THE "SAROS" AND THE PERIODICITY OF ECLIPSES.
To bring about an eclipse of the Sun, two things must combine: (1) the
Moon must be at or near one of its Nodes; and (2), this must be at a
time when the Moon is also in "Conjunction" with the Sun. Now the Moon
is in Conjunction with the Sun (= "New Moon") 12 or 13 times in a year,
but the Sun only passes through the Nodes of the Moon's orbit twice a
year. Hence an eclipse of the Sun does not and cannot occur at every New
Moon, but only occasionally. An _exact_ coincidence of Earth, Moon, and
Sun, in a straight line at a Node is not necessary to ensure an eclipse
of the Sun. So long as the Moon is within about 18½° of its Node, with a
latitude of not more than 1° 34', an eclipse _may_ take place. If,
however, the distance is less than 15¼° and the latitude less than
1° 23' an eclipse _must_ take place, though between these limits[4] the
occurrence of an eclipse is uncertain and depends on what are called the
"horizontal parallaxes" and the "apparent semi-diameters" of the two
bodies at the moment of conjunction, in other words, on the nearness or
"far-offness" of the bodies in question. Another complication is
introduced into these matters by reason of the fact that the Nodes of
the Moon's orbit do not occupy a fixed position, but have an annual
retrograde motion of about 19¼°, in virtue of which a complete
revolution of the Nodes round the ecliptic is accomplished in 18 years
218-7/8 days (= 18.5997 years).
The backward movement of the Moon's Nodes combined with the apparent
motion of the Sun in the ecliptic causes the Moon in its monthly course
round the Earth to complete a revolution with respect to its Nodes in a
less time (27.2 days) than it takes to get back to Conjunction with the
Sun (29.5 days); and a curious consequence, as we shall see directly,
flows from these facts and from one other fact. The other fact is to the
Sun starting coincident with one of the Moon's Nodes, returns on the
Ecliptic to the same Node in 346.6 days. The first named period of 27.2
days is called the "_Nodical_ Revolution of the Moon" or "Draconic
Month," the other period of 29.5 days is called the "_Synodical_
Revolution of the Moon." Now the curious consequence of these figures
being what they are is that 242 Draconic Months, 223 Lunations, and 19
Returns of the Sun to one and the same Node of the Moon's orbit, are all
accomplished in the same time within 11 hours. Thus (ignoring
refinements of decimals):--
Days Days. Years. Days. Hours.
242 times 27.2 = 6585.36 = 18 10 8½
223 times 29.5 = 6585.32 = 18 10 7¾
19 times 346.6 = 6585.78 = 18 10 18¾
The interpretation to be put upon these coincidences is this: that
supposing Sun and Moon to start together from a Node they would, after
the lapse of 6585 days and a fraction, be found again together very near
the same Node. During the interval there would have been 223 New and
Full Moons. The exact time required for 223 Lunations is such that in
the case supposed the 223rd conjunction of the two bodies would happen a
little before they reached the Node; their distance therefrom would be
28' of arc. And the final fact is that eclipses recur in almost, though
not quite, the same regular order every 6585-1/3 days, or more exactly, 18
years, 10 days, 7 hours, 42 minutes.[5] This is the celebrated Chaldean
"SAROS," and was used by the ancients (and can still be used by the
moderns in the way of a pastime) for the prediction of eclipses alike of
the Sun and of the Moon.
* * * * *
At the end of a Saros period, starting from any date that may have been
chosen, the Moon will be in the same position with respect to the Sun,
nearly in the same part of the heavens, nearly in the same part of its
orbit, and very nearly indeed at the same distance from its Node as at
the date chosen for the _terminus a quo_ of the Saros. But there are
trifling discrepancies in the case (the difference of about 11 hours
between 223 lunations and 19 returns of the Sun to the Moon's Node is
one) and these have an appreciable effect in disturbing not so much the
sequence of the eclipses in the next following Saros as their magnitude
and visibility at given places on the Earth's surface. Hence, a more
accurate succession will be obtained by combining 3 Saros periods,
making 54 years, 31 days; while, best of all, to secure an almost
perfect repetition of a series of eclipses will be a combination of 48
Saroses, making 865 years for the Moon; and of about 70 Saroses, or more
than 1200 years for the Sun.
These considerations are leading us rather too far afield. Let us return
to a more simple condition of things. The practical use of the Saros in
its most elementary conception is somewhat on this wise. Given 18 or 19
old Almanacs ranging, say, from 1880 to 1898, how can we turn to account
the information they afford us in order to obtain from them information
respecting the eclipses which will happen between 1899 and 1917?
