46. The Saros and Halley

Updated: May 16

The Saros cycle is an astronomical period and a calendrical device: after this period, the relative positions of the moon and the sun return to roughly the same spot, in such a way that it is possible to predict eclipses. It was the 17th century astronomer Edmond Halley who named it Saros, seemingly after reading an entry he had read in an old encyclopedia, the Suda, on a Babylonian astronomical cycle, and also Pliny's Natural History, a Roman encyclopedic work. Halley wrote a piece for the Royal Society about Pliny's discussion of a peiod of 222 or 223 months, and the question of whether he meant 222 (as was written in Halley's copy) or 223 months (as it is written in the sky). Modern translations of Pliny give us 223 months, unhesitatingly, but it seems the text Halley was reading did need correcting.


Antikythera mechanism fragment (fragment A). The mechanism consists of a complex system of 30 wheels and plates with inscriptions relating to signs of the zodiac, months, and eclipses. Wikimedia Commons

It certainly seems that a period of 223 lunar months was known by the Ancient Greeks, and could have been known also by other cultures of the ancient world. There is a wheel with 223 grooves on the Anthikera mechanism, an ancient Greek analogue computer used to predict astronomical positions and eclipses, found in a shipwreck. So the ability of the ancient Greek astronomers to predict eclipses is not in question. Neither is the accuracy of a 223 month period in predicting eclipses. However, what Halley says he actually read about, in both Pliny and the Suda, was a period of 222 months. Halley corrected this, in good faith, and based on personal experience of astonomical obeservation backing the 223 lunar month period as essential to predicting eclipses. However, the Suda didn't mention the 222 month period in relation to eclipse prediction. Pliny did however talk about eclipses in the same chapter. Was Halley justified in assuming both texts meant 223 months? Could the original Saros be something else altogether? Could a 222 month period be simply a useful calendrical period?


What's the Saros?

Moon, photo by Sean McClean, Wikimedia Commons

The Saros - today - is a period of exactly 223 lunar synodic months of 29.53059 days, just over 18 solar years, or 6,585.321347 days long. It's the period after which the moon also completes 242 draconic months and 239 anomalistic months, and the relative positions of the earth, the moon and the sun return to a very similar point to the start. The moon's motions, as seen from earth, are not just about whether it is full or new, or a crescent somewhere in between. They are also about its changing distance from the earth, as the moon's orbit is not perfectly circular, and the two points where the moon's path crosses the sun's apparent path (the ecliptic). These two lunar intersections with the ecliptic are known as nodes. A draconic month is about the moon returning to one of these nodes periodically, and the anomalisitic month is about the orientation of the ellipse, the oval shape, that the moon moves in, as this ellipse itself turns. As the moon's distance from earth changes, so it appears slightly bigger or smaller. In a Saros cycle of 223 lunar months, all these elements come together, the revolving elliptical orbit, the crossing of ecliptic, and the phases of the moon (anomalistic, draconic and synodic months). The Saros is really an amazing coincience of all these elements of the moon's motion, of all the different kinds of lunar month. Given the date of an eclipse, one Saros later, a nearly identical eclipse can be predicted. While eclipses happen much more frequently than every 18 years or so, this is because there are many Saros cycles in operation at any given time, with their own 223 lunar month cycles. Or you could see this as a circle having no beginning and no end. So basically the Saros is a cycle that can be taken at any point and will bring you back to that same point after an almost exact period of time, 223 synodic lunar months.

Edmond Halley, knowing about this way of predicting eclipses, and having read about a cycle named Saros, decided to christen this time period of 223 lunar months in this way. It's because of him that we refer to the period of time which enables us to predict eclipses as Saros.


Other interesting luni-solar periods


There are time spans when the cycles of the sun and the moon seem to meet nicely, in integer numbers of synodic lunar months and solar years, which don't have anything to do with eclipses. These are crucial to calendars, which are all based on approximations based on averages, derived from long term observation. This is how we have come to calculate a year not as simply 365 days but 365.242199 days. Of course, it is not possible to have a non-integer number of days in a year. The same thing goes for the moon's cycles. A synodic cycle is thought of as 29.53059 days, a number derived from many years and generations of astronomers. Averages are arrived at, and then corrections are inserted periodocally, usually in the form of leap days and months. And these averages are derived from cycles such as the Metonic, in which 19 years correspond to 235 synodic lunar months. The idea is that the moon and the sun can be rationalised in their movement, because we measure the moon's movements in solar days, so we have to then measure the sun's movement in lunar months to start with. Below are some examples of cycles in which the sun and moon's travels in the sky, as seen from down here, seem to coincide, in integer numbers of synodic lunar months and years. The list below is in order of accuracy, the most accurate match being at the top. It includes a period of 100 Saros, which is a nice integer number of solar years, 1803. This has the advantage of bringing the solar year and three types of lunar month (synodic, draconic and anomalistic) in line.


