# 1911 Encyclopædia Britannica/Aurora Polaris

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​AURORA POLARIS (Aurora Borealis and Australis, Polar Light, Northern Lights), a natural phenomenon which occurs in many forms, some of great beauty.
1. Forms.—Various schemes of classification have been proposed, but none has met with universal acceptance; the following are at least the principal types. (1) Arcs. These most commonly resemble segments of circles, but are not infrequently elliptical or irregular in outline. The ends of arcs frequently extend to the horizon, but often one or both ends stop short of this. Several arcs may be visible at the same time. Usually the under or concave edge of the arc is the more clearly defined, and adjacent to it the sky often seems darker than elsewhere. It is rather a disputed point whether this dark segment—through which starlight has been seen to pass—represents a real atmospheric condition or is merely a contrast effect. (2) Bands. These may be nearly straight and regular in outline, as if broken portions of arcs; frequently they are ribbon-like serpentine forms showing numerous sinuosities. (3) Rays. Frequently an arc or band is visibly composed of innumerable short rays separated by distinctly less luminous intervals. These rays are more or less perpendicular to the arc or band; sometimes they are very approximately parallel to one another, on other occasions they converge towards a point. Longer rays often show an independent existence. Not infrequently rays extend from the upper edge of an arc towards the zenith. Combinations of rays sometimes resemble a luminous fan, or a series of fans, or part of a hollow luminous cylinder. Rays often alter suddenly in length, seeming to stretch down towards the horizon or mount towards the zenith. This accounts for the description of aurora as “Merry Dancers.” (4) Curtains or Draperies. This form is rare except in Arctic regions, where it is sometimes fairly frequent. It is one of the most imposing forms. As a rule the higher portion is visibly made up of rays, the light tending to become more continuous towards the lower edge; the combination suggests a connected whole, like a curtain whose alternate portions are in light and shade. The curtain often shows several conspicuous folds, and the lower ​edge often resembles frilled drapery. At several stations in Greenland auroral curtains have been observed when passing right overhead to narrow to a thin luminous streak, exactly as a vertical sheet of light would seem to do to one passing underneath it. (5) Corona. A fully developed corona is perhaps the finest form of aurora. As the name implies, there is a sort of crown of light surrounding a comparatively or wholly dark centre. Farther from the centre the ray structure is usually prominent. The rays may lie very close together, or may be widely separated from one another. (6) Patches. During some displays, auroral light appears in irregular areas or patches, which sometimes bear a very close resemblance to illuminated detached clouds. (7) Diffused Aurora. Sometimes a large part of the sky shows a diffuse illumination, which, though brighter in some parts than others, possesses no definite outlines. How far the different forms indicate real difference in the nature of the phenomenon, and how far they are determined by the position of the observer, it is difficult to say. Not infrequently several different forms are visible at the same time.
2. Isochasms.—Aurora is seldom observed in low latitudes. In the southern hemisphere there is comparatively little inhabited land in high latitudes and observational data are few; thus little is known as to how the frequency varies with latitude and longitude. Even in the northern hemisphere there are large areas in the Arctic about which little is known. H. Fritz (2) has, however, drawn a series of curves which are believed to give a good general idea of the relative frequency of aurora throughout the northern hemisphere. Fritz’ curves, shown in the illustration, are termed isochasms, from the Greek word employed by Aristotle to denote aurora. Points on the same curve are supposed to have the same average number of auroras in the year, and this average number is shown adjacent to the curve. Starting from the equator and travelling northwards we find in the extreme south of Spain an average of only one aurora in ten years. In the north of France the average rises to five a year; in the north of Ireland to thirty a year; a little to the north of the Shetlands to one hundred a year. Between the Shetlands and Iceland we cross the curve of maximum frequency, and farther north the frequency diminishes. The curve of maximum frequency forms a slightly irregular oval, whose centre, the auroral pole, is according to Fritz at about 81° N. lat., 70° W. long. Isochasms reach a good deal farther south in America than in Europe. In other words, auroras are much more numerous in the southern parts of Canada and in the United States than in the same latitudes of Europe.
3. Annual Variation.—Table I. shows the annual variation observed in the frequency of aurora. It has been compiled from several authorities, especially Joseph Lovering (4) and Sophus Tromholt (5). The monthly figures denote the percentages of the total number seen in the year. The stations are arranged in order of latitude. Individual places are first considered, then a few large areas.
The Godthaab data in Table I. are essentially those given by Prof. A. Paulsen (6) as observed by Kleinschmidt in the winters of 1865 to 1882, supplemented by Lovering’s data for summer. Starting at the extreme north, we have a simple period with a well-marked maximum at midwinter, and no auroras during several months at midsummer. This applies to Hammerfest, Jakobshavn, Godthaab and the most northern division of Scandinavia. The next division of Scandinavia shows a transition stage. To the south of this in Europe the single maximum at mid-winter is replaced by two maxima, somewhere about the equinoxes.
4. In considering what is the real significance of the great difference apparent in Table I. between higher and middle latitudes, a primary consideration is that aurora is seldom seen until the sun is some degrees below the horizon. There is no reason to suppose that the physical causes whose effects we see as aurora are in existence only when aurora is visible. Until means are devised for detecting aurora during bright sunshine, our knowledge as to the hour at which these causes are most frequently or most powerfully in operation must remain incomplete. But it can hardly be doubted that the differences apparent in Table I. are largely due to the influence of sunlight. In high latitudes for several months in summer it is never dark, and consequently a total absence of visible aurora is practically inevitable. Some idea of this influence can be derived from figures obtained by the Swedish International Expedition of 1882–1883 at Cape Thorsden, Spitsbergen, lat. 78° 28′ N. (7). The original gives the relative frequency of aurora for each degree of depression of the sun below the horizon, assuming the effect of twilight to be nil (i.e. the relative frequency to be 100) when the depression is 18·5° or more. The following are a selection of the figures:—
| Angle of depression | 4·5° | 7·5° | 10·5° | 12·5° | 15·5°. |
| Relative frequency | 0·3 | 9·3 | 44·9 | 74·5 | 95·9. |
These figures are not wholly free from uncertainties, arising from true diurnal and annual variations in the frequency, but they give a good general idea of the influence of twilight.
