Chapter XV: Part 15

AURORA, a village of Cayuga county, New York, U.S.A., on Cayuga Lake, 16 m. S.W. of Auburn. Pop. (1905) 623; (1910) 493. It is served by the Lehigh Valley railway. Aurora is a beautiful place and a popular summer resort, but it is best known as the seat of Wells College, a non-sectarian college for women, founded in 1868 by Henry Wells (1805-1878), of the Wells Fargo Express Company, and liberally endowed by Edwin B. Morgan (1806-1881), also connected with the same company, and by others. At Aurora are also the Somes school (a preparatory school for boys), founded in 1798 and until 1904 known as the Cayuga Lake Academy, and the Wells school (a preparatory school for girls). The village has a public library. Aurora was settled in 1789 chiefly by residents of New England, and was incorporated in 1905.

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 deg. N. lat., 70 deg. 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 deg. 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 deg. or more.
The following are a selection of the figures:--

Angle of depression 4.5 deg. 7.5 deg. 10.5 deg. 12.5 deg. 15.5 deg.
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 deg. 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 deg. 52') + 2.53 sin(60t + 309 deg. 5')
+ 0.16 sin(90t + 213 deg. 31') + 0.56 sin(120t + 162 deg. 45')
+ 0.27 sin(150t + 32 deg. 38').

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.]

TABLE I.--_Annual Frequency (Relative)._

+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+
| Place. | Latitude. | Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sep. | Oct. | Nov. | Dec. |
+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+
| | deg. | | | | | | | | | | | | |
| Hammerfest | 70-1/2 | 20.9 | 17.6 | 8.8 | 0 | 0 | 0 | 0 | 0 | 4.4 | 9.9 | 17.6 | 20.9 |
| Jakobshavn | 69 | 14.6 | 13.0 | 9.2 | .5 | 0 | 0 | 0 | 0 | 9.2 | 15.1 | 18.4 | 20.0 |
| Godthaab | 64 | 15.5 | 12.4 | 9.7 | 4.9 | 0 | 0 | 0 | 1.2 | 8.7 | 13.3 | 17.0 | 17.4 |
| St Petersburg | 60 | 6.5 | 9.1 | 16.8 | 13.8 | 3.5 | 1.2 | 1.4 | 5.9 | 13.8 | 13.1 | 7.6 | 7.3 |
| Christiania | 60 | 8.6 | 11.4 | 14.0 | 11.2 | 0.6 | 0 | 0.2 | 6.5 | 14.6 | 12.2 | 10.3 | 10.3 |
| Upsala | 60 | 8.4 | 12.9 | 14.9 | 7.4 | 0.7 | 0.2 | 0.4 | 7.1 | 12.4 | 14.3 | 10.7 | 10.7 |
| Stockholm | 59 | 7.6 | 10.0 | 14.7 | 16.4 3.8 | 0.0 | 0.0 | 5.6 | 12.9 | 11.4 | 10.0 | 7.3 |
| Edinburgh | 56 | 9.6 | 12.6 | 14.0 | 9.5 | 3.4 | 0.0 | 1.7 | 6.0 | 12.6 | 13.5 | 11.8 | 5.2 |
| Berlin | 52-1/2 | 7.6 | 10.8 | 16.4 | 15.5 | 11.4 | 0.6 | 2.9 | 2.9 | 6.5 | 13.2 | 8.5 | 4.1 |
| London | 51-1/2 | 8.6 | 10.5 | 10.2 | 10.7 | 4.0 | 1.1 | 1.9 | 5.6 | 14.5 | 16.9 | 9.6 | 6.4 |
| Quebec | 47 | 3.6 | 14.8 | 8.3 | 14.2 | 4.1 | 5.9 | 7.7 | 5.9 | 11.2 | 12.4 | 7.7 | 4.1 |
| Toronto | 43-1/2 | 5.4 | 9.5 | 8.7 | 11.8 | 9.0 | 6.2 | 8.0 | 6.4 | 8.5 | 11.1 | 8.7 | 6.7 |
| Cambridge, Mass.| 42-1/2 | 5.1 | 8.2 | 11.8 | 10.2 | 6.4 | 5.1 | 10.3 | 8.5 | 13.3 | 9.2 | 6.8 | 5.1 |
| New Haven, Conn.| 41-1/2 | 7.7 | 7.3 | 8.9 | 8.2 | 7.6 | 5.7 | 8.9 | 8.1 | 11.9 | 7.6 | 10.6 | 7.5 |
| Scandinavia | N. of 68-1/2 | 16.4 | 13.8 | 14.8 | 1.6 | 0.0 | 0.0 | 0.0 | 0.4 | 7.8 | 15.1 | 14.4 | 15.7 |
| " | 68-1/2 to 65| 15.3 | 14.6 | 13.7 | 2.9 | 0.0 | 0.0 | 0.0 | 1.1 | 9.7 | 14.6 | 14.0 | 14.1 |
| " | 65 to 61-1/2 | 13.2 | 12.3 | 14.5 | 5.4 | 0.2 | 0.0 | 0.0 | 2.8 | 13.1 | 14.2 | 12.8 | 11.5 |
| " | 61-1/2 to 58| 9.5 | 11.2 | 13.5 | 10.9 | 1.3 | 0.1 | 0.4 | 5.7 | 13.6 | 13.8 | 10.4 | 9.6 |
| " | S. of 58 | 8.2 | 11.9 | 12.6 | 13.3 | 1.5 | 0.1 | 0.6 | 4.9 | 14.9 | 13.5 | 10.3 | 8.2 |
| New York State | 45 to 40-1/2 | 6.3 | 7.4 | 9.1 | 11.0 | 7.4 | 6.6 | 8.8 | 10.4 | 11.7 | 9.7 | 6.2 | 5.4 |
+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+