353 years or 4366 lunar months (cycle put forward by Irv Bromberg) (2)

  • 353 x 365.242199 / 29.53059 = 4365.9979786

  • 4365.9979786 / 4366 = 0.999999537

1803 years or 22300 lunar months (cycle put forward by Irv Bromberg, which is 223 synodic months, or a saros, multiplied by 100)(3)

  • 1803 x 365.242199 / 29.53059 = 22299.98401

  • 22299.98401 / 22300 = 0.9999992829

Multiply this by 3:

5409 years or 66900 lunar months (Babylonian)

  • 5409 x 365.242199 = 66899.952029

  • 66899.952029 / 66900 = 0.9999992829

600 years or 7421 lunar months (cycle used by the Babylonians, mentioned by Josephus)

  • 600 x 365.242199 / 29.53059 = 7420.959737

  • 7420.959737 / 7421 = 0.99999457


19 years or 235 lunar months (Metonic cycle)

  • 19 x 365.242199 / 29.53059 = 234.99705834

  • 234.99705834/235 = 0.99998748

The French astronomer and historian of astronomy, Jean-Sylvain Bailly, wrote:

The Chaldeans, being in possession of the period of 223 lunar months, or 6585 days and one third, could predict lunar eclipses; but they only had an imperfect theory of eclipses of the sun, and they do not dare to announce them, because this period which brings back the eclipses of the moon, does not bring back the same eclipses of the sun for a long time. The Chaldeans tripled this period to avoid the fraction of day, & formed a new one of 669 whole months or 1975 6d. They knew very well the advantage it has of bringing the sun & the moon to the same distance from the node & the apogee. We believe that this climax remark belongs to the Chaldeans. This was a new advantage which they discovered in the long-known period of eclipses. They perceived that the movement of the moon in its orbit was not always equal, that the greatest inequality which results from it did not always arrive at the same points of this orbit: but that these points seemed to advance according to the order of the signs of the zodiac; so that the period of this inequality is longer than the revolution of the moon with respect to the ecliptic or the stars. They made these remarks, and determined with exactness the average revolutions of the moon, as much with regard to its knot and its inequality, as with regard to the sun and the stars. But if they have determined the quantity of this inequality, this is what we would not say, and what does not seem to us at all probable. This was the work of the school of Alexandria. (10)


In his Histoire de l'Astronomie Ancienne, p 140, Bailly notes that the Chaldeans had a cycle of 669 months, or 19756 days, to bring the sun and the moon to the same distance from the node and the apogy. These 669 months are clearly 3 x 223. The question is: was Halley right to name this period 'Saros'?

Clay cuneiform tablet. Astronomical, lunar eclipse table for at least 609-447 BC. Dated 4th century BC. From Babylon. Refers to the murder of the Persian king Xerxes I (485-465 BC) by his son. BM 32234. https://www.britishmuseum.org/collection/object/W_1876-1117-1961, Wikimedia Commons



Halley's Reading of Pliny and the Souda


Portrait of Edmond Halley (1656-1742) Wikimedia Commons
1. The Souda

Halley quotes an entry from the Souda in his piece for the Royal Society. This is what the entry says:


[The saros is] a measure and a number among Chaldeans. For 120 saroi make 2220 years (years of 12 lunar months) according to the Chaldeans' reckoning, if indeed the saros makes 222 lunar months, which are 18 years and 6 months (i.e. years of 12 lunar months). (1)

It is a very brief entry. There isn't much to go one. But it's clear that there seems to be an error if you are familiar with a very useful 223 month cycle, as Halley was. The cycle mentioned in the Souda is 2220 lunar years, or 26640 lunar months. Eighteen and a half years are, if they are lunar years of twelve synodic months (12 x 29.53059 days), 222 lunar months, so this tallies (18.5 x 12 = 222 months). Perhaps if the author had meant 223 lunar months, they would have said this was the equivalent of eighteen years and seven months, not six. The period of 2220 lunar years is made up of 120 saroi, and since 26640 / 120 = 222, then one saros must therefore last 222 lunar months. The entry is consistent at least, and doesn't suggest a mistake anywhere.


