66 
ME. GEOEGE W. WALKEE ON THE MAGNETIC EE-SUEVEY OF THE 
We note that H changes sign at ^ = +0’109 and —4'609, while V changes 
sign at ^ = 2 and ^ = — 1. 
These cases show that important quantitative tests can and must be applied in 
seeking to explain observed disturbing forces in this way. The rapid fall in the 
values of V as we pass to increasing distances raises a difficulty in actual cases, to 
which we shall return later. The difficulty can be met, at least partially, by 
considering the magnetic disturbing system to extend horizontally over a considerable 
area. We accordingly examine : 
Case 4. A very oblate spheroid magnetised vertically. 
The total magnetic moment is and the disc extends horizontally in a circle of 
radius a at a depth ^ beneath the surface. The magnetic potential at any point is 
(/, = -3/x ^ A + cot V-j, 
where xfr is determined from the equation 
(x^ + y^) cos^ + coffi xfy = cA 
The forces at the surface in any vertical plane through the centre of the disc are 
a 
TT 
9 
(1+r^siid Vr) 
(1+7’^ sild ^)J ’ 
where 
P — _ A 
(l + 7'^ siid i/r) ’ 
= {x^ + 7f)/^\ 
and the appropriate positive values of \fr given by 
7’^ cos^ \p'+ coffi -v/r = 
are used. 
Fig. 5 shows the values of V and E, in the same way as before, the unit of distance 
being ^ the depth of the disc. In the figure ^ is now taken as 1 cm. and a is assumed 
to be 5 times The scale of the ordinates is now 1 cm. = ju/a^. 
The curves show the important feature we require, viz., that the changes of V are 
now less rapid. Thus the + maximum of V at 7‘ = 5'9 is now about one-fourth of 
the value at 7* = 0, whereas in Case 1 the -1- maximum of V at 7’ = 2 was sVth of the 
value at r = 0. 
Let us now examine the special case that suggested these calculations. 
At Strachur the disturbing forces are 324y upwards and 164y horizontally, while 
at Lochgoilhead we have 278y upwards and 148y horizontally. The horizontal 
disturbing forces intersect at a point nearly G km. from each station. It will simplify 