Nothing easier. Add 18^y 10^d 7^h 42^m to the middle time of every
eclipse which took place between 1880 and 1898 beginning, say, with the
last of 1879 or the first of 1880, and we shall find what eclipses will
happen in 1898 and 17 following years, as witness by way of example the
following table:--
Error of Saros by
d. h. m. Exact Calculation.
MOON. 1879 Dec. 28 4 26 p.m.
(Mag. 0.17) 18 10 7 42
---------------------------------------------
(Mag. 0.16) 1898 Jan. 8 12 8 a.m. (civil time) +3 m.
d. h. m.
SUN. 1880 Jan. 11 10 48 p.m.
(Total) 18 10 7 42
---------------------------------------------
(Total) 1898 Jan. 22 6 30 a.m. (civil time) -1 h. 7 m.
d. h. m.
MOON. 1880 June 22 1 50 p.m.
(Mag. Total) 18 11 7 42
---------------------------------------------
(Mag. 0.93) 1898 July 3 9 32 p.m. +35 m.
d. h. m.
SUN. 1880 July 7 1 35 p.m.
(Mag. Annular) 18 11 7 42
---------------------------------------------
(Mag. Annular) 1898 July 18 9 17 p.m. +1 h. 10 m.
d. h. m.
SUN. 1880 Dec. 2 3 11 a.m. (civil time).
(Mag. 0.04) 18 11 7 42
---------------------------------------------
(Mag. 0.02) 1898 Dec. 13 10 53 a.m. -1 h. 5 m.
d. h. m.
MOON. 1880 Dec. 16 3 39 p.m.
(Mag. Total) 18 11 7 42
---------------------------------------------
(Mag. Total) 1898 Dec. 27 11 21 p.m. -13 m.
d. h. m.
SUN. 1880 Dec. 31 1 45 p.m.
(Mag. 0.71) 18 11 7 42
---------------------------------------------
(Mag. 0.72) 1899 Jan. 11 9 27 p.m. -1 h. 11 m.
There having been 5 recurrences of Feb. 29 between Dec. 1879 and Jan.
1899, 5 leap years having intervened, we have to add an extra day to the
Saros period in the later part of the above Table.[6]
Let us make another start and see what we can learn from the eclipses,
say, of 1883.
Error of Saros by
Exact Calculation.
h. m.
MOON 1883 April 22 11 39 a.m.
(Mag. 0.8) 18 11 7 42
--------------------------------------------
(Mag. Penumbral) 1901 May 3 7 21 p.m. +51 m.
h. m.
SUN 1883 May 6 9 45 p.m. Visible, Philippines.
(Mag. Total) 18 11 7 42
--------------------------------------------
(Mag. Total) 1901 May 18 5 27 a.m. (civil time). -2 m.
h. m.
MOON 1883 Oct. 16 6 54 a.m. Visible, California.
(Mag. 0.28) 18 11 7 42
--------------------------------------------
(Mag. 0.23) 1901 Oct. 27 2 36 p.m. -39 m.
h. m.
SUN 1883 Oct. 30 11 37 p.m. Visible, N. Japan.
(Mag. Annular) 18 11 7 42
--------------------------------------------
(Mag. Annular) 1901 Nov. 11 7 19 a.m. (civil time) +1 m.
The foregoing does not by any means exhaust all that can be said
respecting the Saros even on the popular side.
If the Saros comprised an exact number of days, each eclipse of a second
Saros series would be visible in the same regions of the Earth as the
corresponding eclipse in the previous series. But since there is a
surplus fraction of nearly one-third of a day, each subsequent eclipse
will be visible in another region of the Earth, which will be roughly a
third of the Earth's circumference in longitude backwards (_i.e._ about
120° to the W.), because the Earth itself will be turned on its axis
one-third forwards.