However, there is no mention of eclipses. This is only what Halley seems to have read into it. What Halley did was presume there had been an error in the text, and correct it to 223 lunar months. With only a month difference between the two, it seems fair, on the face of it, to have made that decision. But perhaps this period of 222 months corresponded simply to a calendrical device, a useful coincidence of solar years and lunar months, which can be divied up into average lengths for a solar year and lunar month.


2. Pliny

Halley offered several corrections to Pliny's work, not just in astronomy. However, his suggestion that the name Saros should be given to this period that Pliny wrote about comes from this essay. Before reading these corrections, I thought that Halley had Pliny's authority on a period of 223 lunar months, because in the modern translations of Pliny, it says:


It is certain that eclipses recur in cycles of 223 months - eclipses of the sun only when the moon is in her last or first phase (this is called their 'conjunction'), eclipses of the moon only at full moon - and always within the period of their last occurrence; but that yearly at fixed days and hours eclipses of either star occur below the earth, and that even when they occur above the earth they are not visible everywhere, sometimes owing to clouds, more often because the earth's globe stands in the way of the world's curvature. [57] Less than 200 years ago the penetration of Hipparchus discovered that an eclipse of the moon also sometimes occurs four months after the one before and an eclipse of the sun six months, and that the latter when above earth is hidden twice in thirty days, but that this eclipse is visible to different nations, and - the most remarkable features of this remarkable occurrence - that when it comes about that the moon is obscured by the shadow of the earth, this sometimes happens to it from the west side and sometimes from the east; and he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth. For the eclipse of both sun and moon within 15 days of each other has occurred even in our time, in the year of the third consulship of the elder Emperor Vespasian and the second consulship of the younger{71 AD}.(4)

This translation is by H. Rackham in 1952. Another translation has it this way:


It is ascertained that the eclipses complete their whole revolution in the space of 223 months194, that the eclipse of the sun takes place only at the conclusion or the commencement of a lunation, which is termed conjunction195,39 while an eclipse of the moon takes place only when she is at the full, and is always a little farther advanced than the preceding eclipse196. Now there are eclipses of both these stars in every year, which take place below the earth, at stated days and hours; and when they are above it197 they are not always visible, sometimes on account of the clouds, but more frequently, from the globe of the earth being opposed to the vault of the heavens198. It was discovered two hundred years ago, by the sagacity of Hipparchus, that the moon is sometimes eclipsed after an interval of five months, and the sun after an interval of seven199; also, that he becomes invisible, while above the horizon, twice in every thirty days, but that this is seen in different places at different times. But the most wonderful circumstance is, that while it is admitted that the moon is darkened by the shadow of the earth, this occurs at one time on its western, and at another time on its eastern side. And farther, that although, after the rising of the sun, that darkening shadow ought to be below the earth, yet it has once happened, that the moon has been eclipsed in the west, while both the luminaries have been above the horizon200. And as to their both being invisible in the space of fifteen days, this very thing happened while the Vespasians were emperors, the father being consul for the third time, and the son for the second201.

The Project Gutenberg eBook of The Natural History of Pliny, Vol I., by Pliny the Elder.

This is translated by John Bostock and H.T. Riley.


Even Latin versions of Pliny's text available online carry a 223 month rather than 222 month period. For example:


Defectus CCXXIII mensibus redire in suos orbes certum est, solis defectus non nisi novissima primavefieri luna, quod vocant coitum, lunae autem non nisiplena, semperque citra quam proxime fuerint; omnibusautem annis fieri utriusque sideris defectus statis diebus horisque sub terra nec tamen, cum superne fiant, ubiquecerni, aliquando propter nubila, saepius globo terraeobstante convexitatibus mundi. intra ducentos annos. Hipparchi sagacitate compertum est et lunae defectumaliquando quinto mense a priore fieri, solis vero septimo,eundem bis in XXX diebus super terras occultari, sed abaliis hoc cerni, quaeque sunt in hoc miraculo maxime mira, cum conveniat umbra terrae lunam hebetari, nuncab occasus parte hoc ei accidere, nunc ab exortus, quanamratione, cum solis exortu umbra illa hebetatrix sub terraesse debeat, semel iam acciderit ut in occasu luna deficeretutroque super terram conspicuo sidere. nam ut XV diebus utrumque sidus quaereretur, et nostro aevo accidit impera-toribus Vespasianis patre III. filio consulibus.