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.
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 X 30 deg. + 100 deg. 52' = 450 deg. 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 deg. 52', 309 deg. 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.

TABLE II.

+----------------------+--------------+--------------+--------------+
| | Annual Term. | 6-Month Term.| 4-Month Term.|
| Station. +-------+------+-------+------+-------+------+
| | Amp. |Phase.| Amp. |Phase.| Amp. |Phase.|
+----------------------+-------+------+-------+------+-------+------+
| | | deg. | | deg. | | deg. |
| Jakobshavn | 10.40 | 123 | 1.13 | 206 | 1.41 | 333 |
| Godthaab | 8.21 | 111 | 1.54 | 316 | 0.64 | 335 |
| St Petersburg | 2.81 | 96 | 5.99 | 309 | 0.57 | 208 |
| Christiania | 4.83 | 116 | 4.99 | 317 | 0.76 | 189 |
| Upsala | 5.41 | 119 | 4.57 | 322 | 0.86 | 296 |
| Stockholm | 3.68 | 91 | 5.80 | 303 | 1.31 | 180 |
| Makerstown (Scotland)| 5.79 | 102 | 4.47 | 310 | 2.00 | 342 |
| Great Britain | 3.87 | 126 | 4.24 | 287 | 0.40 | 73 |
| Toronto | 0.18 | 12 | 2.13 | 260 | 0.52 | 305 |
| Cambridge, Mass. | 1.02 | 262 | 2.84 | 339 | 1.28 | 253 |
| New Haven, Conn. | 0.99 | 183 | 1.02 | 313 | 0.57 | 197 |
| New York State | 1.34 | 264 | 2.29 | 325 | 0.54 | 157 |
+----------------------+-------+------+-------+------+-------+------+

Speaking generally, the annual term diminishes in importance as we
travel south. North of 55 deg. in Europe its phase angle seems fairly
constant, not differing very much from the value 110 deg. in
Lovering's general formula. The 6-month term is small, in the two most
northern stations, but south of 60 deg. 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 deg.
in Lovering's general formula. North of lat. 50 deg. 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-Gyllenskold 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 deg. 28' N. lat., 15 deg. 42' E. long.), those under B to Jan Mayen (8) (71 deg. 0' N. lat., 8 deg. 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 70-1/2 deg. S. lat., 86-1/2 deg. 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 Gottingen 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 deg. 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 deg. 37' N. lat., 37 deg. 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._