If sunlight and twilight were the sole cause of the apparent annual variation, the frequency would have a simple period, with a maximum at midwinter and a minimum at midsummer. This is what is actually shown by the most northern stations and districts in Table I. When we come, however, below 65° lat. in Europe the frequency near the equinoxes rises above that at midwinter, and we have a distinct double period, with a principal minimum at midsummer and a secondary minimum at midwinter. In southern Europe—where, however, auroras are too few to give smooth results in a limited number of years—in southern Canada, and in the United States, the difference between the winter and summer months is much reduced. Whether there is any real difference between high and mean latitudes in the annual frequency of the causes rendered visible by aurora, it is difficult to say. The Scandinavian data, from the wealth of observations, are probably the most representative, and even in the most northern district of Scandinavia the smallness of the excess of the frequencies in December and January over those in March and October suggests that some influence tending to create maxima at the equinoxes has largely counterbalanced the influence of sunlight and twilight in reducing the frequency at these seasons.
5. Fourier Analysis.—With a view to more minute examination, the annual frequency can be expressed in Fourier series, whose terms represent waves, whose periods are 12, 6, 4, 3, &c. months. This has been done by Lovering (4) for thirty-five stations. The nature of the results will best be explained by reference to the formula given by Lovering as a mean from all the stations considered, viz.:—
8·33 + 3·03 sin (30t + 100° 52′) + 2·53 sin (60t + 309° 5′) + 0·16 sin (90t + 213° 31′) + 0·56 sin (120t + 162° 45′) + 0·27 sin (150t + 32° 38′).
The total number of auroras in the year is taken as 100, and t denotes the time, in months, that has elapsed since the middle of January.
* Fig. 1—TWO TYPES OF AURORAL ARCS.
* Fig. 2—TWO TYPES OF AURORAL RAYS.
(From the Internationale Polarforschung, 1882–1883, by permission of the Kaiserlichen Akademie der Wissenschaften, Vienna.)
* Fig. 3—AURORAL BANDS.
* Fig. 4—AURORAL CURTAIN BELOW AN ARC.
* Fig. 5.—AURORAL CORONA.
​Putting t＝0, 1, &c., in succession, we get the percentages of the total number of auroras which occur in January, February, and so on. The first periodic term has a period of twelve, the second of six months, and similarly for the others. The first periodic term is largest when t × 30° + 100° 52′＝450°. This makes t＝11·6 months after the middle of January, otherwise the 3rd of January, approximately. The 6-month term has the earliest of its two equal maxima about the 26th of March. These two are much the most important of the periodic terms. The angles 100° 52′, 309° 5′, &c., are known as the phase angles of the respective periodic terms, while 3·03, 2·53, &c., are the corresponding amplitudes. Table II. gives a selection of Lovering’s results. The stations are arranged according to latitude.
Speaking generally, the annual term diminishes in importance as we travel south. North of 55° in Europe its phase angle seems fairly constant, not differing very much from the value 110° in Lovering’s general formula. The 6-month term is small, in the two most northern stations, but south of 60° N. lat. it is on the whole the most important term. Excluding Jakobshavn, the phase angles in the 6-month term vary wonderfully little, and approach the value 309° in Lovering’s general formula. North of lat. 50° the 4-month term is, as a rule, comparatively unimportant, but in the American stations its relative importance is increased. The phase angle, however, varies so much as to suggest that the term mainly represents local causes or observational uncertainties. Lovering’s general formula suggests that the 4-month term is really less important than the 3-month term, but he gives no data for the latter at individual stations.
6. Sunlight is not the only disturbing cause in estimates of auroral frequency. An idea of the disturbing influence of cloud may be derived from some interesting results from the Cape Thorsden (7) observations. These show how the frequency of visible auroras diminished as cloud increased from 0 (sky quite clear) to 10 (sky wholly overcast).
Grouping the results, we have:
| Amount of cloud | 0 | 1 to 3 | 4 to 6 | 7 to 9 | 10 |
| Relative frequency | 100 | 82 | 57 | 46 | 8 |
Out of a total of 1714 hours during which the sky was wholly overcast the Swedish expedition saw auroras on 17, occurring on 14 separate days, whereas 226 hours of aurora would have occurred out of an equal number of hours with the sky quite clear. The figures being based on only one season’s observations are somewhat irregular. Smoothing them, Carlheim-Gyllensköld gives f＝100′−7·3c as the most probable linear relation between c, the amount of cloud, and f, the frequency, assuming the latter to be 100 when there is no cloud.
7. Diurnal Variation.—The apparent daily period at most stations is largely determined by the influence of daylight on the visibility. It is only during winter and in high latitudes that we can hope to ascertain anything directly as to the real diurnal variation of the causes whose influence is visible at night as aurora. Table III. gives particulars of the number of occasions when aurora was seen at each hour of the twenty-four during three expeditions in high latitudes when a special outlook was kept.