Gaius Plinius Secundus, Dubius Sermo 2.56.1 (packhum.org)


While the word 'eclipsis' isn't actually used, the word 'defectus' is translated as 'eclipse'.

There are many medieval manuscripts of Pliny's work (curiously, I came across the suggestion that there were 222 of them!), all liable to carry copying mistakes in them. IIt's unless likely that 222 be corrected to 223, than 223 be mistakenly written as 222. This is a screenshot from a manuscript on the British Library website, which shows the number 223 (about half way down: "CCXXIII mensibus").




However, Halley himself seems to be under the impressions that Pliny wrote about eclipses within a 222 lunar month period. I think Halley's copy did have a genuine mistake in it, which was not Pliny's. The translator of Pliny's text that Halley wrote was named Harduin, whom Halley says was aware off "corruptions" in the text he was translating.

It took me a while to find a copy of Halley's corrections of Pliny online to read, and when I did, it was in Latin. While I was lucky enough to have done a bit of Latin in school, I still had some trouble making sense of the essay - even after I'd typed it all up in Google Translate! Anyway, here is what Halley said, the original Latin can be read here, or here, and I will put the whole text in. It's not the best translation but the best I can do. The Greek quotations I have left out altogether, as I couldn't copy and paste them into Google Translate, and I don't know how to translate them or type them here.


Edits and Notes in three places incorrectly published in the published text of Pliny's Natural History
by E. Halley.
(...)
It will be seen with C. Plinii's Natural History (?),(...) when this book is by far the best among the ancient philosophical writings. He is considered the most distinguished, he will not be unimportant, nor will he be earnest of the truth. It is unpleasant to maintain a light in one place or another from a more obscure position, as if it could restore the authentic meaning of the author. For it is possible that R. P. Harduin in his elegant edition of Pliny collated with the Codex MSS, corrects many things that are corrupted; some things are however untouched. He frankly admits that he could not achieve this on his own. The places that are [corrupted] we hope will be corrected by us.
I. Eclipse (Sun & Moon) "Two hundred and twenty-two months, it is certain to return into his own circles." Plin. Book. 2. ch. 13.
Thus we read in all printed books, so in Harduin, although there really is no such period of the Moon's motions, in whatever way these months are taken. If solar months, of which twelve complete the year, 222 Months are eighteen and a half years, at the end of which the moon does not cycle back to the Sun nor to the nodes. Then if these are synodic lunar months, the revolutions of the moon to the sun, each of which are 29d 12h 44' 3", the 222 months will constitute 13 years, taking off the same number of days, and having completed this period after some eclipse, the moon never fails but the shadow of the earth passes away. The excellent period before the lunar motions is completed in 223 months, namely, by which the moon is rotated fairly accurately to the sun and to the same node, and is far from the same relative to its Apogee. Moreover, it is only a few degrees from the same point of heaven. So that after this interval, eclipses actually return to the world, and the sequence of events repeating each other in so much quantity, and in all other circumstances, is similar.
This amendment was presented to the Royal Society by a highly educated and late President of the Society and an outstanding honour, Sir D.J. Hoskyns, baronet, with his usual flair, who suspects that it was once written in Roman numerals 223, but in some more prominent codex, from which perhaps the others were transcribed, the last perished by antiquity or by chance. as Dalecampius attests, both in MS. The Royal Society of Norfolk inscription found at 223; This period provides excellent use in predicting by the motion of the moon, as well as in eclipses as well as others: whatever there was an error in the counter at some location Monday, even after it had been completed two hundred and twenty-three lunar months will be mistaken again. And from the observation of some kind when compared to the counter, safe. You may conclude that the moon will take place after you have just finished it a little earth, even where the most outstanding astronomical numbers stray more than a quarter of a degree from heaven; which I have experienced many times with accurate consent. But it is not in the present institute to confuse the astronomy, especially since this particular article claims a treatise with the best right to anyone; it is also in my mind to work hard in writing, if it is vacant. But there are two things which I do not think should be overlooked on this occasion: first error, that noteworthy thing that R. P. Harduin admitted to this place in the notes. L P, 159. In these words: "There are also 222 lunar months, and eighteen solar years, with seven and a half months. For the same number of months, he returns to the same spare part of the sky from which it had digressed (the moon) while the Sun hid the earth by its interposition. For 222 the lunar months do not consist in the twenty-sixth entire solar years, as has been said, much less with the seven and a half months adjoined; then it is wrongly said that the Moon returns to the same part of the heaven from which it departed, after the complete period which it presupposes; for by the examples he quotes he has sufficiently proved that their eclipses occur in the opposite direction of the sky, namely, in October and April, at the signs of Taurus and Scorpio. Finally from the same examples it is clear that this space is an Eclipse that corresponds not to 7 1/2 months, but only 6 1/4 to exceed 13 years. The aforesaid period is not 222 lunar months but 229, eaq; completed under certain conditions they suffer, but more often than not; The moon moves past the eclipse. It is undeniable to wonder how an otherwise literate man could assemble at the same time so many absurd and contradictory words in so few words.
In the second place I'd like to note that this period was formerly Chaldean. The discoverers of astronomy said that Saron, by which word Diodorus of Sicily indicates the times of the ancient kings; but these things have been little known to ancient writers, as well as to modern writers, and have been exposed in various ways. But the Suda, in a place printed in damaged books (which he had recently restored from the Vatican MS. The Very Reverend Pearson, Bishop of Chester, in his most learned Exposition of the Apostles' Creed) reports the matter with these words,
[Greek]
"The measure and number of the Sari among the Chaldeans, in fact 120 Sari constitute 222 years, according to the calculation of the Chaldeans, namely, that the Saros consist of 222 lunar months, which are 18 years with six months. The words [GREEK] are missing in printed Codes"
Whence, in a disturbed sense, this place remained unexplained. See Pearson Expos. Symb. Apost. Edit. Lond. 1683, Fol 59. But what is written here is Greek, and it may have flowed from the fact that this number could be missing from Pliny, even when Suidas was alive. A Chaldean voice began indicating [GREEK], this voice seems to be derived from the Saros; as if it was the beginning of the update period for Eclipses. But I leave this to those who are more knowledgeable in traditional languages. (5)

