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.
| Place. | Latitude. | Jan. | Feb. | March. | April. | May. | June. | July. | Aug. | Sep. | Oct. | Nov. | Dec. |
Hammerfest Jakobshavn Godthaab St Petersburg Christiania Upsala Stockholm Edinburgh Berlin London Quebec Toronto Cambridge, Mass. New Haven, Conn. Scandinavia ” ” ” ” New York State |
° 7012 69 64 60 60 60 59 56 5212 5112 47 4312 4212 4112 N. of 6812° 6812° to 65° 65° to 6112° 6112° to 58° S. of 58° 45° to 4012° |
20·9 14·6 15·5 6·5 8·6 8·4 7·9 9·5 7·0 8·6 3·6 5·4 5·1 7·7 16·4 15·3 13·2 9·5 8·2 6·3 |
17·6 13·0 12·4 9·1 11·4 12·9 10·0 12·6 10·8 10·5 14·8 9·5 8·2 7·3 13·8 14·6 12·3 11·2 11·9 7·4 |
8·8 9·2 9·7 16·8 14·0 14·9 14·7 14·0 16·4 10·2 8·3 8·7 11·8 8·9 14·8 13·7 14·5 13·5 12·6 9·1 |
0 0·5 4·9 13·8 11·2 7·4 16·4 9·5 15·5 10·7 14·2 11·8 10·2 8·2 1·6 2·9 5·4 10·9 13·3 11·0 |
0 0 0 3·5 0·6 0·7 3·8 3·4 11·4 4·0 4·1 9·0 6·4 7·6 0·0 0·0 0·2 1·3 1·5 7·4 |
0 0 0 1·2 0 0·2 0·0 0·0 0·6 1·1 5·9 6·2 5·1 5·7 0·0 0·0 0·0 0·1 0·1 6·6 |
0 0 0 1·4 0·2 0·4 0·0 1·7 2·9 1·9 7·7 8·0 10·3 8·9 0·0 0·0 0·0 0·4 0·6 8·8 |
0 0 1·2 5·9 6·5 7·1 5·6 6·0 2·9 5·6 5·9 6·4 8·5 8·1 0·4 1·1 2·8 5·7 4·9 10·4 |
4·4 9·2 8·7 13·8 14·6 12·4 12·9 12·6 6·5 14·5 11·2 8·5 13·3 11·9 7·8 9·7 13·1 13·6 14·9 11·7 |
9·9 15·1 13·3 13·1 12·2 14·3 11·4 13·5 13·2 16·9 12·4 11·1 9·2 7·6 15·1 14·6 14·2 13·8 13·5 9·7 |
17·6 18·4 17·0 7·6 10·3 10·7 10·0 11·8 8·5 9·6 7·7 8·7 6·8 10·6 14·4 14·0 12·8 10·4 10·3 6·2 |
20·9 20·0 17·4 7·3 10·3 10·7 7·3 5·2 4·1 6·4 4·1 6·7 5·1 7·5 15·7 14·1 11·5 9·6 8·2 5·4 |
| Station. | Annual Term. | 6-Month Term. | 4-Month Term. | |||
| Amp. | Phase. | Amp. | Phase. | Amp. | Phase. | |
Jakobshavn Godthaab St Petersburg Christiania Upsala Stockholm Makerstown (Scotland) Great Britain Toronto Cambridge, Mass. New Haven, Conn. New York State |
10·40 8·21 2·81 4·83 5·41 3·68 5·79 3·87 0·18 1·02 0·99 1·34 |
° 123 111 96 116 119 91 102 126 12 262 183 264 |
1·13 1·54 5·99 4·99 4·57 5·80 4·47 4·24 2·13 2·84 1·02 2·29 |
° 206 316 309 317 322 303 310 287 260 339 313 325 |
1·41 0·64 0·57 0·76 0·86 1·31 2·00 0·40 0·52 1·28 0·57 0·54 |
° 333 335 208 189 296 180 342 73 305 253 197 157 |
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 7012° S. lat., 8612° 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.
