MISCELLANEOUS THEORETICAL MATTERS CONNECTED
WITH ECLIPSES OF THE SUN (CHIEFLY).
One or two miscellaneous matters respecting eclipses of the Sun
(chiefly) will be dealt with in this chapter. It is not easy to explain
or define in words the circumstances which control the duration of a
Solar eclipse, whereas in the case of a lunar eclipse the obscuration is
the same in degree at all parts of the Earth where the Moon is visible.
In the case of a Solar eclipse it may be total, perhaps, in Africa, may
be of six digits only in Spain, and of two only in England. Under the
most favourable circumstances the breadth of the track of totality
across the Earth cannot be more than 170 miles, and it may be anything
less than that down to zero where the eclipse will cease to be total at
all, and will become annular. The question whether a given eclipse shall
exhibit itself on its central line as a total or an annular one depends,
as has been already explained, on the varying distances of the Earth and
the Moon from the Sun in different parts of their respective orbits.
Hence it follows that not only may an eclipse show itself for several
Saros appearances as total and afterwards become annular, and _vice
versâ_, but on rare occasions one and the same eclipse may be annular in
one part of its track across the Earth and total in another part, a
short time earlier or later. This last-named condition might arise
because the Moon's distance from the Earth or the Sun had varied
sufficiently during the progress of the eclipse to bring about such a
result; or because the shadow just reaching the Earth and no more the
eclipse would be total only for the moment when a view perpendicular
upwards could be had of it, and would be annular for the minutes
preceding and the minutes following the perpendicular glimpse obtained
by observers actually on the central line. The eclipse of December 12,
1890, was an instance of this.
If the paths of several central eclipses of the Sun are compared by
placing side by side a series of charts, such as those given in the
_Nautical Almanac_ or in Oppolzer's _Canon_, it will be noticed that the
direction of the central line varies with the season of the year. In the
month of March the line runs from S.W. to N.E., and in September from
N.W. to S.E. In June the line is a curve, going first to the N.E. and
then to the S.E. In December the state of things is reversed, the curve
going first to the S.E. and then to the N.E. At all places within about
2000 miles of the central line the eclipse will be visible, and the
nearer a place is to the central line, so much the larger will be the
portion of the Sun's disc concealed from observers there by the Moon.
If the central line runs but a little to the N. of the Equator in Winter
or of 25° of N. latitude in Summer, the eclipse will be visible all over
the Northern Hemisphere, and the converse will apply to the Southern
Hemisphere. It is something like a general rule in the case of total and
annular eclipses, though subject to many modifications, that places
within 200-250 miles of the central line will have partial eclipse of 11
digits; from thence to 500 miles of 10 digits, and so on, diminishing
something like 1 digit for every 250 miles, so that at 2000 miles, or
rather more, the Sun will be only to a very slight extent eclipsed, or
will escape eclipse altogether.
The diameter of the Sun being 866,000 miles and the Moon being only 2160
miles or 1/400th how comes it to be possible that such a tiny object
should be capable of concealing a globe 400 times bigger than itself?
The answer is--Distance. The increased distance does it. The Moon at its
normal distance from the Earth of 237,000 miles could only conceal by
eclipse a body of its own size or smaller, but the Sun being 93,000,000
miles away, or 392 times the distance of the Moon, the fraction 1/392
representing the main distance of the Moon, more than wipes out the
fraction 1/400 which represents our satellite's smaller size.
During a total eclipse of the Sun, the Moon's shadow travels across the
Earth at a prodigious pace--1830 miles an hour; 30½ miles a minute; or
rather more than a ½ mile a second. This great velocity is at once a
clue to the fact that the total phase during an eclipse of the Sun
lasts for so brief a time as a few minutes; and also to the fact that
the shadow comes and goes almost without being seen unless a very sharp
watch is kept for it. Indeed, it is only observers posted on high ground
with some miles of open low ground spread out under their eyes who have
much chance of detecting the shadow come up, go over them, and pass
forwards.
Places at or near the Earth's equator enjoy the best opportunities for
seeing total eclipses of the Sun, because whilst the Moon's shadow
travels eastwards along the Earth's surface at something like 2000 miles
an hour, an observer at the equator is carried in the same direction by
virtue of the Earth's axial rotation at the rate of 1040 miles an hour.
But the speed imparted to an observer as the result of the Earth's axial
rotation diminishes from the equator towards the poles where it is
_nil_, so that the nearer he is to a pole the slower he goes, and
therefore the sooner will the Moon's shadow overtake and pass him, and
the less the time at his disposal for seeing the Sun hidden by the Moon.
It was calculated by Du Sèjour that the greatest possible duration of
the total phase of a Solar eclipse at the equator would be 7^m 58^s, and
for the latitude of Paris 6^m 10^s. In the case of an annular eclipse
the figures would be 12^m 24^s for the equator, and 9^m 56^s for the
latitude of Paris. These figures contemplate a combination of all the
most favourable circumstances possible; as a matter of fact, I believe
that the greatest length of total phase which has been actually known
was 6½^m and that was in the case of the eclipse of August 29, 1886. It
was in the open Atlantic that this duration occurred, but it was not
observed. The maximum observed obscuration during this eclipse was no
more than 4^m.
Though total eclipses of the Sun happen with tolerable frequency so far
as regards the Earth as a whole, yet they are exceedingly rare at any
given place. Take London, for instance. From the calculations of Hind,
confirmed by Maguire,[11] it may be considered as an established fact
that there was no total eclipse visible at London between A.D. 878 and
1715, an interval of 837 years. The next one visible at London, though
uncertain, is also a very long way off. There will be a total eclipse on
August 11, 1999, which will come as near to London as the Isle of Wight,
but Hind, writing in 1871, said that he doubted whether there would be
any other total eclipse "visible _in England_ for 250 years[12] from the
present time." Maguire states that the Sun has been eclipsed, besides
twice at London, also twice at Dublin, and no fewer than five times at
Edinburgh during the 846 years examined by him. In fact that every part
of the British Isles has seen a total eclipse at some time or other
between A.D. 878 and 1724 except a small tract of country at Dingle, on
the West coast of Ireland. The longest totality was on June 15, 885,
namely, 4^m 55^s, and the shortest in July 16, 1330, namely, 0^m 56^s.
Contrast with this the obscure island of Blanquilla, off the northern
coast of Venezuela. The inhabitants of that island not long ago had the
choice of two total eclipses within three and a half years, namely,
August 29, 1886, and December 22, 1889; whilst Yellowstone, U.S., had
two in twelve years (July 29, 1878, and January 1, 1889).
Counting from first to last, Du Sèjour found that at the equator an
eclipse of the Sun might last 4^h 29^m, and at the latitude of Paris 3^h
26^m. These intervals, of course, cover all the subordinate phases. The
total phase which alone (with perhaps a couple of minutes added) is
productive of spectacular effects, and interesting scientific results is
a mere matter of minutes which may be as few as one (or less), or only
as many as 6 or 8.
As a rule, a summer eclipse will last longer than a winter one, because
in summer the Earth (and the Moon with it), being at its maximum
distance from the Sun, the Sun will be at its minimum apparent size, and
therefore the Moon will be able to conceal it the longer.
FOOTNOTES:
[Footnote 11: _Month. Not._, _R.A.S._, vol. xlv., p. 400. June
1885.]
[Footnote 12: Johnson makes the eclipse of June 14, 2151, to be
"nearly, if not quite, total at London." Possibly it was this
eclipse which Hind had in his thoughts when he wrote in the _Times_
(July 28, 1871) the passage quoted above.]