DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
o t 
The amplitudes of the magnetic variations Q„” produced by an atmospheric 
oscillation Q.f, corresponding to this law of variation of conductivity, are proportional 
to the values of (m +1)/( 2m + 1)} pj\ where p m n is obtainable from Table O by 
writing a 2 = 0. For the present we shall consider only the “ annual ’ harmonics 
Q" n+ i at the equinoxes, so that we shall also write S = 0. Since the atmospheric 
conductivity cannot be negative, a x cannot exceed unity. Table 0 shows that the 
subsidiary ( i.e ., non-semi-diurnal) harmonics are greater the greater the value of a v 
If we take a l —\, the theoretical amplitudes are found to have the following relative 
values, k being an undetermined constant; the observed equinoctial amplitudes in 
the lunar diurnal magnetic variation are added for comparison {cf. Table J) ; the 
ratios of the two sets of numbers are also given, assuming k to be such that the 
ratio for Q 3 2 is unity :— 
Table P. 
Qs 1 - 
QA 
QA 
Qot 
Theoretical relative amplitudes . 
15-87 
7 • 3 k 
0-417 
-0-000197 
Observed amplitudes. 
20-5 
5 * 5 
0-43 
0-022 
Ratio. 
0-68 
1-00 
0-71 
-0-007 
The law (71) would clearly account for a considerable proportion of the harmonics 
Qd and Q/, but wholly fails in the case of the fourth harmonic Q/, both as regards 
magnitude and sign. This comparison shows, however, that the daily variation of 
electrical conductivity is at least as great as that indicated by the formula 1 + cos «, 
since if a i were less than unity the amplitudes of Qd and Q 4 3 would be still smaller 
in comparison with Q 3 2 ; also it shows that the sign of oq must be positive, i.e., that 
the conductivity must be great by day and small by night, since the observed phases 
of Qa 1 and Q/ are the same as that of Q 3 2 . If «, were negative, their theoretical 
phases would be opposite to that of Q 3 2 . 
A more pronounced variation of the atmospheric conductivity can be represented 
by the law 
(72) 1 + cos w + a 2 cos 2 «. 
In my first paper on the lunar diurnal magnetic variation I considered the following 
special case of this law* 
(73) 1 + 3 cos to + f- cos 2 w = (l +-§ cos to) 2 , 
which is never negative, and gives a much greater ratio of day to night conductivity 
than does (71). With the aid of Table O the following values of the relative 
* ‘ Phil. Trans.,’ A, vol. 213. On p. 304 a graph of this expression is given. 
VOL. OCXVIII.——-A. 
I 