After what has been said as to the Saros and its use it might be
supposed that a correct list of eclipses for 18.03 years would suffice
for all ordinary purposes of eclipse prediction, and that the sequence
of eclipses at any future time might be ascertained by adding to some
one eclipse which had already happened so many Saros periods as might
embrace the years future whose eclipses it was desired to study. This
would be true in a sense, but would not be literally and effectively
true, because corresponding eclipses do not recur exactly under the same
conditions, for there are small residual discrepancies in the times and
circumstances affecting the real movements of the Earth and Moon and the
apparent movement of the Sun which, in the lapse of years and centuries,
accumulate sufficiently to dislocate what otherwise would be exact
coincidences. Thus an eclipse of the Moon which in A.D. 565 was of 6
digits[7] was in 583 of 7 digits, and in 601 nearly 8. In 908 the
eclipse became total, and remained so for about twelve periods, or until
1088. This eclipse continued to diminish until the beginning of the 15th
century, when it disappeared in 1413. Let us take now the life of an
eclipse of the Sun. One appeared at the North Pole in June A.D. 1295,
and showed itself more and more towards the S. at each subsequent
period. On August 27, 1367, it made its first appearance in the North of
Europe; in 1439 it was visible all over Europe; in 1601, being its 19th
appearance, it was central and annular in England; on May 5, 1818, it
was visible in London, and again on May 15, 1836. Its three next
appearances were on May 26, 1854, June 6, 1872, and June 17, 1890. At
its 39th appearance, on August 10, 1980, the Moon's shadow will have
passed the equator, and as the eclipse will take place nearly at
midnight (Greenwich M.T.), the phenomenon will be invisible in Europe,
Africa, and Asia. At every succeeding period the central line of the
eclipse will lie more and more to the S., until finally, on September
30, 2665, which will be its 78th appearance, it will vanish at the South
Pole.[8]
The operation of the Saros effects which have been specified above, may
be noticed in some of the groups of eclipses which have been much in
evidence (as will appear from a subsequent chapter), during the second
half of the 19th century. The following are two noteworthy Saros groups
of Solar eclipses:--
1842 July 8. | 1850 Aug. 7.
1860 " 18. | 1868 " 17.
1878 " 29. | 1886 " 29.
1896 Aug. 9. | 1904 Sept. 9.
If the curious reader will trace, by means of the _Nautical Almanac_
(or some other Almanac which deals with eclipses in adequate detail),
the geographical distribution of the foregoing eclipses on the Earth's
surface, he will see that they fulfil the statement made on p. 24
(_ante_), that a Saros eclipse when it reappears, does so in regions of
the Earth averaging 120° of longitude to the W. of those in which it
had, on the last preceding occasion, been seen; and also that it
gradually works northwards or southwards.
But a given Saros eclipse in its successive reappearances undergoes
other transformations besides that of Terrestrial longitude. These are
well set forth by Professor Newcomb[9]:--
"Since every successive recurrence of such an eclipse throws the
conjunction 28' further toward the W. of the node, the conjunction must,
in process of time, take place so far back from the node that no eclipse
will occur, and the series will end. For the same reason there must be a
commencement to the series, the first eclipse being E. of the node. A
new eclipse thus entering will at first be a very small one, but will be
larger at every recurrence in each Saros. If it is an eclipse of the
Moon, it will be total from its 13th until its 36th recurrence. There
will be then about 13 partial eclipses, each of which will be smaller
than the last, when they will fail entirely, the conjunction taking
place so far from the node that the Moon does not touch the Earth's
shadow. The whole interval of time over which a series of lunar eclipses
thus extend will be about 48 periods, or 865 years. When a series of
solar eclipses begins, the penumbra of the first will just graze the
earth not far from one of the poles. There will then be, on the average,
11 or 12 partial eclipses of the Sun, each larger than the preceding
one, occurring at regular intervals of one Saros. Then the central line,
whether it be that of a total or annular eclipse, will begin to touch
the Earth, and we shall have a series of 40 or 50 central eclipses. The
central line will strike near one pole in the first part of the series;
in the equatorial regions about the middle of the series, and will leave
the Earth by the other pole at the end. Ten or twelve partial eclipses
will follow, and this particular series will cease."
These facts deserve to be expanded a little.
We have seen that all eclipses may be grouped in a series, and that 18
years or thereabouts is the duration of each series, or Saros cycle. But
these cycles are themselves subject to cycles, so that the Saros itself
passes through a cycle of about 64 Saroses before the conditions under
which any given start was made, come quite round again. Sixty-four times
18 make 1152, so that the duration of a Solar eclipse Great Cycle may be
taken at about 1150 years. The progression of such a series across the
face of the Earth is thus described by Mrs. Todd, who gives a very clear
account of the matter:--
"The advent of a slight partial eclipse near either pole of the Earth
will herald the beginning of the new series. At each succeeding return
conformably to the Saros, the partial eclipse will move a little further
towards the opposite pole, its magnitude gradually increasing for about
200 years, but during all this time only the lunar penumbra will impinge
upon the Earth. But when the true shadow begins to touch, the
obscuration will have become annular or total near the pole where it
first appeared. The eclipse has now acquired a track, which will cross
the Earth slightly farther from that pole every time it returns, for
about 750 years. At the conclusion of this interval, the shadow path
will have reached the opposite pole; the eclipse will then become
partial again, and continue to grow smaller and smaller for about 200
years additional. The series then ceases to exist, its entire duration
having been about 1150 years. The series of "great eclipses" of which
two occurred in 1865 and 1883, while others will happen in 1901, 1919,
1937, 1955, and 1973, affords an excellent instance of the northward
progression of eclipse tracks; and another series, with totality nearly
as great (1850, 1868, 1886, 1904, and 1922), is progressing slowly
southwards."
