1921 .] 
Departmental Eeports. 
195 
DEPARTMENTAL REPORTS. 
Some Results from the Preliminary Discussion of the Annual 
Variation of Horizontal Magnetic Force at Christchurch. 
By H. F. Skey, B.Sc., Director of the Magnetic Observatory. 
(Communicated by the Surveyor-General.) 
« 
In view of the relations shown in the last Annual Report of the Department 
of Lands and Survey to exist between the annual changes of H in 1905, 1910, 
1914, and 1919 it was of exceeding interest and importance to investigate 
further, and as a preliminary the apparent annual variations in each avail¬ 
able year have been subjected to a preliminary degree of harmonic analysis. 
The results have fully confirmed expectations, and indicate the way to 
further research. 
Corrections for non-cyclic secular change have been applied to the data 
throughout each individual year; and in order to detect periodic variations 
the amplitudes and phase angles at January 0 d. have been calculated for 
the first four harmonic components of the year’s variation in H, treated 
as entirely cyclic within the twelve months. The amplitudes and phase 
angles are found to exhibit exact relationships between different years in 
the series to such a degree that it is confidently expected the exact laws 
followed by these relationships will be discovered, and that we shall thus be 
enabled to predict the value of H in future years and months, and incidentally 
to evaluate the true annual cyclic variation. 
It has also been found that the two usually principal harmonic com¬ 
ponents of P 4 and P 2 amplitudes and of initial phase angles A 4 and A 2 
at January Od. are in the same phase at intervals of 328-7 days, or the 
period of twelve solar synodic rotations. The reality of this period is 
confirmed by other considerations ; and it is probably the principal period, 
of next importance to the year, in the variations. The influence of the sun¬ 
spot period is also seen, but an exact eleven-year period seems very 
doubtful. 
As an instance of the surprising exactness of the relations obtained it 
may be noted that the value of P 3 is 2-8 y in the analysis of each of the 
years 1910, 1916, 1920 ; that P 4 = 1-44 in each of the years 1905 and 1920 ; 
that P 2 in 1.920 = twice P 4 in 1918 ; that P 2 1920 — P 3 1920 = 5-88 = 
P 2 in 1905 exactly ; that in 1918 (the year of sun-spot maximum) P., -f- P 3 
= 7-63 — 2 (P 2 —- P 4 ). 
With regard to initial amplitude, it is noted more especially that 1914 
a 3 = + 1-44 ; 1917 a 3 = — 1-44 ; and with regard to the b co-efficients, 
it is noted more especially that 1917 & 4 = — 1-21 ; 1918 & 4 = -4- 1-21. 
Note also 1910 a, (+ 7-12) - 1915 a, (+ 2-77) = + 4-37 = P 4 in 1918 ; 
and 1917 a t (+ 0-51) ~f 1918 a 2 (+ 4-58) = 5-09 = P 2 in 1918. 
It is also true that a 2 in 1918 — exactly P 2 in the annual analysis of 
the mean year for the period 1914 to 1919 inclusive—an attempt b) 7 
the method of jumbles to get average value for the twelve-monthly 
period. 
