# Are Saros series separated by “40” in numbering related in any way?

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Can anyone help with this question? My question arose from an eclipse related observation that I made while looking into lunar Saros series 129. It is the Saros series number for the lunar eclipse that occurred on this past July 27, 2018.

First I saw that this Saros 129 series was "born" June 10, 1351 and the series will end June 24, 2613 (70 saros cycles of 18 years = roughly 1260 years). So, I became curious to see if another Saros series had ended just before Saros 129 began. I saw that Saros 89 (less by 40 in series numbering) had ended just four years earlier on July 23, 1347. Investigating further, I learned that there are roughly 40 different Saros series that are "active" at any one given time. So then I looked back further to lunar Saros 49 and observed that there does indeed seem to be a pattern involving roughly "40" less in the numbering (i.e. yes indeed, series 49 also ended just as series 89 began). These observations do seem to me as more than mere coincidences.

So, my question now is - Are these particular lunar Saros series (separated by "40" in numbering) related in any way? - series 49, 89, and 129. Is there another cycle or a "greater" cycle also at work here that I am unaware of?

Edit - I checked several other Saros series numbers separated by 40. I am adding additional information below - hoping that it might help find an answer to this question about relatedness of the "40 apart" series.

Checking other series spaced by 40 numbering, these Saros series (that are numbered 40 apart - i.e. 40, 80, 120 etc.) always contain eclipses that are separated by ~1418 days between eclipses in each respective series (i.e. exactly 4 lunar years/48 lunar months).

Small Saros series (those containing fewer cycles - i.e. 70-74 saros cycles in the series) contain saros cycles that overlap minimally (Saros 129 which is only 70 eclipse cycles in length has no overlap and began just after Saros 89 came to an end 1418 days earlier). Note - zero eclipse cycles between them overlap.

Large Saros series (those containing more cycles - i.e. 80-84 saros cycles in the series) contain saros cycles that overlap accordingly (Saros 120 which is 83 cycles long thus began 13 cycles before Saros 80 came to an end with the overlapping eclipses each gapped by 1418 days). Note - 13 eclipse cycles overlap accordingly - again about 70 eclipse cycles with no overlap between these series.

It seems like about 70 eclipse cycles (constituting ~1262 solar years or ~1300 lunar years) is the standard length of each adjacent Saros series - considering the non-overlapping portion only - each non-overlapping portion separated by 4 lunar years.

Edit - Thanks to anyone who can shed any additional light on this.

Eclipses may occur when Earth and the Moon are aligned with the Sun, and the shadow of one body projected by the Sun falls on the other. So at new moon, when the Moon is in conjunction with the Sun, the Moon may pass in front of the Sun as viewed from a narrow region on the surface of Earth and cause a solar eclipse. At full moon, when the Moon is in opposition to the Sun, the Moon may pass through the shadow of Earth, and a lunar eclipse is visible from the night half of Earth. The conjunction and opposition of the Moon together have a special name: syzygy (Greek for "junction"), because of the importance of these lunar phases.

An eclipse does not occur at every new or full moon, because the plane of the Moon's orbit around Earth is tilted with respect to the plane of Earth's orbit around the Sun (the ecliptic): so as viewed from Earth, when the Moon appears nearest the Sun (at new moon) or furthest from it (at full moon), the three bodies are usually not exactly on the same line.

This inclination is on average about 5° 9′, much larger than the apparent mean diameter of the Sun (32′ 2″), the Moon as viewed from Earth's surface directly below the Moon (31′ 37″), and Earth's shadow at the mean lunar distance (1° 23′).

Therefore, at most new moons, Earth passes too far north or south of the lunar shadow, and at most full moons, the Moon misses Earth's shadow. Also, at most solar eclipses, the apparent angular diameter of the Moon is insufficient to fully occlude the solar disc, unless the Moon is around its perigee, i.e. nearer Earth and apparently larger than average. In any case, the alignment must be almost perfect to cause an eclipse.

