129 
surface, according to a surface harmonic of order iy Y^, the 
current function will he given by 
(2^ + 1)A 
the potential just outside the sphere 
\=-{i+l)-Y, 
' 'a 
that just outside 
a 
or if the current sheet is just outside the earth, therefore, 
which supposition would, as we have seen, give a good 
agreement for the vertical force, we find 
2^+1 1 , 
*+r47T^ 
It follows from this, that the currents flow at right angles 
to the magnetic force at the point. If, however, the dis- 
tribution of potential cannot be represented by a single 
surface harmonic, then, as the coefficient of V differs for 
harmonics of different orders the currents, need not necessarily 
be at right angles to the magnetic force. If i is infinitely 
large the fraction depending on i is two, if i is two the 
fraction is five third, and it must always lie between those 
limits if i varies between two and infinity. There seems 
for diurnal variation no term of the first order, and we may, 
therefore, take very approximately the currents to be at 
right angles to the magnetic force at any place. In order 
to obtain the currents in C.G.S. measure from the magnetic 
force we have to apply a factor, which, as we have seen, is 
approximately obtained by putting i = 2; and therefore is 
equal to 5/1 27 t. 
In the following table, I give the direction and intensity 
of the currents at Greenwich and Bombay for the local 
solar hours. The direction of the current is as accurate as 
the observations will permit, the intensity is calculated as 
* Maxwell, Electricity and Magnetism, Vol. II., p. 281; 