(There then follows a discussion on other aspects of Pliny's work, about the liver, various bodily fluids, and mint.)


It is curious that the Souda doesn't mention eclipses. Curiously, Halley's copy of Pliny and the Souda both mentioned a period of 222 months, not 223. It's curious that both texts carry the same 'mistake'. Halley assumes this is because the Souda is based upon Pliny, which is possible, but not certain. There is in any case often a tendency in Western thought to attribute the beginnings of science and philosophy to the Greeks, despite all the evidence of science further east, from Egypt, to Babylon, Syria, Persia, all the way to China. As a result, it is often assumed that ancient writers, scientists, mathematicians and calendar makers borrowed from the Greeks, when it fact where there are similarities in the sciences and arts of ancient cultures, there is no need to always give all the praise and credit to Greece. There is a persistent cultural bias.

Speaking of giving credit, Halley is the one who is remembered for correcting Pliny (or at least, as we have seen, according to what was contained in Halley's own copy of Pliny), and suggesting that it should read 223 months. However, reading this essay, it is clear that the credit is in fact due to Sir D.J. Hoskyns, one of the founders of the Royal Society, and its president from 1682 to 1683.

2: Le Gentil's Reading of Halley


In 1686, a French astronomer, Le Gentil, also interested in the history of astronomy, challenged Halley's reading of the ancient texts, based on the use of the word 'Saros'.

An essay from the Histoire de l'Académie royale des sciences in 1756 seems to suggest there has been some confusion on Halley's part: (6)


The name of Saros, which Mr. Halley assures us that the Chaldeans gave to this period of two hundred and twenty-three lunations, forms the subject of the second part of the Investigations of M. le Gentil. The learned English astronomer does not say where he drew this point from literature, and his silence obliged M. le Gentil to supplement it with the research he made on this subject, and in which he was helped by very versed in the knowledge of Oriental languages ​​& Antiquity.