An eclipse can occur only when the Moon is on or near the plane of Earth's orbit, i.e. when its ecliptic latitude is low. This happens when the Moon is around either of the two orbital nodes on the ecliptic at the time of the syzygy. Of course, to produce an eclipse, the Sun must also be around a node at that time – the same node for a solar eclipse or the opposite node for a lunar eclipse.

Up to three eclipses may occur during an eclipse season, a one- or two-month period that happens twice a year, around the time when the Sun is near the nodes of the Moon's orbit.

An eclipse does not occur every month, because one month after an eclipse the relative geometry of the Sun, Moon, and Earth has changed.

If a solar eclipse occurs at one new moon, which must be close to a node, then at the next full moon the Moon is already more than a day past its opposite node, and may or may not miss the Earth's shadow. By the next new moon it is even further ahead of the node, so it is less likely that there will be a solar eclipse somewhere on Earth. By the next month, there will certainly be no event.

However, about 5 or 6 lunations later the new moon will fall close to the opposite node. In that time (half an eclipse year) the Sun will have moved to the opposite node too, so the circumstances will again be suitable for one or more eclipses.

P = S × (synodic month length) = D × (Draconic month length)

Given an eclipse, then there is likely to be another eclipse after every period P. This remains true for a limited time, because the relation is only approximate.

Another thing to consider is that the motion of the Moon is not a perfect circle. Its orbit is distinctly elliptic, so the lunar distance from Earth varies throughout the lunar cycle. This varying distance changes the apparent diameter of the Moon, and therefore influences the chances, duration, and type (partial, annular, total, mixed) of an eclipse. This orbital period is called the anomalistic month, and together with the synodic month causes the so-called "full moon cycle" of about 14 lunations in the timings and appearances of full (and new) Moons. The Moon moves faster when it is closer to the Earth (near perigee) and slower when it is near apogee (furthest distance), thus periodically changing the timing of syzygies by up to 14 hours either side (relative to their mean timing), and causing the apparent lunar angular diameter to increase or decrease by about 6%. An eclipse cycle must comprise close to an integer number of anomalistic months in order to perform well in predicting eclipses.

These are the lengths of the various types of months as discussed above (according to the lunar ephemeris ELP2000-85, valid for the epoch J2000.0 taken from (e.g.) Meeus (1991) ):

SM = 29.530588853 days (Synodic month) [2] DM = 27.212220817 days (Draconic month) [3] AM = 27.55454988 days (Anomalistic month) [4] EY = 346.620076 days (Eclipse year)

Note that there are three main moving points: the Sun, the Moon, and the (ascending) node and that there are three main periods, when each of the three possible pairs of moving points meet one another: the synodic month when the Moon returns to the Sun, the draconic month when the Moon returns to the node, and the eclipse year when the Sun returns to the node. These three 2-way relations are not independent (i.e. both the synodic month and eclipse year are dependent on the apparent motion of the Sun, both the draconic month and eclipse year are dependent on the motion of the nodes), and indeed the eclipse year can be described as the beat period of the synodic and draconic months (i.e. the period of the difference between the synodic and draconic months) in formula:

as can be checked by filling in the numerical values listed above.

Eclipse cycles have a period in which a certain number of synodic months closely equals an integer or half-integer number of draconic months: one such period after an eclipse, a syzygy (new moon or full moon) takes place again near a node of the Moon's orbit on the ecliptic, and an eclipse can occur again. However, the synodic and draconic months are incommensurate: their ratio is not an integer number. We need to approximate this ratio by common fractions: the numerators and denominators then give the multiples of the two periods – draconic and synodic months – that (approximately) span the same amount of time, representing an eclipse cycle.

These fractions can be found by the method of continued fractions: this arithmetical technique provides a series of progressively better approximations of any real numeric value by proper fractions.