The data under A refer to Cape Thorsden (78° 28′ N. lat., 15° 42′ E. long.), those under B to Jan Mayen (8) (71° 0′ N. lat., 8° 28′ W. long.), both for the winter of 1882–1883. The data under C are given by H. Arctowski (9) for the “Belgica” Expedition in 1898. They may be regarded as applying approximately to the mean position of the “Belgica,” or 701/2° S. lat., 861/2° W. long. The method of counting frequencies was fairly alike, at least in the case of A and B, but in comparing the different stations the data should be regarded as relative rather than absolute. The Jan Mayen data refer really to Göttingen mean time, but this was only twenty-three minutes late on local time. In calculating the percentages of forenoon and afternoon occurrences half the entries under noon and midnight were assigned to each half of the day. Even at Cape Thorsden, the sun at midwinter is only 11° below the horizon at noon, and its effect on the visibility is thus not wholly negligible. The influence of daylight is presumably the principal cause of the difference between the phenomena during November, December and January at Cape Thorsden and Jan Mayen, for in the equinoctial months the results from these two stations are closely similar. Whilst daylight is the principal cause of the diurnal inequality, it is not the only cause, otherwise there would be as many auroras in the morning (forenoon) as in the evening (afternoon). The number seen in the evening is, however, according to Table III., considerably in excess at all seasons. Taking the whole winter, the percentage seen in the evening was the same for the “Belgica” as for Jan Mayen, i.e. for practically the same latitudes South and North. At Cape Thorsden from November to January there seems a distinct double period, with minima near noon and midnight. The other months at Cape Thorsden show a single maximum and minimum, the former before midnight. ​The same phenomenon appears at Jan Mayen especially in November, December and January, and it is the normal state of matters in temperate latitudes, where the frequency is usually greatest between 8 and 10 p.m. An excess of evening over morning occurrences is also the rule, and it is not infrequently more pronounced than in Table III. Thus at Tasiusak (65° 37′ N. lat., 37° 33′ W. long.) the Danish Arctic Expedition (10) of 1904 found seventy-five out of every hundred occurrences to take place before midnight.
Table III.—Diurnal Variation.
| Hour. | Dec. | Dec. | Nov. and Jan. | Nov. and Jan. | Feb., March, Sept. and Oct. | Feb., March, Sept. and Oct. | Sept. to March (N. Lat.). March to Sept. (S. Lat.). | Sept. to March (N. Lat.). March to Sept. (S. Lat.). | Sept. to March (N. Lat.). March to Sept. (S. Lat.). |
| Hour. | A | B | A | B | A | B | A | B | C |
| 1  2  3  4  5  6  7  8  9 10 11 Noon  1  2  3  4  5  6  7  8  9 10 11 Midnight | 14 10 9 10 13 11 9 5 7 10 9 10 10 14 18 16 12 14 16 15 14 12 10 9 | 7 6 4 5 5 3 2 1 2 0 0 0 0 0 1 7 11 10 13 12 15 15 12 9 | 14 15 15 21 20 15 13 6 9 5 6 4 6 10 20 19 22 21 23 22 18 19 18 13 | 8 6 5 7 3 4 3 1 0 0 0 0 0 0 3 7 10 16 16 18 17 15 17 11 | 27 20 15 14 10 2 1 0 0 0 0 0 0 0 0 1 5 8 20 24 27 31 33 28 | 23 25 21 18 10 3 2 0 0 0 0 0 0 0 0 1 2 5 9 24 28 25 26 22 | 55 45 39 45 43 28 23 11 16 15 15 14 16 24 38 36 39 43 59 61 59 62 61 50 | 38 37 30 30 18 10 7 2 2 0 0 0 0 0 4 15 23 31 38 54 60 55 55 42 | 24 23 10 4 2 1 0 0 0 0 0 0 0 0 0 0 3 3 14 25 31 29 26 26 |
| Totals | 277 | 140 | 354 | 167 | 266 | 244 | 897 | 551 | 221 |
| Percentages—  Forenoon  Afternoon | 42  58 | 28  72 | 42  58 | 25  75 | 39  61 | 46  54 | 41  59 | 35  65 | 35  65 |
8. The preceding remarks relate to auroras as a whole; the different forms differ considerably in their diurnal variation. Arcs, bands and, generally speaking, the more regular and persistent forms, show their greatest frequencies earlier in the night than rays or patches. Table IV. shows the percentages of e. (evening) and m. (morning) occurrences of the principal forms as recorded by the Arctic observers at Cape Thorsden, Jan Mayen and Tasiusak.
Table IV.
| | Arcs. | Arcs. | Bands. | Bands. | Rays. | Rays. | Patches. | Patches. |
| Cape Thorsden Jan Mayen Tasiusak | e. | m. | e. | m. | e. | m. | e. | m. |
| Cape Thorsden Jan Mayen Tasiusak | 76 78 85 | 24 22 15 | 66 68 85 | 34 32 15 | 52 60 65 | 48 40 35 | 51 60 62 | 49 40 38 |
At Cape Thorsden diffused auroral light had percentages e. 65, m. 35, practically identical with those for bands. At Tasiusak, 8 p.m. was the hour of most frequent occurrence for arcs and bands, whereas patches had their maximum frequency at 11 p.m. and rays at midnight.
9. Lunar and other Periods.—The action of moonlight necessarily gives rise to a true lunar period in the visibility of aurora. The extent to which it renders aurora invisible depends, however, so much on the natural brightness of the aurora—which depends on the time and the place—and on the sharpness of the outlook kept, that it is difficult to gauge it. Ekholm and Arrhenius (11) claim to have established the existence of a true tropical lunar period of 27·32 days, and also of a 26-day period, or, as they make it, a 25·929-day period. A 26-day period has also been derived by J. Liznar (12), after an elaborate allowance for the disturbing effects of moonlight from the observations in 1882–1883 at Bossekop, Fort Rae and Jan Mayen. Neither of these periods is universally conceded. The connexion between aurora and earth magnetic disturbances renders it practically certain that if a 26-day or similar period exists in the one phenomenon it exists also in the other, and of the two terrestrial magnetism (q.v.) is probably the element least affected by external complications, such as the action of moonlight.