+-------------+-----------+-----------+-----------+-----------------------+
| | | |Feb., Mar.,|Sep. to Mar. (N. Lat.).|
| Hour. | Dec. |Nov. & Jan.|Sep. & Oct.|Mar. to Sep. (S. Lat.).|
| +-----+-----+-----+-----+-----+-----+-------+-------+-------+
| | A | B | A | B | A | B | A | B | C |
+-------------+-----+-----+-----+-----+-----+-----+-------+-------+-------+
| 1 | 14 | 7 | 14 | 8 | 27 | 23 | 55 | 38 | 24 |
| 2 | 10 | 6 | 15 | 6 | 20 | 25 | 45 | 37 | 23 |
| 3 | 9 | 4 | 15 | 5 | 15 | 21 | 39 | 30 | 10 |
| 4 | 10 | 5 | 21 | 7 | 14 | 18 | 45 | 30 | 4 |
| 5 | 13 | 5 | 20 | 3 | 10 | 10 | 43 | 18 | 2 |
| 6 | 11 | 3 | 15 | 4 | 2 | 3 | 28 | 10 | 1 |
| 7 | 9 | 2 | 13 | 3 | 1 | 2 | 23 | 7 | 0 |
| 8 | 5 | 1 | 6 | 1 | 0 | 0 | 11 | 2 | 0 |
| 9 | 7 | 2 | 9 | 0 | 0 | 0 | 16 | 2 | 0 |
| 10 | 10 | 0 | 5 | 0 | 0 | 0 | 15 | 0 | 0 |
| 11 | 9 | 0 | 6 | 0 | 0 | 0 | 15 | 0 | 0 |
| Noon | 10 | 0 | 4 | 0 | 0 | 0 | 14 | 0 | 0 |
| 1 | 10 | 0 | 6 | 0 | 0 | 0 | 16 | 0 | 0 |
| 2 | 14 | 0 | 10 | 0 | 0 | 0 | 24 | 0 | 0 |
| 3 | 18 | 1 | 20 | 3 | 0 | 0 | 38 | 4 | 0 |
| 4 | 16 | 7 | 19 | 7 | 1 | 1 | 36 | 15 | 0 |
| 5 | 12 | 11 | 22 | 10 | 5 | 2 | 39 | 23 | 3 |
| 6 | 14 | 10 | 21 | 16 | 8 | 5 | 43 | 31 | 3 |
| 7 | 16 | 13 | 23 | 16 | 20 | 9 | 59 | 38 | 14 |
| 8 | 15 | 12 | 22 | 18 | 24 | 24 | 61 | 54 | 25 |
| 9 | 14 | 15 | 18 | 17 | 27 | 28 | 59 | 60 | 31 |
| 10 | 12 | 15 | 19 | 15 | 31 | 25 | 62 | 55 | 29 |
| 11 | 10 | 12 | 18 | 17 | 33 | 26 | 61 | 55 | 26 |
| Midnight | 9 | 9 | 13 | 11 | 28 | 22 | 50 | 42 | 26 |
+-------------+-----+-----+-----+-----+-----+-----+-------+-------+-------+
| Totals | 277 | 140 | 354 | 167 | 266 | 244 | 897 | 551 | 221 |
+-------------+-----+-----+-----+-----+-----+-----+-------+-------+-------+
|Percentages--| | | | | | | | | |
| Forenoon | 42 | 28 | 42 | 25 | 39 | 46 | 41 | 35 | 35 |
| Afternoon | 58 | 72 | 58 | 75 | 61 | 54 | 59 | 65 | 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. | Bands. | Rays. | Patches. |
+----------------+-----+-----+-----+-----+-----+-----+-----+-----+
| | e. | m. | e. | m. | e. | m. | e. | m. |
| +-----+-----+-----+-----+-----+-----+-----+-----+
| Cape Thorsden. | 76 | 24 | 66 | 34 | 52 | 48 | 51 | 49 |
| Jan Mayen. | 78 | 22 | 68 | 32 | 60 | 40 | 60 | 40 |
| Tasiusak | 85 | 15 | 85 | 15 | 65 | 35 | 62 | 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:--