This is a surprising comment, as Halley is quite clear about the two sources for his 222 or 223 month period, as well as the translation he used for his copy of Pliny. It almost seems as if Halley is being made out to be a bad scholar. The text continues:

In a Memoir read by M. Fréret at the Academy of Inscriptions & Belles-Lettres, he says that the Saros, according to the Chaldean meaning, marked the restitution of the conjunctions of the Sun & the Moon at approximately the same place of the ecliptic, after the revolution of a period similar to that of Meton, that is to say, of nineteen years and a half: we can therefore give the name of Saros to the latter, as well as to that of Pliny, who has no other advantage than giving eclipses for more revolutions than that of Meton, who no longer brings them back after three times nineteen and a half years.

If we want to go back to the highest antiquity, we will still find in the Chaldean Saros a very different value to two hundred and twenty-three lunar months, as given by M. Halley.(...)
Berose, priest of Belus in Babylon, and who sees about three hundred years before the Christian era, had spoken of it (...)
In one of these fragments Berossus asserts that there were in Babylon before the Flood, ten Kings who reigned for one hundred and twenty Saros, that the Saros was composed of Neros & Sossos; that the latter was worth sixty years, the Neros six hundred, and the Saros three thousand six hundred, so that the one hundred and twenty Saros would be four hundred and thirty-two thousand years for the reign of the ten Kings of Babylon.

Far from confirming a period of 222 or 223 months, the suggestion is made that a Saros lasted 3600 years, which works out as 44,525.7584 lunar months. Le Gentil correctly states that the 600 year period is named the Neros, the Sossos is 60 years, and the Saros 3600 years

222.628792 x 200 = 44,525.758422.

While this is tantalisingly close to both 222 and 223 lunar months multiplied by 200, it matches neither. The entry in the Suda says the Saros is a number and a measure, so while it is correct to say that a Sar or Saros refers to the number 3600, it does not follow that it should be 3600 years, or days, or any specific entity. In any case, the entry in the Souda is clear: a Saros is 222 lunar months. Is Le Gentil is challenging Halley's reading of Pliny based on a presumed misunderstanding of the Souda? It's not clear that le Gentil actually read Halley's corrections of Pliny, or the entry in the Souda.



God Ea, a statue from Khorsabad, late 8th century BCE, Iraq, now in the Iraq Museum Osama Shukir Muhammed Amin FRCP(Glasg) - Own work God "Ea" (Sumerian Enki), holding a cup from which water emerges and flows. Initially, Ea was the patron god of Eridu. This is one of a pair of statues of Ea which were found at the entrance to the Sin Temple at Khorsabad, Ninawa, Iraq. 710-705 BCE. On display at the Iraq Museum in Baghdad, Iraq. Wikimedia Commons

In any case, there could well be several meanings of Sar and Saros. An essay by Jules Oppert from 1902 mentions a number called Sar which is different again, in relation to king Sargon I, of the Neo Assyrian Empire (c. 722 BC to his death in battle in 705), specifically about the wall around the city of Sargon.

Sargon dit qu'il a fait le mur « d'après le nombre de son nom ». Le nom de Sargon, Sar-kin en assyrien, se décompose en effet en sar qui a la valeur cabalistique de 20, et en kin, nom du dieu Ea, qui est 40.
Sargon says he made the wall "after the number of his name". The name Sargon, Sar-Kin, in Assyrian, breaks down into sar which has the cabalistic value of 20, and kin, name of the god Ea, which is 40. (11)

According to this text, sar means 20. It seems that sar can mean different things, be it 20, 3600, or 222.


Alabaster bas-relief from the royal palace of Sargon II at Khorsabad, c. 722-705 BCE. Part of along tributary scene depicting tribute bearers from Urartu. The Iraq Museum, Baghdad. This sculpture was made circa 700 BCE. Photo by Osama Shukir Muhammed Amin FRCP(Glasg) Wikimedia Commons



The importance of the sexagesimal system in historical astronomy

Jean Sylvain Bailly, French astronomer, mathematician,and political leader the French Revolution.

Le Gentil's challenge opens an interesting question however on the importance of the number 6 and it's multiples in astronomy. The French astronomer Jean-Sylvain Bailly writes about various luni-solar periods, including 60 and 600 years. Indeed, 600 years of 365.242199 work out as very nearly 7421 synodic months of 29.53059 days. Also, 6000 years are very close to 80532 draconic months. As a result of this, Bailly notes (page 111) that a day is divided into 60 hours in all the known peoples of the ancient world.


