196 The N.Z. Journal oe Science and Technology. [Aug. 
It was to be expected that analysis would show that the variations in 
1905, 1910, 1914, and 1919 were especially related. It must be a fact 
that all four melodics must be simple which, when played two together in 
pairs, produce almost exactly the same symphony instead of discord ; and 
it was found to be so, in that not only were the amplitudes of the com¬ 
ponents related in magnitude, but the phase angles in each year evinced 
curious simple relations. For example, in— 
1905 A 2 = 1241°, A 4 = 551°; sum = 180°. 
-.q^fAj = 123°, Ag = 243°; differing by 120°. 
{A 2 = 109°, A 4 — 197° ; differing by nearly 90°. 
•jo-, a f A 2 = 71 J°, A 4 = 200° ; sum - 270° very nearly. 
| A 4 ='240°, A 3 = 52° ; differing by 180° nearly. 
1919 A 4 = 169J°, A 3 = 231° ; differing by 60° nearly. 
As further evidence of a connection over a nine-years period we have— 
1904, P 4 - P 3 = 4-87 - 2*28 = 2-59 y 
1913, P 2 — P 4 = 3-61 — 1-03 = 2-58 
1902, P' + P 4 = 2*77 + 2-95 = 5-72 
= 2 X 2-86 (noted above) ; 
also 1918, P 0 + P 4 = 5-09 + 1-26 = 6-35 
1913, P 2 + P 4 = 3-61 4- 2-70 = 6-31 ; 
and P 4 in 1915 = 3*05 = P 4 in 1917. 
The year 1916 seems rather a centre of interest. 
1902, P 4 — 2-77 = P 4 in the average year of 1914 to 1919 inclusive. 
In 1914-1919 inclusive (average annual variation) :— 
P 4 = 2-77 ; A, = 101° = 90° + 11°. 
P 9 = 4-59 ; A 2 = 971°. 
P 3 = 1-34 ; A 3 = 349° = 360° — 11°. 
P 4 = 0-42 ; A 4 = 22°. 
It may be said that all these relations are very important, and that an 
extended analysis in a 328-7-day period (or succession of periods, rather) 
is of the utmost importance to evaluate the influences at work in that 
period. The evidence of the vast compelling-power of the sun’s rotation is 
indisputable. 
The analysis will be proceeded with. As an interesting and perhaps 
very important fact it is remarkable that, taking the annual curve for a 
year of sun-spot minimum (1913), and the annual curve for a year of sun¬ 
spot maximum (1918), the areal difference of the curves for the first half 
of the years is exactly equal to the areal difference in the second half. 
Nowhere previously have such exact relations been shown to exist in the 
separate analyses, and the discussion of annual inequalities has received 
little attention of late years. Proceeding on different lines, Dr. L. A. 
Bauer has lately achieved considerable success in correlating the variations 
of solar-spottedness with magnetic values at a few stations with a view 
to future prediction, but the correlation is far from exact, and only approxi¬ 
mately so in the case of some equatorial stations. 
The publication of the above results may lead to further activity in 
this particular branch of analytical investigation, which is undoubtedly 
the correct way of proceeding to accurate prediction, but much patient 
work remains to be done. It must not be lost sight of that in the annual 
