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CHAPTER III.

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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 218⅞ 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 6585⅓ 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 18y 10d 7h 42m 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:—

d. h. m. Error of Saros by 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.

d. h. m. Error of Saros by Exact Calculation.
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.
d. 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.
d. 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.
d. 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 19⅔ 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.

1894. March 21. ☾ } March 29. *
April 6. ☉
Sept. 15. ☾ } Sept. 22. **
Sept. 29. ☉
1895. March 11. ☾ } March 18. *
March 26. ☉
Aug. 20. ☉ } Sept. 4. **
Sept. 4. ☾
Sept. 18. ☉
1896. Feb. 13. ☉ } Feb. 20. *
Feb. 28. ☾
Aug. 9. ☉ } Aug. 16. **
Aug. 23. ☾
1897. Feb. 1. ☉ Feb. 1. *
July 29. ☉ July 29. **
1898. Jan. 7. ☾ } Jan. 14. *
Jan. 22. ☉
July 3. ☾ } July 10. **
July 18. ☉
Dec. 13. ☉ } Dec. 27. *
Dec. 27. ☾
1899. Jan. 11. ☉
June 8. ☉ } June 15. **
June 23. ☾
Dec. 2. ☉ } Dec. 9. *
Dec. 16. ☾
1900. May 28. ☉ } June 5. **
June 13. ☾
Nov. 22. ☉ Nov. 22. *
1901. May 3. ☾ } May 10. **
May 18. ☉
Oct. 27. ☾ } Nov. 3. *
Nov. 11. ☉
1902. April 8. ☉ } April 22. **
April 22. ☾
May 7. ☉
Oct. 17. ☾ } Oct. 24. *
Oct. 31. ☉

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 19⅔ 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.

The Story of Eclipses

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