The word "Digit," formerly used in connection with eclipses, requires
some explanation. The origin of the word is obvious enough, coming as it
does from the Latin word _Digitus_, a finger. But as human beings have
only eight fingers and two thumbs it is by no means clear how the word
came to be used for twelfths of the disc of the Sun or Moon instead of
tenths. However, such was the case; and when a 16th-century astronomer
spoke of an eclipse of six digits, he meant that one-half of the
luminary in question, be it Sun or Moon, was covered. The earliest use
of the word "Digit" in this connection was to refer to the twelfth part
of the visible _surface_ of the Sun or Moon; but before the word went
out of use, it came to be applied to twelfths of the visible _diameter_
of the disc of the Sun or Moon, which was much more convenient. However,
the word is now almost obsolete in both senses, and partial eclipses,
alike of the Sun and of the Moon, are defined in decimal parts of the
diameter of the luminary--tenths or hundredths according to the amount of
precision which is aimed at. Where an eclipse of the Moon is described
as being of more than 12 Digits or more than 1.0 (= 1 diameter) it is to
be understood that the eclipse will be (or was) not only total, but that
the Moon will be (or was) immersed in the Earth's shadow with a more or
less considerable extent of shadow encompassing it.
There are some further matters which require to be mentioned connected
with the periodicity of eclipses. To use a phrase which is often
employed, there is such a thing as an "Eclipse Season," and what this is
can only be adequately comprehended by looking through a catalogue of
eclipses for a number of years arranged in a tabular form, and by
collating the months or groups of months in which batches of eclipses
occur. This is not an obvious matter to the casual purchaser of an
almanac, who, feeling just a slight interest in the eclipses of a coming
new year, dips into his new purchase to see what those eclipses will be.
A haphazard glance at the almanacs of even two or three successive years
will probably fail to bring home to him the idea that each year has its
own eclipse season in which eclipses may occur, and that eclipses are
not to be looked for save at two special epochs, which last about a
month each, and which are separated from one another and from the
eclipse seasons of the previous and of the following years by intervals
of about six months, within a few days more or less. Such, however, is
the case. A little thought will soon make it clear why such should be
the case. We have already seen that the Moon's orbit, like that of every
other planetary member of the Solar System, has two crossing places with
respect to the ecliptic which are called "Nodes." We know also that the
apparent motion of the Sun causes that body to traverse the whole of the
ecliptic in the course of the year. The conjoint result of all this is
that the Moon passes through a Node twice in every lunar month of 27
days, and the Sun passes (apparently) through a Node twice in every
year. The first ultimate result of these facts is that eclipses can only
take place at or near the nodal passages of the Moon and the Sun, and
that as the Sun's nodal passages are separated by six months in every
case the average interval between each set of eclipses, if there is more
than one, must in all cases be six months, more or less by a few days,
dependent upon the latitude and longitude of the Moon at or about the
time of its Conjunction or Opposition under the circumstances already
detailed. If the logic of this commends itself to the reader's mind, he
will see at once why eclipses or groups of eclipses must be separated by
intervals of about half an ordinary year. Hence it comes about that,
taking one year with another, it may be said that we shall always have a
couple of principal eclipses with an interval of half a year (say 183
days) between each; and that on either side of these dominant eclipses
there will, or may be, a fortnight before or a fortnight after, two
other pairs of eclipses with, in occasional years, one extra thrown in.
It is in this way that we obtain what it has already been said
dogmatically that we do obtain; namely, always in one year two eclipses,
which must be both of the Sun, or any number of eclipses up to seven,
which number will be unequally allotted to the Sun or to the Moon
according to circumstances.
Though it is roughly correct to say that the two eclipse seasons of
every year run to about a month each, in length, yet it may be desirable
to be a little more precise, and to say that the limits of time for
solar eclipses cover 36 days (namely 18 days before and 18 days after
the Sun's nodal passages); whilst in the case of the Moon, the limits
are the lesser interval of 23 days, being 11½ on either side of the
Moon's nodal passages.