The Indians regulate their chronology by periods of sixty years. This period, as well as the division of the day, appears to us, as we have said (1), based solely on the property of the sexagesimal number (2). The Indians do not know the antediluvian period of 600 years; but, as M. le Gentil remarks, they make use of it without knowing it; they use in their astronomical calculations a period of 3600 years, which is luni-solar, composed of fixed periods of 600 years, & only a little less exact, because the error there is fixed times greater. We believe this to be a more modern invention than the others; & the fruit of the remark that the average movement of the sun, after an interval of 3600 years, needed correction. (7)

More recently, Robert Temple has written:


The Sigui among the Dogon is celebrated every sixty years... The Egyptians had such a period associated with Opsiris [principle of renwal]... My own predilection, when considering the period of sixty years, is to think in terms of a synchronisation of the orbital periods of the two panets, Jupiter and Saturn, for they come together in nearly sixty years ... Stonehenge has sixty stones in its outer circle... (This) outer circle is the oriental cycle of Vrihaspati... It is therefore interesting that the dogon say that sixty is the count of the cosmic placenta. (8)

John Anthony West, after quoting these words in Serpent in the Sky, writes:

The sixty year cycle also provides a link between the Egyptian Sothic year and the Great Year of the precession of the equinoxes, which bear a relationship to each other similar to the Egyptian civil year of 360 days to the tropical year of 365 days. A precessional 'month' of 2160 years divides into three 'decans' of 720 years each. Two 'great' civil years of 360 years (6 x 60) plus five epagomenal years per 'great' year 2(360 x 5) make up the precessional 'decan' of 730 years. Conceivably, it is this relationship that determined the Egyptian year of 360 + 5 days to begin with; a reckoning which, as far as I know, has not been satisfactorily accounted for otherwise. In any case, 72 Sothic hemidemicycles of 360 years each plus one great epagomenal year (72 x 5 years) make up a precessional year. To construct a pentagon within a circle, it must be divided into 5 72 degree angles, and thus on a grand scale the Sothic and precessional cycles again reflect the relationsips btween 5 and 6, and their multipls and powers. The sixty-year Dogon cycle and Egyptian Osirian cycle is therefore a 'day' of the precessional scheme, Sirius plays a role similar to that played by Jupiter within the solar system; her Egyptian title of 'Great Provider' perhaps furnishes a clue that further research could elaborate upon. (9)

Jupiter, Saturn, and Sirius have joined the sun and the moon's cycles within a sexagesimal framework. Sirius is a star that held an important place in Ancient Egyptian culture, and is intimately linked with the number 6, or at least 360. One of the reasons for the importance of this star is that the helical rising of Sirius coincided with the annual flooding of the Nile. This means that after a period of time during which Sirius was not visible in the night sky, it reappeared, once a year, at dawn, just before sunrise, on the eastern horizon. Another reason for it's importance is the cycle associated with Sirius of 360 days, very close to a solar year. The Egyptians had three calendars running at once, and one of these was the sothic one, meaning the one guided by Sirius. Sirius is easy to see in the night sky. It's Orion's dog. If you follow the line created by the three stars of Orion's Belt down to the left, you'll find Sirius. While it is considered the hunter's dog, and it is in the constellation Canis, the star was also connected to Orion's consort Isis for the Ancient Egyptians. It's scientific name today is α Canis Majoris. It's very bright because not only is it in fact a double star, but it's also one of our closest neighbours.

Sixty, and its multiples are of great importance to astronomical cycles in the ancient calendars, even though no eclipses depend on them. A saros, or sar as a number, is clearly important within this context. However, Halley was still justified in correcting 222 to 223 to describe the number of synodic lunar months in a cycle capable of predicting eclipses accurately. Whether Halley was justified in using the term Saros or not to describe the period within which the sun and moon's motions form a cycle useul in predicting eclipses is an open question. Serendipity placed a 'typo' in Halley's copy of Pliny: he put 'two and two together', and made 223. Assuming the number 222 was an error of Pliny's, not a copyist's, or assuming that a faulty copy reached the author of the Souda, and assuming (once more) that the Souda was based on Pliny, Halley decided the Souda was referring to this same cycle of 223 lunar months.