Since there may be an eclipse every half draconic month, we need to find approximations for the number of half draconic months per synodic month: so the target ratio to approximate is: SM / (DM/2) = 29.530588853 / (27.212220817/2) = 2.170391682

The continued fractions expansion for this ratio is:

The ratio of synodic months per half eclipse year yields the same series:

Each of these is an eclipse cycle. Less accurate cycles may be constructed by combinations of these.

This table summarizes the characteristics of various eclipse cycles, and can be computed from the numerical results of the preceding paragraphs cf. Meeus (1997) Ch.9. More details are given in the comments below, and several notable cycles have their own pages.

Any eclipse cycle, and indeed the interval between any two eclipses, can be expressed as a combination of saros (s) and inex (i) intervals. These are listed in the column "formula".

Any eclipse can be assigned to a given saros series and inex series. The year of a solar eclipse (in the Gregorian calendar) is then given approximately by: [8]

year = 28.945 × number of the saros series + 18.030 × number of the inex series − 2882.55

When this is greater than 1, the integer part gives the year AD, but when it is negative the year BC is obtained by taking the integer part and adding 2. For instance, the eclipse in saros series 0 and inex series 0 was in the middle of 2884 BC.

## Contents

"Old" Babylonian astronomy was practiced during and after the First Babylonian dynasty (ca. 1830 BCE) and before the Neo-Babylonian Empire (ca. 626 BCE).

The Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. [ citation needed ] Tablets dating back to the Old Babylonian period document the application of mathematics to the variation in the length of daylight over a solar year. Centuries of Babylonian observations of celestial phenomena were recorded in the series of cuneiform tablets known as the Enûma Anu Enlil—the oldest significant astronomical text that we possess is Tablet 63 of the Enûma Anu Enlil, the Venus tablet of Ammisaduqa, which lists the first and last visible risings of Venus over a period of about 21 years. It is the earliest evidence that planetary phenomena were recognized as periodic. [ citation needed ]

An object labelled the ivory prism was recovered from the ruins of Nineveh. First presumed to be describing rules to a game, its use was later deciphered to be a unit converter for calculating the movement of celestial bodies and constellations. [7]

Babylonian astronomers developed zodiacal signs. They are made up of the division of the sky into three sets of thirty degrees and the constellations that inhabit each sector. [8]

The MUL.APIN contains catalogues of stars and constellations as well as schemes for predicting heliacal risings and settings of the planets, and lengths of daylight as measured by a water clock, gnomon, shadows, and intercalations. The Babylonian GU text arranges stars in 'strings' that lie along declination circles and thus measure right-ascensions or time intervals, and also employs the stars of the zenith, which are also separated by given right-ascensional differences. [9] [10] [11] There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, mainly from Babylonia.

### Planetary theory Edit

The Babylonians were the first civilization known to possess a functional theory of the planets. [11] The oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BCE copy of a list of observations of the motions of the planet Venus that probably dates as early as the second millennium BCE. The Babylonian astrologers also laid the foundations of what would eventually become Western astrology. [12] The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BCE, [13] comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets. [14]

### Cosmology Edit

In contrast to the world view presented in Mesopotamian and Assyro-Babylonian literature, particularly in Mesopotamian and Babylonian mythology, very little is known about the cosmology and world view of the ancient Babylonian astrologers and astronomers. [15] This is largely due to the current fragmentary state of Babylonian planetary theory, [4] and also due to Babylonian astronomy being independent from cosmology at the time. [16] Nevertheless, traces of cosmology can be found in Babylonian literature and mythology.

