Table XXVIII.—Fourier Coefficients in Years of many and few Sun-spots.

Year. Winter. Equinox. Summer.
S max. S min. S max. S min. S max. S min. S max. S min.
′ ′ ′ ′ ′ ′ ′ ′
c1 3.47 2.21 2.41 1.43 3.76 2.41 4.38 2.98
c2 2.04 1.51 1.15 0.78 2.33 1.71 2.73 2.06
c3 0.89 0.72 0.55 0.42 1.16 0.97 0.97 0.77
c4 0.28 0.27 0.30 0.27 0.42 0.42 0.11 0.11
° ° ° ° ° ° ° °
α1 228.5  232.4  243.0  256.0  231.3  233.7  218.2  220.3 
α2 41.7 46.6 23.5 36.9 40.6 43.9 50.6 52.5
α3 232.6  243.6  234.0  257.6  228.4  236.2  236.8  245.4 
α4 58.0 57.3 52.3 60.8 62.0 58.2 57.4 45.2

§ 29. There have already been references to quiet days, for instance in the tables of diurnal inequalities. It seems to have been originally supposed that quiet days differed from other days only Quiet Day Phenomena. in the absence of irregular disturbances, and that mean annual values, or secular change data, or diurnal inequalities, derived from them might be regarded as truly normal or representative of the station. It was found, however, by P. A. Müller[29] that mean annual values of the magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885 derived from quiet days alone differed in a systematic fashion from those derived from all days, and analogous results were obtained by Ellis[30] at Greenwich for the period 1889-1896. The average excesses for the quiet-day over the all-day means in these two cases were as follows:—

Westerly
Declination.		Inclination.Horizontal
Force.		Vertical
Force.
St Petersburg+0.24−0.23+3.2γ−0.8γ
Greenwich+0.08 +3.2γ−0.9γ

The sign of the difference in the case of D, I and H was the same in each year examined by Müller, and the same was true of H at Greenwich. In the case of V, and of D at Greenwich, the differences are small and might be accidental. In the case of D at Greenwich 1891 differed from the other years, and of two more recent years examined by Ellis[31] one, 1904, agreed with 1891. At Kew, on the average of the 11 years 1890 to 1900, the quiet-day mean annual value of declination exceeded the ordinary day value, but the apparent excess 0′.02 is too small to possess much significance.

Another property more recently discovered in quiet days is the non-cyclic change. The nature of this phenomenon will be readily Non-cyclic Change. understood from the following data from the 11-year period 1890 to 1900 at Kew[32]. The mean daily change for all days is calculated from the observed annual change.

D.I.H.V.
′′
Mean annual change−5.79 −2.38 +25.9γ −22.6γ 
Mean daily change, all days−0.016−0.007+0.07γ−0.06γ
Mean daily change, quiet days+0.044−0.245+3.34γ−0.84γ

Thus the changes during the representative quiet day differed from those of the average day. Before accepting such a phenomenon as natural, instrumental peculiarities must be carefully considered. The secular change is really based on the absolute instruments, the diurnal changes on the magnetographs, and the first idea likely to occur to a critical mind is that the apparent abnormal change on quiet days represents in reality change of zero in the magnetographs. If, however, the phenomenon were instrumental, it should appear equally on days other than quiet days, and we should thus have a shift of zero amounting in a year to over 1,200γ in H, and to about 90′ in I. Under such circumstances the curve would be continually drifting off the sheet. In the case of the Kew magnetographs, a careful investigation showed that if any instrumental change occurred in the declination magnetograph during the 11 years it did not exceed a few tenths of a minute. In the case of the H and V magnetographs at Kew there is a slight drift, of instrumental origin, due to weakening of the magnets, but it is exceedingly small, and in the case of H is in the opposite direction to the non-cyclic change on quiet days. It only remains to add that the hypothesis of instrumental origin was positively disproved by measurement of the curves on ordinary days.

It must not be supposed that every quiet day agrees with the average quiet day in the order of magnitude, or even in the sign, of the non-cyclic change. In fact, in not a few months the sign of the non-cyclic change on the mean of the quiet days differs from that obtained for the average quiet day of a period of years. At Kew, between 1890 and 1900, the number of months during which the mean non-cyclic change for the five quiet days selected by the astronomer royal (Sir W. H. M. Christie) was plus, zero, or minus, was as follows:—

Element.D.I.H.V.
Number +63 1311247
Number 014 16 11 9
Number −55101 974