VARIATION OF TERRESTRIAL MAGNETISM. 
515 
It remains to introduce the conditions to be satisfied at the surface of the sphere 
(r = R). The continuity of electromotive force, i.e., of 0, H, requires 
(^’It) . oin 
n + 1 
. ['C - RJ 
The continuity of the magnetic force involves the continuity of the space- 
derivatives of F, G, H, and, therefore, of dF/dr, dGjdr, dFL/dr. Hence 
{iEx'. (^-R) + »x. ('•^R)! = dh + 'Gr • [’■ = 
We thence find 
, . 2ft -H 1 ^ 
. V ) • oy^i — _ 15 
/V \ / 
{Z;Ry',j (Z:R) fi- {2n + 1) y?* (^■Ft)] o)n = 1 “TT 
OV “1“ J. 
which are equivalent to 
/d-Pd 
Hence 
2ft + 1.2ft + 3 +• "" ~ ft ’ I 
1 f 
X«-i = ~+l J 
^ . /^-Fd _ y.^i(tP) 
fl,j ?t + 1 2ft S- 1.2?i + 3 (/up) 
[r = R] 
R] 
This gives the ratio of surface potentials, and, therefore, of horizontal forces, due 
to internal and external influences respectively. Since this ratio is “complex,” there 
will be a difference of phase, as well as of amplitude. The corresponding ratio of 
vertical forces is 
dFl _ n _ 1 
dr 
dVL,^ 
dr — 
ft -j- 1 O _ a _ 1 
ft XIa 
2ft -f- 1.2ft -T 3 %ji-i (HI) 
r = 'R 
To interpret these results it is necessary to calculate the function 
where 
_ . %«+i(G_ 
2ft + 1.2ft 4-3 
^2 = . ,• ^ ,-s gay. 
p 
3 u 2 
