DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
49 
currents. The Stewart-Schuster theory of their origin will form the basis of this 
enquiry, and the data to be considered will be those of Table F, p. 27, for the solar 
diurnal magnetic variations, and Table J, p. 35, for the lunar diurnal variations. 
The former data are the more accurate, and are alone suitable for exact numerical 
comparison with the results of theoretical calculation. But it will be found that 
great advantage accrues from the possession of data relating to these two closely 
similar yet independent sets of magnetic variations. 
For convenience later in the discussion it is necessary at this stage to outline 
the mathematical analysis of the above theory. The following investigation is a 
continuation of two earlier studies of the same problem by Schuster* and the 
present writer.!' It is more general than the first of these, and also embodies certain 
simplifications of the methods of both papers. The details of the calculations are. in 
all cases similar, however, and will be omitted here. 
We suppose that the phenomenon takes its rise in a spherical shell of mean radius 
r and thickness e (small compared with /•). The conductivity of the air in this shell 
will be denoted by p, and we shall suppose that p (or pe) is a function of « (the zenith 
distance of the sun from the point considered) expressible in the most general terms 
as a power series in cos w. Clearly, if is the declination of the sun, and 6 , A are the 
co-latitude and longitude of the point, we shall have 
(39) 
cos w = sin S cos 0 + cos $ sin 0 cos t 
at local time t (t 
= \ + t', cf. § 9). We suppose, therefore, that 
(40) 
00 
pe — K 1' a s cos 5 «. 
s = 0 
K — i) 
Consequently 
(41) 
{pe) 2 = K 2 2 b s cos 5 w, 
,9 = 0 
(&o= 1) 
where 
(42) 
6* 
b s = 2 a r a s _ r . 
r = 0 
It is convenient to transform pe and {pe) 2 into Fourier series in 
cos st as follows : 
(43) 
00 00 
pe = K 2 f s cos st, {pe) 2 = K 3 2 g s cos st. 
— y. _oo 
Here 
(44) 
oo 
fs = f-s = 2 s+2q C q . d s+2q . (f cos S sin 0) s+2s , 
<1 = 0 
(45) 
■00 
g s = Q-, = 2 S+2? C ? . e s+2q . (£ cos 8 sin 0) s+2g , 
? = 0 
VOL. CCXVIII.— 
* Schustei!, ‘ Phil. Trans.,’ A, vol. 208, p. 185. 
t ‘ Phil. Trans.,’ A, vol. 213, p. 288. 
-A. H 
