range in the mean diurnal inequality for the year, however this latter is formed. Other causes, moreover, are at work tending in the same direction. Even in central Europe, the magnetic curves for individual days of an ordinary month often differ widely amongst themselves, and show maxima and minima at different times of the day. In high latitudes, the variation from day to day is sometimes so great that mere eye inspection of magnetograph curves may leave one with but little idea as to the probable shape of the resultant diurnal curve for the month. Table XXII. gives the arithmetic mean of the absolute daily ranges from a few stations. The values which it assigns to the year are the arithmetic means of the 12 monthly values. The Mauritius data are for different periods, viz. declination 1875, 1880 and 1883 to 1890, horizontal force 1883 to 1890, vertical force 1884 to 1890. The other data are all for the period 1890 to 1900.
Table XXII.—Mean Absolute Daily Ranges (Units 1′ for Declination, 1γ for H and V).
| Jan. | Feb. | Mar. | April. | May. | June. | July. | Aug. | Sept. | Oct. | Nov. | Dec. | Year. | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Declination. | |||||||||||||
| Pavlovsk | 13.42 | 17.20 | 18.22 | 17.25 | 17.76 | 15.91 | 16.89 | 16.57 | 16.75 | 15.70 | 13.87 | 12.37 | 15.99 |
| Ekatarinburg | 7.33 | 9.54 | 11.90 | 12.89 | 13.63 | 13.03 | 12.78 | 12.21 | 11.23 | 9.44 | 7.86 | 6.85 | 10.72 |
| Kew. All days | 11.16 | 13.69 | 15.93 | 15.00 | 14.90 | 13.65 | 14.13 | 14.22 | 14.57 | 14.07 | 11.71 | 9.80 | 13.57 |
| Kew. Ordinary days | 10.14 | 11.87 | 14.19 | 14.24 | 13.85 | 13.26 | 13.47 | 13.67 | 13.71 | 13.10 | 10.40 | 9.00 | 12.58 |
| Kew. Quiet days | 6.12 | 7.57 | 10.59 | 11.84 | 12.09 | 11.95 | 11.60 | 11.93 | 10.86 | 9.16 | 6.54 | 5.08 | 9.61 |
| Zi-ka-wei | 3.88 | 3.25 | 6.22 | 7.04 | 7.15 | 7.40 | 7.77 | 8.06 | 6.73 | 4.68 | 2.91 | 2.52 | 5.63 |
| Mauritius | 6.93 | 7.79 | 7.11 | 5.75 | 4.87 | 4.03 | 4.36 | 6.00 | 6.28 | 6.71 | 6.99 | 6.78 | 6.13 |
| Horizontal force. | |||||||||||||
| Pavlovsk | 52.4 | 74.5 | 79.1 | 80.1 | 86.2 | 79.0 | 86.7 | 77.6 | 76.7 | 67.3 | 55.7 | 45.9 | 71.8 |
| Ekatarinburg | 33.2 | 43.1 | 48.4 | 51.7 | 56.2 | 54.1 | 56.7 | 51.7 | 49.3 | 44.1 | 34.1 | 29.3 | 46.0 |
| Mauritius | 37.9 | 35.0 | 36.2 | 37.6 | 35.0 | 34.1 | 33.8 | 34.5 | 36.6 | 37.4 | 37.8 | 35.3 | 35.9 |
| Vertical force. | |||||||||||||
| Pavlovsk | 27.0 | 50.4 | 54.7 | 43.2 | 45.3 | 34.8 | 42.1 | 35.5 | 42.5 | 37.5 | 33.5 | 25.5 | 39.3 |
| Ekatarinburg | 17.4 | 26.6 | 29.2 | 30.1 | 29.6 | 27.6 | 29.6 | 26.1 | 25.2 | 22.1 | 19.6 | 16.4 | 24.9 |
| Mauritius | 17.1 | 19.5 | 20.1 | 17.3 | 16.5 | 15.5 | 17.1 | 22.0 | 22.7 | 19.4 | 16.7 | 15.2 | 18.2 |
A comparison of the absolute ranges in Table XXII. with the inequality ranges for the same stations derivable from Tables VIII. to X. is most instructive. At Mauritius the ratio of the absolute to the inequality range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and 2.05 for V. The declination data for Kew in Table XXII. illustrate other points. The first set of data are derived from all days of the year. The second omit the highly disturbed days. The third answer to the 5 days a month selected as typically quiet. The yearly mean absolute range from ordinary days at Kew in Table XXII. is 1.49 times the mean inequality range in Table VIII.; comparing individual months the ratio of the absolute to the inequality range varies from 2.06 in January to 1.21 in June. Even confining ourselves to the quiet days at Kew, which are free from any but the most trifling disturbances, we find that the mean absolute range for the year is 1.20 times the arithmetic mean of the inequality ranges for the individual months of the year, and 1.22 times the range from the mean diurnal inequality for the year. In this case the ratio of the absolute to the inequality range varies from 1.55 in December to only 1.09 in May.