10. Sun-spot Connexion.—The frequency of auroral displays is much greater in some years than others. At most places the variation in the frequency has shown a general similarity to that of sun-spots. Table V. gives contemporaneous data for the frequency of sun-spots and of auroras seen in Scandinavia. The sun-spot data prior to 1902 are from A. Wolfer’s table in the Met. Zeitschrift for 1902, p. 195; the more recent data are from his quarterly lists. All are observed frequencies, derived after Wolf’s method; maxima and minima are in heavy type.
The auroral data are from Table E of Tromholt’s catalogue (5), with certain modifications. In Tromholt’s yearly data the year commences with July. This being inconvenient for comparison with sun-spots, use was made of his monthly values to obtain corresponding data for years commencing with January. The Tromholt-Schroeter data for Scandinavia as a whole commenced with 1761; the figures for earlier years were obtained by multiplying the data for Sweden by 1·356, the factor being derived by comparing the figures for Sweden alone and for the whole of Scandinavia from July 1761 to June 1783.
In a general way Table V. warrants the conclusion that years of many sun-spots are years of many auroras, and years of few sun-spots years of few auroras; but it does not disclose any very definite relationship between the two frequencies. The maxima and minima in the two phenomena in a good many cases are not found in the same years. On the other hand, there is absolute coincidence in a number of cases, some of them very striking, as for instance the remarkably low minima of 1810 and 1823.
11. During the period 1764 to 1872 there have been ten years of maximum, and ten of minimum, in sun-spot frequency. Taking the three years of greatest frequency at each maximum, and the three years of least frequency at each minimum, we get thirty years of many and thirty of few sun-spots. Also we can split the period into an earlier half, 1764 to 1817, and a later half, 1818 to 1872, containing respectively the earlier five and the later five of the above groups of sun-spot maximum and minimum years. The annual means derived from the whole group, and the two sub-groups, of years of many and few sun-spots are as follows:—
| Years of | 1764–1872. | 1764–1872. | 1764–1817. | 1764–1817. | 1818–1872. | 1818–1872. |
| Years of | Spots. | Auroras. | Spots. | Auroras. | Spots. | Auroras. |
| Many sun-spots Few sun-spots | 93·4 13·4 | 99·9 61·5 | 86·7 13·6 | 70·7 51·6 | 100·1  13·1 | 129·1  71·3 |
In each case the excess of auroras in the group of years of many sun-spots is decided, but the results from the two sub-periods do not harmonize closely. The mean sun-spot frequency for the group of years of few sun-spots is almost exactly the same for the two sub-periods, but the auroral frequency for the later group is nearly 40% in excess of that for the earlier, and even exceeds the auroral ​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. | Frequency. | Year. | Frequency. | Frequency. | Year. | Frequency. | Frequency. | Year. | Frequency. | Frequency. |
| Year. | Sun-spot. | Auroral. | Year. | Sun-spot. | Auroral. | Year. | Sun-spot. | Auroral. | Year. | 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 ​points changes rapidly with change of latitude and longitude, and has a large diurnal variation. Thus there must in general be a difference between the observer’s magnetic meridian—answering to the mean position of the magnetic needle at his station—and the direction the needle would have at a given hour, if undisturbed by the aurora, at any spot where the phenomena which the observer sees as aurora exist.
Very elaborate observations have been made during several Arctic expeditions of the azimuths of the summits of auroral arcs. At Cape Thorsden (7) in 1882–1883 the mean azimuth derived from 371 arcs was 24° 12′ W., or 11° 27′ to the W. of the magnetic meridian. As to the azimuths in individual cases, 130 differed from the mean by less than 10°, 118 by from 10° to 20°, 82 by from 20° to 30°, 21 by from 30° to 40°, 14 by from 40° to 50°; in six cases the departure exceeded 50°, and in one case it exceeded 70°. Also, whilst the mean azimuths deduced from the observations between 6 a.m. and noon, between noon and 6 p.m., and between 6 p.m. and midnight, were closely alike, their united mean being 22·4° W. of N. (or E. of S.), the mean derived from the 113 arcs observed between midnight and 6 a.m. was 47·8° W. At Jan Mayen (8) in 1882–1883 the mean azimuth of the summit of the arcs was 28·8° W. of N., thus approaching much more closely to the magnetic meridian 29·9° W. As to individual azimuths, 113 lay within 10° of the mean, 37 differed by from 10° to 20°, 18 by from 20° to 30°, 6 by from 30° to 40°, whilst 6 differed by over 40°. Azimuths were also measured at Jan Mayen for 338 auroral bands, the mean being 22·0° W., or 7·9° to the east of the magnetic meridian. Combining the results from arcs and bands, Carlheim-Gyllensköld gives the “anomaly” of the auroral meridian at Jan Mayen as 5·7° E. At the British Polar station of 1882, Fort Rae (62° 23′ N. lat., 115° 44′ W. long.), he makes it 15·7° W. At Godthaab in 1882–1883 the auroral anomaly was, according to Paulsen, 15·5° E., the magnetic meridian lying 57·6° W. of the astronomical.
14. Auroral Zenith.—Another auroral direction having apparently a close relation to terrestrial magnetism is the imaginary line drawn to the eye of an observer from the centre of the corona—i.e. the point to which the auroral rays converge. This seems in general to be nearly coincident with the direction of the dipping needle.