+-----------------+------------------+------------------+------------------+
| | 1764-1872. | 1764-1817. | 1818-1872. |
| Years of +--------+---------+--------+---------+--------+---------+
| | Spots. | Auroras.| Spots. | Auroras.| Spots. | Auroras.|
+-----------------+--------+---------+--------+---------+--------+---------+
| Many sun-spots. | 93.4 | 99.9 | 86.7 | 70.7 | 100.1 | 129.1 |
| Few " | 13.4 | 61.5 | 13.6 | 51.6 | 13.1 | 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 " 55.8 " 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 | 65.6 | 76.1 |
| 1794-1826 | 20.3 | 39.5 |
| 1827-1859 | 56.1 | 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 | Total Nights |
| | Frequency. | of Aurora. |
+----------------+----------------+--------------+
| 1865-1868 | 48 | 274 |
| 1869-1872 | 339 | 138 |
| 1876-1879 | 23 | 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.

+-------+----------------------++-------+----------------------+
| | Frequency. || | Frequency. |
| Year. +----------------------++ Year. +----------------------+
| | Sun-spot. | Auroral. || | Sun-spot. | Auroral. |
+-------+-----------+----------++-------+-----------+----------+
| 1749 | 80.9 | 103 || 1829 | 67.0 | 93 |
| 1750 | 83.4 | 134 || 1830 | 71.0 | 132 |
| 1751 | 47.7 | 53 || 1831 | 47.8 | 89 |
| 1752 | 47.8 | 111 || 1832 | 27.5 | 54 |
| 1753 | 30.7 | 96 || 1833 | 8.5 | 79 |
| 1754 | 12.2 | 65 || 1834 | 13.2 | 81 |
| 1755 | 9.6 | 34 || 1835 | 56.9 | 58 |
| 1756 | 10.2 | 60 || 1836 | 121.5 | 98 |
| 1757 | 32.4 | 83 || 1837 | 138.3 | 137 |
| 1758 | 47.6 | 80 || 1838 | 103.2 | 159 |
| 1759 | 54.0 | 113 || 1839 | 85.8 | 165 |
| 1760 | 62.9 | 86 || 1840 | 63.2 | 82 |
| 1761 | 85.9 | 124 || 1841 | 36.8 | 75 |
| 1762 | 61.2 | 114 || 1842 | 24.2 | 91 |
| 1763 | 45.1 | 89 || 1843 | 10.7 | 66 |
| 1764 | 36.4 | 107 || 1844 | 15.0 | 81 |
| 1765 | 20.9 | 76 || 1845 | 40.1 | 26 |
| 1766 | 11.4 | 51 || 1846 | 61.5 | 50 |
| 1767 | 37.8 | 68 || 1847 | 98.5 | 63 |
| 1768 | 69.8 | 80 || 1848 | 124.3 | 107 |
| 1769 | 106.1 | 89 || 1849 | 95.9 | 131 |
| 1770 | 100.8 | 83 || 1850 | 66.5 | 95 |
| 1771 | 81.6 | 62 || 1851 | 64.5 | 60 |
| 1772 | 66.5 | 38 || 1852 | 54.2 | 92 |
| 1773 | 34.8 | 58 || 1853 | 39.0 | 65 |
| 1774 | 30.6 | 98 || 1854 | 20.6 | 64 |
