FROM ORDINARY DAYS OF THE ELEVEN YEARS 1890 TO 1900. 
245 
In the case of the phase angles the difference between sunspot maximum and 
minimum years is much less decisive. a 3 in Y in every month of the year is larger— 
i.e., speaking generally, the maximum occurs earlier in the day—in sunspot minimum 
than in sunspot maximum. There is also a large preponderance of months in which 
the sunspot minimum angle is the larger in the cases of a :) in H and of a 2 in both H 
and Y. a,, however, in Y shows exactly the opposite phenomenon, while in H and 
a i in both H and Y show no decided tendency. 
In H all four phase angles exhibit the same tendency in their annual variation. 
They are distinctly larger in summer than in winter. This is especially conspicuous 
in the case of v . x ; in sunspot minimum the phases of the 24-hour term in January and 
July approach opposition. 
An increase in phase angle means in a general sense an earlier occurrence in the 
maximum and minimum, but this requires special interpretation at times. Take, for 
instance, the 11-year values of a 1 in H. In January and February the values are 
respectively 51° 43' and 70° 49'. The corresponding times of occurrence of the 
maximum are respectively 
In January t = (90 —51'72)/l5 = 28'28/l5 = 1'89 hour = 1 hour 53.minutes. 
In February t — (90 —70‘82)/l5 = 1918/15 = 1*28 hour — 1 hour 17 minutes. 
But when we pass to March the phase angle 101 8' falls in a different quadrant, and 
the time of the maximum is given by 
t — (450 — 101'13)/l5 = 23'3 hour = 23 hours 18 minutes. 
In a sense the maximum has become earlier in March, only it has as it were 
transferred itself to the previous day; the wave, in fact had already passed its 
maximum when the day commenced. The minima in the three months occur in 
January at 13 hours 53 minutes, in February at 13 hours 17 minutes, and in March 
at 11 hours 18 minutes. Thus the statement that the minimum has become earlier 
as the phase angle increased was in this case literally true. 
In the case of Y in Table XXIY. the annual change is on the whole in the opposite 
direction to that in H, the angles a 1 , a 2 and a 3 being all smaller in summer than 
in winter. There seems to be a very appreciable accidental element in the values 
obtained for individual months, especially in the case of a 4 . 
The mode of annual variation of the amplitudes of the several Fourier waves is best 
shown by expressing the values for different months as fractions of their arithmetic 
mean. This has been done for the full 11-year results in Table XXY., data being 
given for both FI and V. The laws of annual variation for the two elements proved 
sufficiently alike to encourage the formation of the arithmetic means from the two. 
These arithmetic means are considerably smoother than the data from H or Y alone. 
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