Thus at Cape Thorsden (7) in 1882–1883 the mean of a considerable number of observations made the angle between the two directions only 1° 7′, the magnetic inclination being 80° 35′, whilst the coronal centre had an altitude of 79° 55′ and lay somewhat to the west of the magnetic meridian. Even smaller mean values have been found for the angle between the auroral and magnetic “zeniths”—as the two directions have been called—e.g. 0° 50′ at Bossekop (16) in 1838–1839, and 0° 7′ at Treurenberg (17) (79° 55′ N. lat., 16° 51′ E. long.) in 1899–1900.
15. Relations to Magnetic Storms.—That there is an intimate connexion between aurora when visible in temperate latitudes and terrestrial magnetism is hardly open to doubt. A bright aurora visible over a large part of Europe seems always accompanied by a magnetic storm and earth currents, and the largest magnetic storms and the most conspicuous auroral displays have occurred simultaneously. Noteworthy examples are afforded by the auroras and magnetic storms of August 28-29 and September 1-2, 1859; February 4, 1872; February 13-14 and August 12, 1892; September 9, 1898; and October 31, 1903. On some of these occasions aurora was brilliant in both the northern and southern hemispheres, whilst magnetic disturbances were experienced the whole world over. In high latitudes, however, where both auroras and magnetic storms are most numerous, the connexion between them is much less uniform. Arctic observers, both Danish and British, have repeatedly reported displays of aurora unaccompanied by any special magnetic disturbance. This has been more especially the case when the auroral light has been of a diffused character, showing only minor variability. When there has been much apparent movement, and brilliant changes of colour in the aurora, magnetic disturbance has nearly always accompanied it. In the Arctic, auroral displays seem sometimes to be very local, and this may be the explanation. On the other hand, Arctic observers have reported an apparent connexion of a particularly definite character. According to Paulsen (18), during the Ryder expedition in 1891–1892, the following phenomenon was seen at least twenty times by Lieut. Vedel at Scoresby Sound (70° 27′ N. lat., 26° 10′ W. long.). An auroral curtain travelling with considerable velocity would approach from the south, pass right overhead and retire to the north. As the curtain approached, the compass needle always deviated to the west, oscillated as the curtain passed the zenith, and then deviated to the east. The behaviour of the needle, as Paulsen points out, is exactly what it should be if the space occupied by the auroral curtain were traversed by electric currents directed upwards from the ground. The Danish observers at Tasiusak (10) in 1898–1899 observed this phenomenon occasionally in a slightly altered form. At Tasiusak the auroral curtain after reaching the zenith usually retired in the direction from which it had come. The direction in which the compass needle deviated was west or east, according as the curtain approached from the south or the north; as the curtain retired the deviation eventually diminished.
Kr. Birkeland (19). who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.
16. In the northern hemisphere to the south of the zone of greatest frequency, the part of the sky in which aurora most generally appears is the magnetic north. In higher latitudes auroras are most often seen in the south. The relative frequency in the two positions seems to vary with the hour, the type of aurora, probably with the season of the year, and possibly with the position of the year in the sun-spot cycle.
At Jan Mayen (8) in 1882–1883, out of 177 arcs whose position was accurately determined, 44 were seen in the north, their summits averaging 38·5° above the northern horizon; 88 were seen in the south, their average altitude above the southern horizon being 33·5°; while 45 were in the zenith. At Tasiusak (10) in 1898–1899 the magnetic directions of the principal types were noted separately. The results are given in Table VI.
Table VI.
| Direction. | Absolute Number for each Type. | Absolute Number for each Type. | Absolute Number for each Type. | Absolute Number for each Type. | Absolute Number for each Type. | Percentage from all Types. |
| Direction. | Arcs. | Bands. | Curtains. | Rays. | Patches. | Percentage from all Types. |
| N. N.E. E. S.E. S. S.W. W. N.W. | 9 9 3 5 45 9 3 2 | 16 13 11 6 43 9 11 8 | 5 2 2 1 1 2 2 2 | 15 20 26 10 16 12 22  8 | 4 4 3 7 15 13 6 5 | 10 9 9 6 24 9 9 5 |
Table VI. accounts for only 81% of the total displays; of the remainder 15% appeared in the zenith, while 4% covered the whole sky. Auroral displays generally cover a considerable area, and are constantly changing, so the figures are necessarily somewhat rough. But clearly, whilst the arcs and bands, and to a lesser extent the patches, showed a marked preference for the magnetic meridian, the rays showed no such preference.
At Cape Thorsden (7) in 1882–1883 auroras as a whole were divided into those seen in the north and those seen in the south. The variation throughout the twenty-four hours in the percentage seen in the south was as follows:—
| Hour. | 0–3. | 3–6. | 6–9. | 9–12. |
| a.m. p.m. | 69 55 | 55 70 | 44 65 | 35 65 |
The mean from the whole twenty-four hours is sixty-three. Between 3 a.m. and 3 p.m. the percentage of auroras seen in the south thus appears decidedly below the mean.
17. The following data for the apparent angular width of arcs were obtained at Cape Thorsden, the arcs being grouped according to the height of the lower edge above the horizon. Group I. contained thirty arcs whose altitudes did not exceed 11° 45′; Group II. thirty arcs whose altitudes lay between 12° and 35°; and Group III, thirty arcs whose altitudes lay between 36° and 80°.
| Group. | I. | II. | III. |
| Greatest width. Least width. Mean width. | 11·5°  1·0° 3·45° | 12·0° 0·75°  4·6° | 21·0°  2·0°  6·9° |
There is here a distinct tendency for the width to increase with the altitude. At the same time, arcs near the horizon often appeared wider than others near the zenith. Furthermore, Gyllensköld says that when arcs mounted, as they not infrequently did, from the horizon, their apparent width might go on increasing right up to the ​zenith, or it might increase until an altitude of about 45° was reached and then diminish, appearing much reduced when the zenith was reached. Of course the phenomenon might be due to actual change in the arc, but it is at least consistent with the view that arcs are of two kinds, one form constituting a layer of no great vertical depth but considerable real horizontal width, the other form having little horizontal width but considerable vertical depth, and resembling to some extent an auroral curtain.