| 1775 | 7.0 | 33 || 1855 | 6.7 | 49 |
| 1776 | 19.8 | 17 || 1856 | 4.3 | 46 |
| 1777 | 92.5 | 64 || 1857 | 22.8 | 38 |
| 1778 | 154.4 | 59 || 1858 | 54.8 | 88 |
| 1779 | 125.9 | 60 || 1859 | 93.8 | 131 |
| 1780 | 84.8 | 67 || 1860 | 95.7 | 119 |
| 1781 | 68.1 | 103 || 1861 | 77.2 | 127 |
| 1782 | 38.5 | 67 || 1862 | 59.1 | 135 |
| 1783 | 22.8 | 70 || 1863 | 44.0 | 135 |
| 1784 | 10.2 | 78 || 1864 | 47.0 | 124 |
| 1785 | 24.1 | 83 || 1865 | 30.5 | 119 |
| 1786 | 82.9 | 136 || 1866 | 16.3 | 130 |
| 1787 | 132.0 | 115 || 1867 | 7.3 | 127 |
| 1788 | 130.9 | 97 || 1868 | 37.3 | 144 |
| 1789 | 118.1 | 89 || 1869 | 73.9 | 160 |
| 1790 | 89.9 | 90 || 1870 | 139.1 | 195 |
| 1791 | 66.6 | 54 || 1871 | 111.2 | 185 |
| 1792 | 60.0 | 64 || 1872 | 101.7 | 200 |
| 1793 | 46.9 | 29 || 1873 | 66.3 | 189 |
| 1794 | 41.0 | 37 || 1874 | 44.7 | 158 |
| 1795 | 21.3 | 34 || 1875 | 17.1 | 133 |
| 1796 | 16.0 | 37 || 1876 | 11.3 | 137 |
| 1797 | 6.4 | 61 || 1877 | 12.3 | 126 |
| 1798 | 4.1 | 35 || 1878 | 3.4 | .. |
| 1799 | 6.8 | 28 || 1879 | 6.0 | .. |
| 1800 | 14.5 | 30 || 1880 | 32.3 | .. |
| 1801 | 34.0 | 34 || 1881 | 54.3 | .. |
| 1802 | 45.0 | 65 || 1882 | 59.7 | .. |
| 1803 | 43.1 | 73 || 1883 | 63.7 | .. |
| 1804 | 47.5 | 101 || 1884 | 63.5 | .. |
| 1805 | 42.2 | 85 || 1885 | 52.2 | .. |
| 1806 | 28.1 | 62 || 1886 | 25.4 | .. |
| 1807 | 10.1 | 42 || 1887 | 13.1 | .. |
| 1808 | 8.1 | 20 || 1888 | 6.8 | .. |
| 1809 | 2.5 | 20 || 1889 | 6.3 | .. |
| 1810 | 0.0 | 4 || 1890 | 7.1 | .. |
| 1811 | 1.4 | 13 || 1891 | 35.6 | .. |
| 1812 | 5.0 | 11 || 1892 | 73.0 | .. |
| 1813 | 12.2 | 18 || 1893 | 84.9 | .. |
| 1814 | 13.9 | 17 || 1894 | 78.0 | .. |
| 1815 | 35.4 | 10 || 1895 | 64.0 | .. |
| 1816 | 45.8 | 33 || 1896 | 41.8 | .. |
| 1817 | 41.1 | 60 || 1897 | 26.2 | .. |
| 1818 | 30.4 | 74 || 1898 | 26.7 | .. |
| 1819 | 23.9 | 43 || 1899 | 12.1 | .. |
| 1820 | 15.7 | 62 || 1900 | 9.5 | .. |
| 1821 | 6.6 | 37 || 1901 | 2.7 | .. |
| 1822 | 4.0 | 33 || 1902 | 5.0 | .. |
| 1823 | 1.8 | 13 || 1903 | 24.4 | .. |
| 1824 | 8.5 | 14 || 1904 | 42.0 | .. |
| 1825 | 16.6 | 40 || 1905 | 62.8 | .. |
| 1826 | 36.3 | 58 || 1906 | 53.8 | .. |
| 1827 | 49.7 | 79 || 1907 | 62.0 | .. |
| 1828 | 62.5 | 60 || 1908 | 48.5 | .. |
+-------+-----------+----------++-------+-----------+----------+

