BEITISH ISLES FOR THE EPOCH JANUARY 1, 1915. 
65 
Case 2. A doublet with axis horizontal with south pole to the right. 
Take axes as before with x in the vertical plane containing the axis of the doublet, 
then 
= — p-xjf?. 
In the vertical plane containing the magnetic axis we find that the forces at the 
surface are 
where 
V = — -fi. 
(f+l)i 
H = 
AdzM!) 
r (f+i)*’ 
The curves are shown in fig. 2 with the same conventions and on the same scale 
as in fig. 1. In this case the points A and R will appear to act as attracting and 
repelling centres respectively. 
We observe also that the maximum vertical force is less than half what it is in 
Case 1, while the maximum horizontal force is not very much increased. Further, in 
Case 2 the changes of both V and H are not so rapid as in Case 1. 
Case 3. A doublet of moment /x with its south pole upwards, the axis being 
inclined to the horizontal at an angle I. 
This case is intermediate between Cases 1 and 2. We have 
0 = —fj. cos I {x-{-z tan I)//3^ 
and for the special case tan 1 = 3, 
0 = 0’316/x {x + Sz)fp^. 
In fig. 3 we show the equipotential curves and the lines of apparent horizontal 
force on the surface. The unit of distance is again the depth of the doublet beneath 
the surface and in the figure is taken as 1 cm. There appears a strong attracting 
centre at A and a weak repelling centre at R. If C is the surface point vertically 
above the doublet CA = + 0T09 and CR = —4‘609. 
In the vertical plane containing the axis of the doublet the forces at the surface 
are 
y _ n-Qi c A ^ (^~^) (^+1) 
H = 0-316 ^ ^Q9)(^-0 109) 1 
r I (f +ir j 
where ^ = x/^. 
The values are shown to scale in fig. 4. The conventions are as in figs. 1 and 2, 
and the unit of distance is but the ordinate scale is now 1 cm, = 0'474^/^^, so that 
it is slightly more open than in Cases 1 and 2. 
VOL. CCXIX.-A. K 