18. According to numerous observations made at Cape Thorsden, the apparent angular velocity of arcs increases on the average with their altitude. Dividing the whole number of arcs, 156, whose angular velocities were measured into three numerically equal groups, according to their altitude, the following were the results in minutes of arc per second of time (or degrees per minute of time):—
| Group. | I. | II. | III. | All. |
| Mean altitude Greatest velocity Mean velocity | 10·5° 4·81 0·48 | 34·6° 15·12 2·42 | 72·3° 109·09 8·67 | .. .. 3·86 |
Each group contained auroras which appeared stationary. The intervals to which the velocities referred were usually from five to ten minutes, but varied widely. The velocity 109·09 was much the largest observed, the next being 52·38; both were from observations lasting under half a minute.
19. In 1882–1883 the direction of motion of arcs was from north to south in 62% of the cases at Jan Mayen, and in 58% of the cases at Cape Thorsden. This seems the more common direction in the northern hemisphere, at least for stations to the south of the zone of maximum frequency, but a considerable preponderance of movements towards the north was observed in Franz Joseph Land by the Austrian Expedition of 1872–1874. The apparent motion of arcs is sometimes of a complicated character. One end only, for example, may appear to move, as if rotating round the other; or the two ends may move in opposite directions, as if the arc were rotating about a vertical axis through its summit.
20. Height.—If an auroral arc represented a definite self-luminous portion of space of small transverse dimensions at a uniform height above the ground, its height could be accurately determined by observations made with theodolites at the two ends of a measured base, provided the base were not too short compared to the height. If a very long base is taken, it becomes increasingly open to doubt whether the portions of space emitting auroral light to the observers at the two ends are the same. There is also difficulty in ensuring that the observations shall be simultaneous, an important matter especially when the apparent velocity is considerable. If the base is short, definite results can hardly be hoped for unless the height is very moderate. Amongst the best-known theodolite determinations of height are those made at Bossekop in Norway by the French Expedition of 1838–1839 (16) and the Norwegian Expedition of 1882–1883, and those made in the latter year by the Swedes at Cape Thorsden and the Danes at Godthaab. At Bossekop and Cape Thorsden there were a considerable proportion of negative or impossible parallaxes. Much the most consistent results were those obtained at Godthaab by Paulsen (15). The base was 5·8 km. (about 31/2 miles) long, the ends being in the same magnetic meridian, on opposite sides of a fiord, and observations were confined to this meridian, strict simultaneity being secured by signals. Heights were calculated only when the observed parallax exceeded 1°, but this happened in three-fourths of the cases. The calculated heights—all referring to the lowest border of the aurora—varied from 0·6 to 67·8 km. (about 0·4 to 42 m.), the average being about 20 km. (12 m.). Regular arcs were selected in most cases, but the lowest height obtained was for a collection of rays forming a curtain which was actually situated between the two stations.
In 1885 Messrs Garde and Eherlin made similar observations at Nanortalik near Cape Farewell in Greenland, but using a base of only 1250 metres (about 3/4 m.). Their results were very similar to Paulsen’s. On one occasion twelve observations, extending over half an hour, were made on a single arc, the calculated heights varying in a fairly regular fashion from 1·6 to 12·9 km. (about 1 to 8 m.). The calculated horizontal distances of this arc varied between 5 and 24 km. (about 3 and 15 m.), the motion being sometimes towards, sometimes away from the observers, but not apparently exceeding 3 km. (nearly 2 m.) per minute. Heights of arcs have often been calculated from the apparent altitudes at stations widely apart in Europe or America. The heights calculated in this way for the under surface of the arc, have usually exceeded 100 m.; some have been much in excess of this figure. None of the results so obtained can be accepted without reserve, but there are several reasons for believing that the average height in Greenland is much below that in lower latitudes. Heights have been calculated in various less direct ways, by observing for instance the angular altitude of the summit of an arc and the angular interval between its extremities, and then making some assumption such as that the portion visible to an observer may be treated as a circle whose centre lies over the so-called auroral pole. The mean height calculated at Arctic stations, where careful observations have been made, in this or analogous ways, has varied from 58 km. (about 36 m.) at Cape Thorsden (Gyllensköld) to 227 km. (about 141 m.) at Bossekop (Bravais). The height has also been calculated on the hypothesis that auroral light has its source where the atmospheric pressure is similar to that at which most brilliancy is observed when electric discharges pass in vacuum tubes. Estimates on this basis have suggested heights of the order of 50 km. (about 31 m.). There are, of course, many uncertainties, as the conditions of discharge in the free atmosphere may differ widely from those in glass vessels. If the Godthaab observations can be trusted, auroral discharges must often occur within a few miles of the earth’s surface in Arctic regions. In confirmation of this view reference may be made to a number of instances where observers—e.g. General Sabine, Sir John Franklin, Prof. Selim Lemström, Dr David Walker (at Fort Kennedy in 1858–1859), Captain Parry (Fort Bowen, 1825) and others—have seen aurora below the clouds or between themselves and mountains. One or two instances of this kind have even been described in Scotland. Prof. Cleveland Abbe (20) has given a full historical account of the subject to which reference may be made for further details.