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 deg. 12' W., or 11 deg. 27' to the W. of the magnetic meridian. As
to the azimuths in individual cases, 130 differed from the mean by
less than 10 deg., 118 by from 10 deg. to 20 deg., 82 by from 20 deg.
to 30 deg., 21 by from 30 deg. to 40 deg., 14 by from 40 deg. to 50
deg.; in six cases the departure exceeded 50 deg., and in one case it
exceeded 70 deg. 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 deg. W. of N. (or E. of S.), the mean derived from the 113
arcs observed between midnight and 6 A.M. was 47.8 deg. W. At Jan
Mayen (8) in 1882-1883 the mean azimuth of the summit of the arcs was
28.8 deg. W. of N., thus approaching much more closely to the magnetic
meridian 29.9 deg. W. As to individual azimuths, 113 lay within 10
deg. of the mean, 37 differed by from 10 deg. to 20 deg., 18 by from
20 deg. to 30 deg., 6 by from 30 deg. to 40 deg., whilst 6 differed by
over 40 deg. Azimuths were also measured at Jan Mayen for 338 auroral
bands, the mean being 22.0 deg. W., or 7.9 deg. to the east of the
magnetic meridian. Combining the results from arcs and bands,
Carlheim-Gyllenskold gives the "anomaly" of the auroral meridian at
Jan Mayen as 5.7 deg. E. At the British Polar station of 1882, Fort
Rae (62 deg. 23' N. lat., 115 deg. 44' W. long.), he makes it 15.7
deg. W. At Godthaab in 1882-1883 the auroral anomaly was, according to
Paulsen, 15.5 deg. E., the magnetic meridian lying 57.6 deg. 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 deg. 7', the magnetic inclination being 80 deg. 35', whilst the
coronal centre had an altitude of 79 deg. 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 deg. 50' at Bossekop (16) in
1838-1839, and 0 deg. 7' at Treurenberg (17) (79 deg. 55' N. lat., 16
deg. 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 deg. 27' N. lat., 26 deg. 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 deg. above the northern horizon; 88 were seen in the
south, their average altitude above the southern horizon being 33.5
deg.; 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.

+--------+----------------------------------------------+------------+
| Direc- | Absolute Number for each Type. | Percentage |
| tion. +-------+--------+-----------+-------+---------+ from all |
| | Arcs. | Bands. | Curtains. | Rays. | Patches.| Types. |
+--------+-------+--------+-----------+-------+---------+------------+
| N. | 9 | 16 | 5 | 15 | 4 | 10 |
| N.E. | 9 | 13 | 2 | 20 | 4 | 9 |
| E. | 3 | 11 | 2 | 26 | 3 | 9 |
| S.E. | 5 | 6 | 1 | 10 | 7 | 6 |
| S. | 45 | 43 | 1 | 16 | 15 | 24 |
| S.W. | 9 | 9 | 2 | 12 | 13 | 9 |
| W. | 3 | 11 | 2 | 22 | 6 | 9 |
| N.W. | 2 | 8 | 2 | 8 | 5 | 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. | 69 | 55 | 44 | 35 |
| P.M. | 55 | 70 | 65 | 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 deg. 45'; Group II. thirty arcs
whose altitudes lay between 12 deg. and 35 deg.; and Group III, thirty
arcs whose altitudes lay between 36 deg. and 80 deg.

+-----------------+----------+----------+----------+
| Group. | I. | II. | III. |
+-----------------+----------+----------+----------+
| Greatest width |11.5 deg. |12.0 deg. | 21.0 deg.|
| Least " | 1.0 deg. | 0.75 deg.| 2.0 deg.|
| Mean " | 3.45 deg.| 4.6 deg. | 6.9 deg.|
+-----------------+----------+----------+----------+

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, Gyllenskold 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 deg. 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 |10.5 deg.|34.6 deg.| 72.3 deg.| .. |
| Greatest velocity | 4.81 | 15.12 |109.09 | .. |
| Mean velocity | 0.48 | 2.42 | 8.67 | 3.86 |
+-------------------+---------+---------+----------+------+