DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
5b 
The general form of 1$ may be written thus 
(64) 6K a 2 KC tan <p 2 2 [g m ” sin {(u— l) t + X 0 —a} + r m n sin {(?i+1) t — X 0 —a_r] Q r/l " 
m = 0 n = — s> 
in place of (51), and from (50) and (62) we obtain the following equations for q Tj 
and r„ 
(65) 
( 66 ) 
■g, (sin 6-2 siir 0) = 22r, n ’*R„” (s' -1), 
2 g, sin :i 6 = 22g„”R„" (*'+1). 
We shall only consider the simple law (a„ + «i cos «) for the conductivity, and we 
shall neglect the seasonal terms containing sin 3. To the first order in a x the 
following are the values of q m n and r m n for the principal 24- and 12-hour longitude 
harmonics :— 
r 
i 
'67) 
r 1 = W 
1 1 — lOi 
4 r>> 
1 
'.»(*> 
>• 0 — 
— - 2 l rh a \ cos r 4 " = -} {) a , cos (\ 
q-f = « 2 s«i cos s, 
qS = - tv4TT«i cos S , 
The values in the first line of (67) necessarily agree with (63). This calculation 
is very incomplete, but it will sufficiently illustrate the discussion of the longitude 
terms in the magnetic variation, and until the main part of the phenomenon is better 
accounted for, it is hardly worth while to make a more elaborate determination of 
q,n and r m n . 
The above investigation gives the method by which the electric current function 
is obtained. Maxwell has shown that the magnetic potential corresponding to 
a term Q m " in at a radius R within the spherical current sheet, is given by 
( 68 ) 
— 4tt (m+1) R m Q m ’7(2m+1) 
Since the lower limit of the current sheet is probably fifty* or more miles above 
the earth’s surface (the radius of which we denote by R), the mean value of r may 
be perhaps 2 per cent, greater than R. In this case, for some of the higher harmonics 
in the Tables F and J, such as Q 5 4 , the factor (R/?-) m will not be quite negligible, and 
later it will be again referred to (§ 23). 
We have so far assumed that t, n, s are all integers, so that the periodicities, with 
regard to time, of the atmospheric oscillation and conductivity are commensurate. 
In the case of the lunar diurnal atmospheric oscillation and the atmospheric con¬ 
ductivity (which depends on solar time) this is not the case. The difficulty may be 
overcome in a fairly accurate way by regarding the conductivity as a function whose 
#§§21, -G- 