In Babylonian cosmology, the Earth and the heavens were depicted as a "spatial whole, even one of round shape" with references to "the circumference of heaven and earth" and "the totality of heaven and earth". Their worldview was not exactly geocentric either. The idea of geocentrism, where the center of the Earth is the exact center of the universe, did not yet exist in Babylonian cosmology, but was established later by the Greek philosopher Aristotle's On the Heavens. In contrast, Babylonian cosmology suggested that the cosmos revolved around circularly with the heavens and the earth being equal and joined as a whole. [17] The Babylonians and their predecessors, the Sumerians, also believed in a plurality of heavens and earths. This idea dates back to Sumerian incantations of the 2nd millennium BCE, which refers to there being seven heavens and seven earths, linked possibly chronologically to the creation by seven generations of gods. [18]

### Omens Edit

It was a common Mesopotamian belief that gods could and did indicate future events to mankind. This indication of future events were considered to be omens. The Mesopotamian belief in omens pertains to astronomy and its predecessor astrology because it was a common practice at the time to look to the sky for omens. The other way to receive omens at the time was to look at animal entrails. This method of recovering omens is classified as a producible omen, meaning it can be produced by humans, but sky omens are produced without human action and therefore seen as much more powerful. Both producible and unproducible omens however, were seen as messages from the gods. Just because gods sent the signs didn't mean that Mesopotamians believed their fate was sealed either, the belief during this time was that omens were avoidable. In mathematical terms, the Mesopotamians viewed omens as “if x, then y”, where “x” is the protasis and “y” is the apodosis. [19] [ page needed ] The relationship Mesopotamians had with omens can be seen in the Omen Compendia, a Babylonian text composed starting from the beginning of the second millennium on-wards. [19] It is the primary source text that tells us that ancient Mesopotamians saw omens as preventable. The text also contains information on Sumerian rites to avert evil, or “nam-bur-bi”. A term later adopted by the Akkadians as “namburbu”, roughly, “[the evil] loosening”. The god Ea was the one believed to send the omens. Concerning the severity of omens, eclipses were seen as the most dangerous. [20]

The Enuma Anu Enlil is a series of cuneiform tablets that gives insight on different sky omens Babylonian astronomers observed. [21] Celestial bodies such as the Sun and Moon were given significant power as omens. Reports from Nineveh and Babylon, circa 2500-670 B.C.E., show lunar omens observed by the Mesopotamians. "When the moon disappears, evil will befall the land. When the moon disappears out of its reckoning, an eclipse will take place". [22]

### Astrolabes Edit

The astrolabes (not to be mistaken for the later astronomical measurement device of the same name) are one of the earliest documented cuneiform tablets that discuss astronomy and date back to the Old Babylonian Kingdom. They are a list of thirty-six stars connected with the months in a year, [8] generally considered to be written between 1800-1100 B.C.E.. No complete texts have been found, but there is a modern compilation by Pinches, assembled from texts housed in the British Museum that is considered excellent by other historians who specialize in Babylonian astronomy. Two other texts concerning the astrolabes that should be mentioned are the Brussels and Berlin compilations. They offer similar information to the Pinches anthology, but do contain some differing information from each other. [23]

The thirty-six stars that make up the astrolabes are believed to be derived from the astronomical traditions from three Mesopotamian city-states, Elam, Akkad, and Amurru. The stars followed and possibly charted by these city-states are identical stars to the ones in the astrolabes. Each region had a set of twelve stars it followed, which combined equals the thirty-six stars in the astrolabes. The twelve stars of each region also correspond to the months of the year. The two cuneiform texts that provide the information for this claim are the large star list “K 250” and “K 8067”. Both of these tablets were translated and transcribed by Weidner. During the reign of Hammurabi these three separate traditions were combined. This combining also ushered in a more scientific approach to astronomy as connections to the original three traditions weakened. The increased use of science in astronomy is evidenced by the traditions from these three regions being arranged in accordance to the paths of the stars of Ea, Anu, and Enlil, an astronomical system contained and discussed in the Mul.apin. [23]

### MUL.APIN Edit

MUL.APIN is a collection of two cuneiform tablets (Tablet 1 and Tablet 2) that document aspects of Babylonian astronomy such as the movement of celestial bodies and records of solstices and eclipses. [7] Each tablet is also split into smaller sections called Lists. It was comprised in the general time frame of the astrolabes and Enuma Anu Enlil, evidenced by similar themes, mathematical principles, and occurrences. [24]

