DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
.°>9 
m the ratio (RJ R) n * (cf. § 9). Similarly, the amplitude of the induced field, which is 
( iff ) times the amplitude of the inducing field at the surface of the core, will at the 
surface of the earth be reduced in the ratio (B/R) m+1 . Hence the amplitude ratio of 
the primary and secondary fields, at the earth’s surface, will be equal to (R/R. c ) 2r ' i+1 /; 
we shall denote this by/', so that 
( 23 ) /' = (R c /Ry m+i f 
The phase differences e m n — i m ”, on the other hand, remain invariable at all radii, so 
that the modified form of the theory enables us to account for larger amplitude ratios, 
corresponding to given phase differences, than was possible in § 16. The right half 
of Table L shows that this is the direction in which change is required in order to 
fit the observational results. 
The adopted procedure was as follows. The phase differences a in Table I were 
taken as the more fundamental observed data, and the various corresponding values 
of S/n (or R/), appropriate to the several “ annual ” harmonics Q” n+1 , were read off 
from Table K. The weighted mean of the deduced values of S/n was then formed, 
less weight being given to the value corresponding to Q 2 * than to Q 3 2 , Q 4 2 , Q 5 4 , on 
account of the discrepancy between the 1902 and 1905 values of ed — i 2 \ The 
adopted value of S/n was 125. The values of a calculated on this basis are given in 
Table M, both for the annual harmonics used in determining. S/n, and for the larger 
of the seasonal harmonics, Q„ n . The value of p/R c 2 calculated from (20), when S/n is 
1*25, is 7‘31 . 10- 6 . 
Table M.—Phase Differences Corresponding to a Conducting Sphere for which 
p/R 2 = 7‘31. 10 ~ 6 . 
Annual harmonics. 
Seasonal harmonics. 
Phase difference. 
Phase difference. 
Observed. 
Calculated. 
Observed. 
Calculated. 
Qd 
o 
(13) 
o 
18-9 
Q2 1 
O 
4 
1 
0 
11 
Qr 
18 
18-7 
Qs 2 
Q 
O 
13 
Qd 
21 
19-3 
Qd 
27 
15 
Qs 4 
23 
20-5 
Qd 
24 
17 
Mean . . 
19 
19 • 3 
Mean . . 
15 
14 
The agreement between the observed and calculated values of a in Table M is good, 
especially for the annual harmonics, which are better determined than are the 