We have already seen[10] that the Moon's nodes are perpetually
undergoing a change of place. Were it not so, eclipses of the Sun and
Moon would always happen year after year in the same pair of months for
us on the Earth. But the operative effect of the shifting of the nodes
is to displace backwards the eclipse seasons by about 20 days. For
instance in 1899 the eclipse seasons fall in June and December. The
middle of the eclipse seasons for the next succeeding 20 or 30 years
will be found by taking the dates of June 8 and December 2, 1899, and
working the months backwards by the amount of 19-2/3 days for each
succeeding year. Thus the eclipse seasons in 1900 will fall in the
months of May and November; accordingly amongst the eclipses of that
year we shall find eclipses on May 28, June 13, and November 22.
Perhaps it would tend to the more complete elucidation of the facts
stated in the last half dozen pages, if I were to set out in a tabular
form all the eclipses of a succession, say of half a Saros or 9 years,
and thus exhibit by an appeal to the eye directly the grouping of
eclipse seasons the principles of which I have been endeavouring to
define and explain in words.
Approximate
Mid-interval.
1894. March 21. [Symbol: Moon] } March 29. *
April 6. [Symbol: Sun] }
Sept. 15. [Symbol: Moon] } Sept. 22. **
Sept. 29. [Symbol: Sun] }
1895. March 11. [Symbol: Moon] } March 18. *
March 26. [Symbol: Sun] }
Aug. 20. [Symbol: Sun] }
Sept. 4. [Symbol: Moon] } Sept. 4. **
Sept. 18. [Symbol: Sun] }
1896. Feb. 13. [Symbol: Sun] } Feb. 20. *
Feb. 28. [Symbol: Moon] }
Aug. 9. [Symbol: Sun] } Aug. 16. **
Aug. 23. [Symbol: Moon] }
1897. Feb. 1. [Symbol: Sun] Feb. 1. *
July 29. [Symbol: Sun] July 29. **
1898. Jan. 7. [Symbol: Moon] } Jan. 14. *
Jan. 22. [Symbol: Sun] }
July 3. [Symbol: Moon] } July. 10. **
July 18. [Symbol: Sun] }
Dec. 13. [Symbol: Sun] }
Dec. 27. [Symbol: Moon] } Dec. 27. *
1899. Jan. 11. [Symbol: Sun] }
June 8. [Symbol: Sun] } June 15. **
June 23. [Symbol: Moon] }
Dec. 2. [Symbol: Sun] } Dec. 9. *
Dec. 16. [Symbol: Moon] }
1900. May 28. [Symbol: Sun] } June 5. **
June 13. [Symbol: Moon] }
Nov. 22. [Symbol: Sun] Nov. 22. *
1901. May 3. [Symbol: Moon] } May 10. **
May 18. [Symbol: Sun] }
Oct. 27. [Symbol: Moon] } Nov. 3. *
Nov. 11. [Symbol: Sun] }
1902. April 8. [Symbol: Sun] }
April 22. [Symbol: Moon] } April 22. **
May 7. [Symbol: Sun] }
Oct. 17. [Symbol: Moon] } Oct. 24. *
Oct. 31. [Symbol: Sun] }
The Epochs in the last column which are marked with stars (*) or (**) as
the case may be, represent corresponding nodes so that from any one
single-star date to the next nearest single-star date means an interval
of one year less (on an average) the 19-2/3 days spoken of on p. 32
(_ante_). A glance at each successive pair of dates will quickly
disclose the periodical retrogradation of the eclipse epochs.
FOOTNOTES:
[Footnote 4: These limits are slightly different in the case of
eclipses of the Moon. (See p. 190, _post_.)]
[Footnote 5: This assumes that 5 of these years are leap years.]
[Footnote 6: If there are 5 leap years in the 18, the odd days will
be 10; if 4 they will be 11; if only 3 leap years (as from 1797 to
1815 and 1897 to 1915), the odd days to be added will be 12.]
[Footnote 7: See p. 28 (_post_) for an explanation of this word.]
[Footnote 8: In Mrs. D. P. Todd's interesting little book, _Total
Eclipses of the Sun_ (Boston, U.S., 1894), which will be several
times referred to in this work, two maps will be found, which will
help to illustrate the successive northerly or southerly progress of
a series of Solar eclipses, during centuries.]
[Footnote 9: In his and Professor Holden's _Astronomy for Schools
and Colleges_, p. 184.]
[Footnote 10: See p. 19 (_ante_).]