the ocean-bed, is probably smallest not only deepest down in the 
base, but also above just below the covering. The following diagram 
represents graphically the result of the calculation. The angular radius of the 
zone is the abscissa, and the ordinate gives the alteration in the acceleration of 
gravity dependent upon the section. Each division indicates 0°02 mm. It 
will be seen that even for an angular radius of 20°, which will correspond 
to a radius of about 2200 km., the interior negative masses will not altogether 
succeed in neutralising the attraction of the external positive shell. The aggre- 
gate effect of the section, however, is only about 0:07 mm. 
1 The numerical values here chosen are of no importance for the following investigation, 
only supposing that the thickness of the crust is considerable in relation to the depth 
of the ocean, and yery small in comparision to the earth’s radius. 
