VARIATION OF TERRESTRIAL MAGNETISM. 
495 
If we, then, take it as proved that the primary cause of the variation comes to us 
from outside the Earth’s surface, we are led to consider that a varying magnetic 
potential must cause induced currents within the Earth, if that body is a sufficiently 
good conductor. These induced currents might be the cause of the apparent reduction 
in amplitude. As my colleague. Professor Lamb, had given considerable attention to 
the problem of currents inside a conducting sphere, I consulted him, and he gave me 
the formulse by means of which the induced currents can be calculated. His investi¬ 
gation is added as an Appendix to this paper. 
V. Discussion of effects clue to Currents Induced in the Inside of the Earth. 
I shall assume, then, for the present, that there is a periodic magnetic disturbance 
having its cause outside the Earth, and being probably due to electric currents in our 
atmosphere. Currents will be induced within the Earth, and we must now discuss 
what the effect of these currents will be, and whether they will account for the reduc¬ 
tion in amplitude of the vertical forces which the observations show. 
The varying potential can be expressed as a sum of terms of the form 
cos -f X), 
where O is a solid harmonic of degree n. Professor Lamb’s formulse allow us to 
calculate for each value of n, and for each value of p, the magnetic effect due to the 
induced currents, on the supposition that the specific resistance p of the Earth is 
uniform. The forces due to these currents will have a different amplitude and a 
different phase from the original forces, and it is the resultant effect which we observe 
in the diurnal variations. The general effect will be to increase the horizontal com¬ 
ponents and to diminish the vertical component. The difference of phase will be the 
same for all components, provided we give a different sign to the amplitude of the 
vertical components of the inside and outside currents respectively. Otherwise the 
difference of phase of the vertical component will be greater by two right angles than 
the difference of phase off the horizontal components. 
If one of the horizontal forces and the vertical force due to the solid harmonic of 
positive degree n are written 
a cos (pt -{■ X) and b cos {pt X -j- e), 
the corresponding components due to the induced potential of negative degree will be 
of the form 
c'a cos {pt -b X -j- a) and ch cos {pt -f- X -|- e -p a). 
Table XX. gives the coefficients c', c, and a for given values of the specific resis¬ 
tance p, if n = 2. The value of S has the same meaning as in Professor Lamb’s 
paper, and is connected with p by tbe equation 
p8 = 47rpR^ 