Tablet 1 houses information that closely parallels information contained in astrolabe B. The similarities between Tablet 1 and astrolabe B show that the authors were inspired by the same source for at least some of the information. There are six lists of stars on this tablet that relate to sixty constellations in charted paths of the three groups of Babylonian star paths, Ea, Anu, and Enlil. there are also additions to the paths of both Anu and Enlil that are not found in astrolabe B. [24]

### Relationship of calendar, mathematics and astronomy Edit

The exploration of the Sun, Moon, and other celestial bodies affected the development of Mesopotamian culture. The study of the sky led to the development of a calendar and advanced mathematics in these societies. The Babylonians were not the first complex society to develop a calendar globally and nearby in North Africa, the Egyptians developed a calendar of their own. The Egyptian calendar was solar based, while the Babylonian calendar was lunar based. A potential blend between the two that has been noted by some historians is the adoption of a crude leap year by the Babylonians after the Egyptians developed one. The Babylonian leap year shares no similarities with the leap year practiced today. it involved the addition of a thirteenth month as a means to re-calibrate the calendar to better match the growing season. [25]

Babylonian priests were the ones responsible for developing new forms of mathematics and did so to better calculate the movements of celestial bodies. One such priest, Nabu-rimanni, is the first documented Babylonian astronomer. He was a priest for the moon god and is credited with writing lunar and eclipse computation tables as well as other elaborate mathematical calculations. The computation tables are organized in seventeen or eighteen tables that document the orbiting speeds of planets and the Moon. His work was later recounted by astronomers during the Seleucid dynasty. [25]

### Aurorae Edit

A team of scientists at the University of Tsukuba studied Assyrian cuneiform tablets, reporting unusual red skies which might be aurorae incidents, caused by geomagnetic storms between 680 and 650 BCE. [26]

Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Achaemenid, Seleucid, and Parthian periods of Mesopotamian history. A significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar (747–734 BCE). The systematic records of ominous phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses, for example. [27] The Greco-Egyptian astronomer Ptolemy later used Nabonassar's reign to fix the beginning of an era, since he felt that the earliest usable observations began at this time.

The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323–60 BCE). In the 3rd century BCE, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous phenomena for each planet. About the same time, or shortly afterwards, astronomers created mathematical models that allowed them to predict these phenomena directly, without consulting past records.

### Arithmetical and geometrical methods Edit

Though there is a lack of surviving material on Babylonian planetary theory, [4] it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. It had been thought that most of the predictive Babylonian planetary models that have survived were usually strictly empirical and arithmetical, and usually did not involve geometry, cosmology, or speculative philosophy like that of the later Hellenistic models, [28] though the Babylonian astronomers were concerned with the philosophy dealing with the ideal nature of the early universe. [3] Babylonian procedure texts describe, and ephemerides employ, arithmetical procedures to compute the time and place of significant astronomical events. [29] More recent analysis of previously unpublished cuneiform tablets in the British Museum, dated between 350 and 50 BCE, demonstrates that Babylonian astronomers sometimes used geometrical methods, prefiguring the methods of the Oxford Calculators, to describe the motion of Jupiter over time in an abstract mathematical space. [30] [31]

In contrast to Greek astronomy which was dependent upon cosmology, Babylonian astronomy was independent from cosmology. [16] Whereas Greek astronomers expressed "prejudice in favor of circles or spheres rotating with uniform motion", such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits. [32] There is no evidence that the celestial bodies moved in uniform circular motion, or along celestial spheres, in Babylonian astronomy. [33]

Contributions made by the Chaldean astronomers during this period include the discovery of eclipse cycles and saros cycles, and many accurate astronomical observations. For example, they observed that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving swifter when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion. [34]

Chaldean astronomers known to have followed this model include Naburimannu (fl. 6th–3rd century BCE), Kidinnu (d. 330 BCE), Berossus (3rd century BCE), and Sudines (fl. 240 BCE). They are known to have had a significant influence on the Greek astronomer Hipparchus and the Egyptian astronomer Ptolemy, as well as other Hellenistic astronomers.

