172 
MR. ARTHUR SCHUSTER ON THE 
and for X = n 
[^o sin 2 6 + b (3 cos 2 0—1)] cos (t—ot) = i-cos (t — a ). 
In these equations the numerical value 0'2 has been introduced for tan <£. 
At the equator the additional terms, therefore, have amplitudes -f and 3 - respectively, 
as compared with the main diurnal term. The force to geographical west being 
proportional to the potential, we may take these numbers to be the amplitude of the 
westerly force variations. The main variation is proportional to sin 6 cos 6, and has 
zero value at the equator in the tropical region. The additional terms are therefore 
the ruling terms at the equator. The horizontal force along the same circle has unit 
amplitude, measured on the same scale, so that the new terms come well within the 
range of our observational powers. It would be interesting to trace them, but it 
should be remarked that only observations made near the equinox are suitable for 
the purpose, as the seasonal terms, which yet remain to be discussed, would otherwise 
interfere. 
7. We may interrupt the progress of our investigation for a moment to inquire into 
the magnitude of the electrostatic effect dependent on the potential S which was found 
equal to — C~^Jn.n + 1 , leading to a vertical electric force Ccn///(n+ 1 ) a. In the 
two cases which concern us, cr = n, and \Jj has values at the equator which were found 
to be SOa/ir and 15 «/ 7 r respectively. It follows that the variation of vertical electric 
force is of the order of 3 C.G.S. units, which is only 1 volt per 300 kilometres. 
This may be disregarded. 
8 . The previous discussion has only taken the earth’s vertical magnetic force 
into consideration. The horizontal force causes, in combination with a horizontal 
atmospheric oscillation, a vertical electromotive force, and so far as this produces 
electric currents, their flow is in opposite directions in strata which are vertically 
above each other. The magnetic effect is therefore of a smaller order of magnitude 
than that due to vertical force. 
9. In calculating the currents from the electric forces, I have applied Ohm’s law, 
and therefore neglected the effects of electric inertia; but it is not difficult to 
estimate the change of phase which results from self-induction. Using the equations 
given by Maxwell'" for spherical current sheets, we find that if R is the function 
defined by equation (3), and </> the current function, 
^ +Lp * =E/) ’ 
where p is the conductivity, and L = (2n+ l)/47ra; provided that R is a surface 
harmonic of degree n. If the latter function is proportional to cos Kt, we find in the 
usual way . 4^*0 
<p = p cos e cos ( Kt — e ), tan e =-. 
r ^ v 2n+l 
* See Clerk Maxwell, ‘Electricity and Magnetism,’ vol. II., § 672. 
