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.

edge often resembles frilled drapery. At several stations in | and Iceland we cross the curve of maximum frequency, and 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.

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

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 1. 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 twi light 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
Relative frequency

4.5 7.5 10.5 12.5° 15.5°. 0-3 9-3 449 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 (301+100°52')+2.53 sin (60t+309°5)+0-16 sin (90+213°31') +0.56 sin (120+162 45 +0-27 sin (150+32°38). The total number of auroras in the year is taken as 100, and denotes the time, in months, that has elapsed since the middle of January.

S. of 58

8.2

11.9 12.6

13.3

1.5

0.6

4.9 14.9

6.3

7.4

9.1

7.4 6.6

8.8 10.4 11.7

New York State

45° to 40° Putting =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 X30° +100° 52' = 450°. This makes 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.

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.

6-Month Term. 4-Month Term. Amp. Phase. Amp. Phase. Amp. Phase.

10.40

123

1-13

206

Godthaab

316

St Petersburg

Christiania

Upsala

Stockholm

3.68

91

5.80

Makerstown (Scotland)

Great Britain

Toronto

Cambridge, Mass.

New Haven, Conn.

New York State.

0-99 '183
1.34 264

253
197
157

73

The data under A refer to Cape Thorsden (78° 28' N. lat., 15° 42′ E. long.), those under B to Jan Mayen (8) (71° o' 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 70° S. lat., 86° 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

Speaking generally, the annual term diminishes in importance | data should be regarded as relative rather than absolute. 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.

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 occur-
rences half the entries under noon and midnight were assigned
to each half of the day. Even at Cape Thorsden, the sun at mid-
winter 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 day-
light 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., consider-
ably 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 | Bossekop, Fort Rae and Jan Mayen Neither of these periods November, December and January, and it is the normal state is universally conceded. The connexion between aurcra and of matters in temperate latitudes, where the frequency is usually earth magnetic disturbances renders it practically certain that greatest between 8 and 10 P.M. An excess of evening over if a 26-day or similar period exists in the one phenomenon it morning occurrences is also the rule, and it is not infrequently exists also in the other, and of the two terrestrial magnetism more pronounced than in Table III. Thus at Tasiusak (65° 37' (q.v.) is probably the element least affected by external comN. lat., 37° 33′ W. long.) the Danish Arctic Expedition (10) plications, such as the action of moonlight. of 1904 found seventy-five out of every hundred occurrences to take place before midnight.

Sept. to March (N. Lat.).
March to Sept. (S. Lat.).

C

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.

Dec.

Nov. and Jan.

Hour.

Feb., March,
Sept. and Oct.

A

B

A

B

A

B

A

B

I

76

27

23

14

123456789

Midnight

Percentages-
Forenoon

Afternoon

42

58

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.

365

35

65

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:

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 aurorawhich 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 | In each case the excess of auroras in the group of years of many 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

sun-spots is decided, but the results from the two sub-periods do not harmonize closely. The mean sun-spot frequency for the group periods, but the auroral frequency for the later group is nearly of years of few sun-spots is almost exactly the same for the two sub40% in excess of that for the earlier, and even exceeds the aurorai