21. Brightness.—In auroral displays the brightness often varies greatly over the illuminated area and changes rapidly. Estimates of the intensity of the light have been based on various arbitrary scales, such for instance as the size of type which the observer can read at a given distance. The estimate depends in the case of reading type on the general illumination. In other cases scales have been employed which make the result mainly depend on the brightest part of the display. At Jan Mayen (8) in 1882–1883 a scale was employed running from 1, taken as corresponding to the brightness of the milky way, to 4, corresponding to full moonlight. The following is an analysis of the results obtained, showing the number of times the different grades were reached:—
| Scale of Intensity. | 1. | 2. | 3. | 4. | Mean Intensity. |
| Arcs Bands Rays Corona | 27 46 30  3 | 53 83 116 14 | 13 49 138 12 | 1 22 28 12 | 1·87 2·24 2·21 2·81 |
On one or two occasions at Jan Mayen auroral light is described as making the full moon look like an ordinary gas jet in presence of electric light, whilst rays could be seen crossing and brighter than the moon’s disk. Such extremely bright auroras seem very rare, however, even in the Arctic. There is a general tendency for both bands and rays to appear brightest at their lowest parts; arcs seldom appear as bright at their summits as nearer the horizon. It is not unusual for arcs and bands to look as if pulses or waves of light were travelling along them; also the direction in which these pulses travel does not seem to be wholly arbitrary. Movements to the east were twice as numerous at Jan Mayen and thrice as numerous at Traurenberg as movements to the west. In some cases changes of intensity take place round the auroral zenith, simulating the effect that would be produced by a cyclonic rotation of luminous matter. In the case of isolated patches the intensity often waxes and wanes as if a search-light were being thrown on and turned off.
22. Colour.—The ordinary colour of aurora is white, usually with a distinct yellow tint in the brighter forms, but silvery white when the light is faint. When the light is intense and changing rapidly, red is not infrequently present, especially towards the lower edge. Under these circumstances, green is also sometimes visible, especially towards the zenith. Thus a bright auroral ray may seem red towards the foot and green at its summit, with yellow intervening. In some cases the green may be only a contrast effect. Other colours, e.g. violet, have occasionally been noticed but are unusual.
23. Spectrum.—The spectrum of aurora consists of a number of lines. Numerous measurements have been made of the wave-lengths of the brightest. One line, in the yellow green, is so dominant optically as often to be described as the auroral line. Its wave-length is probably very near 5571 tenth-metres, and it is very close to, if not absolutely coincident with, a prominent line in the spectrum of krypton. This line is so characteristic that its presence or absence is the usual criterion for deciding ​whether an atmospheric light is aurora. The Swedish Expedition (17) of 1899–1902, engaged in measuring an arc of the meridian in Spitsbergen, were unusually well provided spectrographically, and succeeded in taking photographs of aurora in conjunction with artificial lines—chiefly of hydrogen—which led to results claiming exceptional accuracy. In the spectrograms three auroral rays—including the principal one mentioned above—were pre-eminent. For the two shorter wave-lengths, for whose measurement he claims the highest precision, the observer, J. Westman, gives the values 4276·4 and 3913·5. In addition, he assigns wave-lengths for 156 other auroral lines between wave-lengths 5205 and 3513. The following table gives the wave-lengths of the photographically brightest of these, retaining four significant figures in place of Westman’s five.
Table VII. :
| 4830 4709 4699 4661 4560 4550 | 4489 4420 4371 4356 4344 4337 | 4329 4242 4230 4225 4078 4067 | 3997 3986 3947 3937 3880 3876 | 3861 3804 3793 3704 3607 3589 |
There are a number of optically bright lines of longer wave-length. For the principal of these Angot (1) gives the following wave-lengths (unit 1 µµ or 1 × 10$^{−9}$ metre):—630, 578, 566, 535, 523, 500.
Out of a total of 146 auroral lines, with wave-lengths longer than 3684 tenth-metres, Westman identifies 82 with oxygen or nitrogen lines at the negative pole in vacuum discharges. Amongst the lines thus identified are the two principal auroral lines having wave-lengths 4276·4 and 3913·5. The interval considered by Westman contains at least 300 oxygen and nitrogen lines, so that approximate coincidence with a number of auroral lines was almost inevitable, and an appreciable number of the coincidences may be accidental. E. C. C. Baly (21), making use of the observations of the Russian expedition in Spitsbergen in 1899, accepts as the wave-lengths of the three principal auroral lines 5570, 4276 and 3912; and he identifies all three and ten other auroral lines ranging between 5570 and 3707 with krypton lines measured by himself. In addition to these, he mentions other auroral lines as very probably krypton lines, but in their case the wave-lengths which he quotes from Paulsen (22) are given to only three significant figures, so that the identification is more uncertain. The majority of the krypton lines which Baly identifies with auroral lines require for their production a Leyden jar and spark gap.
If, as is now generally believed, aurora represents some form of electrical discharge, it is only reasonable to suppose that the auroral lines arise from atmospheric gases. The conditions, however, as regards pressure and temperature under which the hypothetical discharges take place must vary greatly in different auroras, or even sometimes in different parts of the same aurora. Further, auroras are often possessed of rapid motion, so that conceivably spectral lines may receive small displacements in accordance with Doppler’s principle. Thus the differences in the wave-lengths of presumably the same lines as measured by different Arctic observers may be only partly due to unfavourable observational conditions. Many of the auroral lines seen in any single aurora are exceedingly faint, so that even their relative positions are difficult to settle with high precision.
24. Whether or not auroral displays are ever accompanied by a characteristic sound is a disputed question. If sound waves originate at the seat of auroral displays they seem hardly likely to be audible on the earth, unless the aurora comes very low and great stillness prevails. It is thus to the Arctic one looks for evidence. According to Captain H. P. Dawson (26), in charge of the British Polar Station at Fort Rae in 1882–1883, “The Indians and voyageurs of the Hudson Bay Company, who often pass their nights in the open, say that it [sound] is not uncommon . . . there can be no doubt that distinct sound does occasionally accompany certain displays of aurora.” On the one occasion when Captain Dawson says he heard it himself, “the sound was like the swishing of a whip or the noise produced by a sharp squall of wind in the upper rigging of a ship, and as the aurora brightened and faded so did the sound which accompanied it.” If under these conditions the sound was really due to the aurora, the latter, as Captain Dawson himself remarks, must have been pretty close.
