BRITISH ISLES FOR THE EPOCH JANUARY 1, 1915. 
67 
the arithmetic without vitiating our inferences if we suppose that at both stations 
the forces are the same and take the vertical disturbance as SOOy and the horizontal 
disturbance as 150y. 
It is clear that if we are to correlate these forces with some magnetic source 
between the stations we cannot do so by south poles alojie, wdiich would have to be 
high up in the air, nor by north poles alone whicli would give the wrong direction 
for the horizontal foices. But a doublet with its axis vertical south pole up, situated 
at a point beneath the point of intersection of the horizontal forces, will meet the 
case. Thus, using the formulae of Case 1, we find that to explain an upward force 
of 300y and a horizontal attraction of 150y at a distance of 6 km. we require a 
magnetic moment of 7'1 x 10^* c.g.s. at a depth of 0‘95 km. 
Now even if this doublet is regarded as a sphere magnetised as strongly as a 
laboratory magnet its moment per unit volume could not exceed 100 units. Thus 
the volume of the sphere required is 7‘1 x 10^^ c.c., and if the density is 7’5 the mass 
of material involved is 5’3 x 10^® gr., or nearly 53 million tons. This is a minimum 
estimate, for if the sphere was magnetised only by the earth’s induction a much 
larger quantity of material would be required. 
Such a large quantity raises a serious difficulty in the explanation, and another 
difficulty must be mentioned. If the explanation is correct the vertical forces 
experienced just above the doublet would come to 40,000y, which is not far short of 
the normal force due to the earth. Only direct test could settle if this is so, but the 
result seems rather improbable. 
To remove this latter difficulty we may apply Case 4 to explain the data. 
We find that the depth required is 075 km., and the magnetic moment of the 
disc 5’3 X 10^^ c.g.s. units, so that on the same supposition as before we must have at 
least about 40 million tons of material as strongly magnetised as a laboratory 
magnet. The maximum vertical force over the centre of the disc is now only 3600y. 
Thus we have considerably reduced the vertical forces to be expected near the 
centre, but we have not substantially reduced the amount of material required, 
although it is spread over a greater area. 
Thus if the disturbing forces are correlated we have to conclude that the existence 
of quantities of magnetic material much larger than would have been suspected at first 
sight has to be admitted. 
The preceding theoretical discussion with its illustrative example taken from the 
survey shows the serious difficulty that arises in giving a quantitative explanation 
of the correlation of disturbing forces over a range even as small as 5 km. 
The difficulty is enormously increased when we attempt correlation over larger 
distances. 
It may be recalled that Rucker and Thorpe considered that the separate examina¬ 
tion of the vertical and horizontal forces provided two independent tests of the 
existence of ridge and valley lines. Their data gave considerable support to the view 
K 2 
