VARIATION OF TERRESTRIAL LIAGNETISM. 
Appendix. 
On the Currents Induced in a Spherdccd Conductor hy Variation of an External 
Magnetic Potential. 
By Horace Lamb, M.A., F.R.S. 
The general formulse for the currents induced in a sphere of uniform conductivity by 
any electric or magnetic disturbances outside it have been given in the ‘ Phil. Trans.,’ 
1883, pp. 526 et secj. I here reproduce (with some further developments) so much of 
the investigation as is required for the discussion in Part V. of the foregoing paper. 
Suppose that, the origin being taken at the centre of the Eartli, we have an external 
disturbing force, whose magnetic potential near the Earth’s surface is 
when is a solid harmonic of positive degree 7 i , and i = ^f — 1. 
The corresponding values of the components of electric momentum are 
^ n + lfclz 
i f d d . 
,Vn v& 
H = 
1 
+ 1 \ dy 
d 
d 
the time-factor being omitted here and elsewhere for shortness. For these values 
make 
, da _ 
djc dy dz ~ 
and also give, for the components of magnetic force, the values 
im _df^ 
dy dz 
\ dn,. 
+1 - b i + +") w 
and, similarly. 
dx ’ 
y8= - 
7 = “ 
dy ’ 
dVL,i 
3 u 
MDCCCLXXXIX.—A. 