25. Usually the electric potential near the ground is positive compared to the earth and increases with the height (see Atmospheric Electricity). Several Arctic observers, however, especially Paulsen (18) have observed a diminution of positive potential, or even a change to negative, for which they could suggest no explanation except the presence of a bright aurora. Other Arctic observers have failed to find any trace of this phenomenon. If it exists, it is presumably confined to cases when the auroral discharge comes unusually low.
26. Artificial Phenomena resembling Aurora.—At Sodankylä, the station occupied by the Finnish Arctic Expedition of 1882–1883, Selim Lemström and Biese (23) described and gave drawings of optical phenomena which they believed to be artificially produced aurora. A number of metallic points, supported on insulators, were connected by wires enclosing several hundred square metres on the top of a hill. Sometimes a Holtz machine was employed, but even without it illumination resembling aurora was seen on several occasions, extending apparently to a considerable height. In the laboratory, Kr. Birkeland (19) has produced phenomena bearing a striking resemblance to several forms of aurora. His apparatus consists of a vacuum vessel containing a magnetic sphere—intended to represent the earth—and the phenomena are produced by sending electric discharges through the vessel.
27. Theories.—A great variety of theories have been advanced to account for aurora. All or nearly all the most recent regard it as some form of electrical discharge. Birkeland (19) supposes the ultimate cause to be cathode rays emanating from the sun; C. Nordmann (24) replaces the cathode rays by Hertzian waves; while Svante Arrhenius (25) believes that negatively charged particles are driven through the sun’s atmosphere by the Maxwell-Bartoli repulsion of light and reach the earth’s atmosphere. For the size and density of particles which he considers most likely, Arrhenius calculates the time required to travel from the sun as forty-six hours. By modifying the hypothesis as to the size and density, times appreciably longer or shorter than the above would be obtained. Cathode rays usually have a velocity about a tenth that of light, but in exceptional cases it may approach a third of that of light. Hertzian waves have the velocity of light itself. On either Birkeland’s or Nordmann’s theory, the electric impulse from the sun acts indirectly by creating secondary cathode rays in the earth’s atmosphere, or ionizing it so that discharges due to natural differences of potential are immensely facilitated. The ionized condition must be supposed to last to a greater or less extent for a good many hours to account for aurora being seen throughout the whole night. The fact that at most places the morning shows a marked decay of auroral frequency and intensity as compared to the evening, the maximum preceding midnight by several hours, is certainly favourable to theories which postulate ionization of the atmosphere by some cause or other emanating from the sun.
Authorities.—The following works are numbered according to the references in the text:—(1) A. Angot, Les Aurores polaires (Paris, 1895); (2) H. Fritz, Das Polarlicht (Leipzig, 1881); (3) Svante August Arrhenius, Lehrbuch der kosmischen Physik; (4) Joseph Lovering, “On the Periodicity of the Aurora Borealis,” Mem. American Acad. vol. x. (1868); (5) Sophus Tromholt, Catalog der in Norwegen bis Juni 1878 beobachteten Nordlichter; (6) Observations internationales polaires (1882–1883), Expédition Danoise, tome i. “Aurores boréales”; (7) Carlheim-Gyllensköld, “Aurores boréales” in Observations faites au Cap Thorsden Spitzberg par l’expédition suédoise, tome ii. 1; (8) “Die Österreichische Polar Station Jan Mayen” in Die Internationale Polarforschung, 1882–1883, Bd. ii. Abth. 1; (9) Henryk Arctowski, “Aurores australes” in Expédition antarctique belge . . . Voyage du S. Y. “Belgica”; (10) G. C. Amdrup, Observations . . . faites par l’expédition danoise; H. Ravn, Observations de l’aurore boréale de Tasiusak; (11) K. Sven. Vet.-Akad. Hand. Bd. 31, Nos. 2, 3, &c.; (12) Sitz. d. k. Akad. d. Wiss. (Vienna), Math. Naturw. Classe, Bd. xcvii. Abth. iia, 1888; (13) Proc. Roy. Soc., 1906, lxxvii. A, 141; (14) Kongl. Sven. Vet.-Akad. Hand. Bd. 15, No. 5, Bd. 18, No. 1; (15) Bull. Acad. Roy. Danoise, 1889, p. 67; (16) Voyages . . . pendant les années 1838, 1839 et 1840 sur . . . la Recherche, “Aurores boréales,” by MM. Lottin, Bravais, &c.; (17) Missions scientifiques . . . au Spitzberg . . . en 1899–1902, Mission suédoise, tome ii. VIIIᵉ Section, C. “Aurores boréales”; (18) Bull. Acad. R. des Sciences de Danemark, 1894, p. 148; (19) Kr. Birkeland, Expédition norvégienne 1899–1900 pour l’étude des aurores boréales (Christiania, 1901); (20) Terrestrial Magnetism, vol. iii. (1898), pp. 5, 53, 149; (21) Astrophysical Journal, 1904, xix. p. 187; (22) Rapports présentés au Congrès International de Physique réuni à Paris, 1900, iii. 438; (23) Expédition polaire finlandaise (1882–1884), tome iii.; (24) Charles Nordmann, Thèses présentées à la Faculté des Sciences de Paris (1903); (25) Terrestrial Magnetism, vol. 10, 1905, p. 1; (26) Observations of the International Polar Expeditions 1882–1883 Fort Rae . . . by Capt. H. P. Dawson, R. A. (C. Ch.)