DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
23 
concerned in this paper. These functions were numerically evaluated for each of 
the twenty-one values of 6 in Table A, and the group means I. to IX. were formed ; 
by means of these the coefficients A„” and B m ”, A m n and B,„" were determined as 
described in § 8, the West and vertical force Fourier coefficients being compared with 
the formulae (9) and (10). The North force values of a n and b n were then calculated 
from A m n and B„" by means of (8). The observed and calculated values of a n and b„ 
for the various components and seasons are tabulated in Tables III. (a) to (S), and 
the values of A m n , &c., are given below in Table C. 
It is clear from the Tables III. that the above harmonic analysis, although of a 
very simple character, gives a fair representation of the main features of the daily 
magnetic variation, except for the 24-hour component of the North force variation ; 
for the other periodic terms of the latter variation the agreement with the potential 
calculated from the West force is better—-perhaps even satisfactory, when the 
irregular “ run” of the North force is considered. 
§ 10. Comparison with Previous Harmonic Analyses of the Solar Diurnal 
Magnetic Variation. 
It is of interest to examine how far the various studies of the solar diurnal 
magnetic variation, which have been made by different methods and with different 
data, agree in their main results. The principal terms in Schuster’s, Fritsche’s 
(1913), and the present analyses, so far as they are comparable with one another, are 
collected in Tables D and E. In the former table the potential functions derived 
from the North and West force variations (or, in the present paper, from the West- 
force variations only) are given. Instead of A /n n and B„”, however, the amplitude C nt ?l 
and phase a m n are given, where 
(14) A m n cos nt + B„ “ sin nt — — C m " cos (nt + a m n ). 
All the results have been modified where necessary, to conform to the notation of 
this paper. In some cases the authors cited carried their analysis further than in the 
present instance, in others, as the table indicates, they stopped short of it; but the 
principal terms were in all cases the same. 
In Tables D and E, the figures for the present paper, under the heading “annual 
terms,” are obtained from the mean of the solstitial and equinoctial results in Table B. 
They therefore represent the mean for a whole year, as in the case of Schuster’s 
and Fritsche’s results. The seasonal terms in the present analysis, on the contrary, 
refer to a half-year only, i.e., the two quarters centred at the solstices. They may 
be expected to be of somewhat larger amplitude than if they had been derived from 
the two half-years, as in the previous discussions. 