§ 25. The variability of the absolute daily range of declination is illustrated by Table XXIII., which contains data for Kew[1] derived from all days of the 11-year period 1890–1900. It gives the total number of times during the 11 years when the absolute range lay within the limits specified at the heads of the first nine columns of figures. The two remaining columns give the arithmetic means of the five largest and the five least absolute ranges encountered each month. The mean of the twelve monthly diurnal inequality ranges from ordinary days was only 8′.44, but the absolute range during the 11 years exceeded 20′ on 492 days, 15′ on 1196 days, and 10′ on 2784 days, i.e. on 69 days out of every 100.
Table XXIII.—Absolute Daily Range of Declination at Kew.
| Number of occasions during 11 years when absolute range was:— | Means from the 5 largest and 5 least ranges of the month on the average of 11 years. | ||||||||||
| 0′ to 5′. | 5′ to 10′. | 10′ to 15′. | 15′ to 20′. | 20′ to 25′. | 25′ to 30′. | 30′ to 35′. | 35′ to 40′. | over 40′. | 5 largest. | 5 least. | |
| ′ | ′ | ||||||||||
| January | 51 | 145 | 69 | 37 | 24 | 7 | 4 | 3 | 1 | 22.90 | 5.07 |
| February | 26 | 99 | 84 | 51 | 26 | 10 | 4 | 2 | 8 | 27.21 | 6.55 |
| March | 1 | 72 | 138 | 61 | 32 | 21 | 8 | 1 | 7 | 29.87 | 8.93 |
| April | 0 | 43 | 167 | 73 | 27 | 10 | 6 | 3 | 1 | 23.69 | 10.31 |
| May | 0 | 57 | 157 | 85 | 20 | 12 | 3 | 0 | 7 | 25.36 | 9.50 |
| June | 0 | 56 | 185 | 67 | 15 | 1 | 3 | 1 | 2 | 19.92 | 9.89 |
| July | 0 | 59 | 185 | 70 | 14 | 5 | 2 | 2 | 4 | 22.49 | 9.96 |
| August | 0 | 37 | 202 | 75 | 22 | 1 | 2 | 0 | 2 | 21.27 | 10.05 |
| September | 1 | 68 | 153 | 71 | 19 | 5 | 4 | 5 | 4 | 24.55 | 9.52 |
| October | 3 | 103 | 111 | 67 | 34 | 10 | 11 | 2 | 0 | 23.92 | 8.01 |
| November | 42 | 140 | 81 | 28 | 14 | 9 | 8 | 5 | 3 | 23.58 | 5.64 |
| December | 64 | 166 | 56 | 29 | 14 | 7 | 1 | 1 | 3 | 20.43 | 4.36 |
| Totals | 188 | 1045 | 1588 | 714 | 261 | 98 | 56 | 25 | 42 | ||
§ 26. Magnetic phenomena, both regular and irregular, at any station vary from year to year. The extent of this variation is illustrated in Tables XXIV. and XXV., both relating to the period 1890 to 1900.[2] Table XXIV. gives the amplitudes of Relations to Sun-spot Frequency. the regular diurnal inequality in the elements stated at the head of the columns. The ordinary day declination data (D0) for Kew represent arithmetic means from the twelve months of the year; the other data all answer to the mean diurnal inequality for the whole year. Table XXV. gives the arithmetic means for each year of the absolute daily range, of the monthly range (or difference between the highest and lowest values in the month), and of the yearly range (or difference between the highest and lowest values of the year). The numerals attached to the years in these tables indicate their order as regards sun-spot frequency according to Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest frequency, and 1890 that of least. The difference in sun-spot frequency between 1897 and 1898 was microscopic; the differences between 1890, 1900 and 1899 were small, and those between 1893, 1894 and 1892 were not very large.
The years 1892–1895 represent high sun-spot frequency, while 1890, 1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to 1895 were in all cases distinguished by the large size of the inequality ranges, and 1890, 1899 and 1900 by the small size. The range in 1893 is usually the largest, and though the H and V
