frequency in the years of many sun-spots in the earlier sub-period. This inconsistency, though startling at first sight, is probably more apparent than real. It is almost certainly due in large measure to a progressive change in one or both of the units of frequency. In the case of sun-spots, A. Schuster (13) has compared J. R. Wolf and A. Wolfer’s frequencies with data obtained by other observers for areas of sun-spots, and his figures show unquestionably that the unit in one or other set of data must have varied appreciably from time to time. Wolf and Wolfer have, however, aimed persistently at securing a definite standard, and there are several reasons for believing that the change of unit has been in the auroral rather than the sun-spot frequency. R. Rubenson (14), from whom Tromholt derives his data for Sweden, seems to accept this view, assigning the apparent increase in auroral frequency since 1860 to the institution by the state of meteorological stations in 1859, and to the increased interest taken in the subject since 1865 by the university of Upsala. The figures themselves in Table V. certainly point to this conclusion, unless we are prepared to believe that auroras have increased enormously in number. If, for instance, we compare the first and the last three 11-year cycles for which Table V. gives complete data, we obtain as yearly means:—
| 1749–1781 | Sun-spots | 56·4 | Auroras | 77·5 |
| 1844–1876 | Sun-spots„ | 55·8 | Auroras„ | 112·2 |
The mean sun-spot frequencies in the two periods differ by only 1%, but the auroral frequency in the later period is 45% in excess of that in the earlier.
The above figures would be almost conclusive if it were not for the conspicuous differences that exist between the mean sun-spot frequencies for different 11-year periods. Schuster, who has considered the matter very fully, has found evidence of the existence of other periods—notably 8·4 and 4·8 years—in addition to the recognized period of 11·125 years, and he regards the difference between the maxima in successive 11-year periods as due at least partly to an overlapping of maxima from the several periodic terms. This cannot, however, account for all the fluctuations observed in sun-spot frequencies, unless other considerably longer periods exist. There has been at least one 33-year period during which the mean value of sun-spot frequency has been exceptionally low, and, as we shall see, there was a corresponding remarkable scarcity of auroras. The period in question may be regarded as extending from 1794 to 1826 inclusive. Comparing it with the two adjacent periods of thirty-three years, we obtain the following for the mean annual frequencies:—
| 33-Year Period. | Sun-spots. | Auroras. |
| 1761–1793 1794–1826 1827–1859 |
65·6 20·3 56·1 |
76·1 39·5 84·4 |
12. The association of high auroral and sun-spot frequencies shown in Table V. is not peculiar to Scandinavia. It is shown, for instance, in Loomis’s auroral data, which are based on observations at a variety of European and American stations (Ency. Brit. 9th ed. art. Meteorology, Table XXVIII.). It does not seem, however, to apply universally. Thus at Godthaab we have, according to Adam Paulsen (15), comparing 3-year periods of few and many sun-spots:—
| 3-Year Period. | Total Sun-spot Frequency. |
Total Nights of Aurora. |
| 1865–1868 1869–1872 1876–1879 |
48 339 23 |
274 138 273 |
The years start in the autumn, and 1865–1868 includes the three winters of 1865 to ’66, ’66 to ’67, and ’67 to ’68. Paulsen also gives data from two other stations in Greenland, viz. Ivigtut (1869 to 1879) and Jakobshavn (1873 to 1879), which show the same phenomenon as at Godthaab in a prominent fashion. Greenland lies to the north of Fritz’s curve of maximum auroral frequency, and the suggestion has been made that the zone of maximum frequency expands to the south as sun-spots increase, and contracts again as they diminish, the number of auroras at a given station increasing or diminishing as the zone of maximum frequency approaches to or recedes from it. This theory, however, does not seem to fit all the facts and stands in want of confirmation.
Table V.
| Year. | Frequency. | Year. | Frequency. | Year. | Frequency. | Year. | Frequency. | ||||
| Sun-spot. | Auroral. | Sun-spot. | Auroral. | Sun-spot. | Auroral. | Sun-spot. | Auroral. | ||||
| 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 |
80·9 83·4 47·7 47·8 30·7 12·2 9·6 10·2 32·4 47·6 54·0 62·9 85·9 61·2 45·1 36·4 20·9 11·4 37·8 69·8 106·1 100·8 81,6 66·5 34·8 30·6 7·0 19·8 92·5 154·4 125·9 84·8 68·1 38·5 22·8 10·2 24·1 82·9 132·0 130·9 |
103 134 53 111 96 65 34 60 83 80 113 86 124 114 89 107 76 51 68 80 89 83 62 38 58 98 33 17 64 59 60 67 103 67 70 78 83 136 115 97 |
1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 |
118·1 89·9 66·6 60·0 46·9 41·0 21·3 16·0 6·4 4·1 6·8 14·5 34·0 45·0 43·1 47·5 42·2 28·1 10·1 8·1 2·5 0·0 1·4 5·0 12·2 13·9 35·4 45·8 41·1 30·4 23·9 15·7 6·6 4·0 1·8 8·5 16·6 36·3 49·7 62·5 |
89 90 54 64 29 37 34 37 61 35 28 30 34 65 73 101 85 62 42 20 20 4 13 11 18 17 10 33 60 74 43 62 37 33 13 14 40 58 79 60 |
1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 |
67·0 71·0 47·8 27·5 8·5 13·2 56·9 121·5 138·3 103·2 85·8 63·2 36·8 24·2 10·7 15·0 40·1 61·5 98·5 124·3 95·9 66·5 64·5 54·2 39·0 20·6 6·7 4·3 22·8 54·8 93·8 95·7 77·2 59·1 44·0 47·0 30·5 16·3 7·3 37·3 |
93 132 89 54 79 81 58 98 137 159 165 82 75 91 66 81 26 50 63 107 131 95 60 92 65 64 49 46 38 88 131 119 127 135 135 124 119 130 127 144 |
1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 |
73·9 139·1 111·2 101·7 66·3 44·7 17·1 11·3 12·3 3·4 6·0 32·3 54·3 59·7 63·7 63·5 52·2 25·4 13·1 6·8 6·3 7·1 35·6 73·0 84·9 78·0 64·0 41·8 26·2 26·7 12·1 9·5 2·7 5·0 24·4 42·0 62·8 53·8 62·0 48·5 |
160 195 185 200 189 158 133 137 126 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. |
13. Auroral Meridian.—It is a common belief that the summit of an auroral arc is to be looked for in the observer’s magnetic meridian. On any theory it would be rather extraordinary if this were invariably true. In temperate latitudes auroral arcs are seldom near the zenith, and there is reason to believe them at very great heights. In high latitudes the average height is probably less, but the direction in which the magnetic needle