It could just be a coincidence that periods of 222 and 223 lunar months are useful, albeit in diferent ways, the first in designing calendars, the second in predicting eclipses and designing calendars too.

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222 Lunar Months as a useful astronomical period?



What might 222 lunar months (of whatever kind) be, assuming there was no mistake in the Suda's entry?


22200 lunar years (of 12 x 29.53059 days) are almost exactly 21539 solar years. This is quite impressive as a soli-lunar cycle for purely calendrical use, not predicting eclipses.

29.53059 x 12 x 2220 / (21539 x 365.242199) = 0.99999968


This is actually marginally more accurate as a way of harmonising the sun and moon's motions over time than the best ones mentioned above:

353 years or 4366 lunar months (cycle put forward by Irv Bromberg) (2)

  • 353 x 365.242199 / 29.53059 = 4365.9979786

  • 4365.9979786 / 4366 = 0.999999537

1803 years or 22300 lunar months

  • 1803 x 365.242199 / 29.53059 = 22299.98401

  • 22299.98401 / 22300 = 0.9999992829

So it is possible that a 22200 lunar year period was used as a soli-lunar period from which to derive average lengths for the year and month.

21539 years are quite close to 21600 years, and while it is pointless to round things up in this context, where accuracy is crucial, it is just 61 years less than 21600. 216 is 6 x 3600. This is potentially an interesting connection to a 3600 year period, or simply to a sexagesimal system. So it becomes: 6 x 6 x 6 x 100 - 61 = 21539.



Notes

  1. SOL Search (uky.edu)

  2. Irv Bromberg, "The Seasonal Drift of the Traditional (Fixed Arithmetic) Hebrew Calendar (הלוח העברי הקבוע)", Seasonal Drift of the Traditional Hebrew Calendar (utoronto.ca).

3. Irv Bromberg, "The Seasonal Drift of the Traditional (Fixed Arithmetic) Hebrew Calendar (הלוח העברי הקבוע)", Seasonal Drift of the Traditional Hebrew Calendar (utoronto.ca). Irv Bromberg writes: "An alternative accurate leap cycle with a superb fixed lunar cycle has 1803 years and 22300 lunar months, including 664 leap months. Its mean year is only about one second too long, its mean month is less than 1/2 second too short". This is a great match, especially as it is 100 Saros eclipse cycles. The 223 lunar months of the saros cycle are very close to 18.0300129 years. Multiply this by 100, and there is an excellent match, 22300 lunar months for approximately 1803 years.


4. Pliny, Natural History, 2 (a) (attalus.org) Pliny, Natural History Translated by H.Rackham (1952) Book 2.


5. Halley, E. “Emendationes & Notae in Tria Loca Vitiose Edita in Textu Vulgato Naturalis Historiae C. Plinii, per E. Halley.” Philosophical Transactions (1683-1775), vol. 16, 1686, pp. 535–40, http://www.jstor.org/stable/101932.Emendationes & Notae in Tria Loca Vitiose Edita in Textu Vulgato Naturalis Historiae C. Plinii, per E. Halley on JSTOR

Emendationes & Notae in Tria Loca Vitiose Edita in Textu Vulgato Naturalis Historiae C. Plinii, per E. Halley (archive.org)

6. Histoire de l'Académie royale des sciences, avec les mémoires de mathématique et de phys (1756)

7. Histoire de l'astronomie ancienne, depuis son origine jusq'a l'établissem ent ... - Jean-Sylvain Bailly - Google Books p 111

8. Temple, Robert, 1976 The Sirius Mystery, Sidgwick & Jackson, p.29, quoted in Serpent in the Sky by John Ahony West p 97

9. West, John Anthony, Serpent in the Sky

10. Histoire de l'astronomie ancienne, depuis son origine jusq'a l'établissement ... - Jean-Sylvain Bailly - Google Books p 140

11. Oppert Jules. Six cent cinquante-trois. Les carrés mystiques chaldéens. In: Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres, 46ᵉ année, N. 4, 1902. pp. 457-468.

DOI : https://doi.org/10.3406/crai.1902.17246

www.persee.fr/doc/crai_0065-0536_1902_num_46_4_17246

Six cent cinquante-trois. Les carrés mystiques chaldéens - Persée (persee.fr)

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