### Heliocentric astronomy Edit

The only surviving planetary model from among the Chaldean astronomers is that of the Hellenistic Seleucus of Seleucia (b. 190 BCE), who supported the Greek Aristarchus of Samos' heliocentric model. [35] [36] [37] Seleucus is known from the writings of Plutarch, Aetius, Strabo, and Muhammad ibn Zakariya al-Razi. The Greek geographer Strabo lists Seleucus as one of the four most influential astronomers, who came from Hellenistic Seleuceia on the Tigris, alongside Kidenas (Kidinnu), Naburianos (Naburimannu), and Sudines. Their works were originally written in the Akkadian language and later translated into Greek. [38] Seleucus, however, was unique among them in that he was the only one known to have supported the heliocentric theory of planetary motion proposed by Aristarchus, [39] [40] [41] where the Earth rotated around its own axis which in turn revolved around the Sun. According to Plutarch, Seleucus even proved the heliocentric system through reasoning, though it is not known what arguments he used. [42]

According to Lucio Russo, his arguments were probably related to the phenomenon of tides. [43] Seleucus correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the Earth's atmosphere. He noted that the tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun. [38]

According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used trigonometric methods that were available in his time, as he was a contemporary of Hipparchus. [44]

None of his original writings or Greek translations have survived, though a fragment of his work has survived only in Arabic translation, which was later referred to by the Persian philosopher Muhammad ibn Zakariya al-Razi (865-925). [45]

Many of the works of ancient Greek and Hellenistic writers (including mathematicians, astronomers, and geographers) have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by earlier ancient Near Eastern civilizations, notably those in Babylonia, were forgotten for a long time. Since the discovery of key archaeological sites in the 19th century, many cuneiform writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by Abraham Sachs and later published by Otto Neugebauer in the Astronomical Cuneiform Texts (ACT). Herodotus writes that the Greeks learned such aspects of astronomy as the gnomon and the idea of the day being split into two halves of twelve from the Babylonians. [23] Other sources point to Greek pardegms, a stone with 365-366 holes carved into it to represent the days in a year, from the Babylonians as well. [7]

Since the rediscovery of the Babylonian civilization, it has been theorized that there was significant information exchange between classical and Hellenistic astronomy and Chaldean. The best documented borrowings are those of Hipparchus (2nd century BCE) and Claudius Ptolemy (2nd century CE).

### Early influence Edit

Some scholars support that the Metonic cycle may have been learned by the Greeks from Babylonian scribes. Meton of Athens, a Greek astronomer of the 5th century BCE, developed a lunisolar calendar based on the fact that 19 solar years is about equal to 235 lunar months, a period relation that perhaps was also known to the Babylonians.

In the 4th century BCE, Eudoxus of Cnidus wrote a book on the fixed stars. His descriptions of many constellations, especially the twelve signs of the zodiac show similarities to Babylonian. The following century Aristarchus of Samos used an eclipse cycle called the Saros cycle to determine the year length. However, the position that there was an early information exchange between Greeks and Chaldeans are weak inferences possibly, there had been a stronger information exchange between the two after Alexander the Great established his empire over Persia in the latter part of the 4th century BCE.

### Influence on Hipparchus and Ptolemy Edit

In 1900, Franz Xaver Kugler demonstrated that Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. Later Greek knowledge of this specific Babylonian theory is confirmed by 2nd-century papyrus, which contains 32 lines of a single column of calculations for the Moon using this same "System B", but written in Greek on papyrus rather than in cuneiform on clay tablets. [46]

It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BCE to CE 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar i.e., 26 February 747 BCE.

This raw material by itself must have been tough to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):

• 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
• 251 (synodic) months = 269 returns in anomaly
• 5458 (synodic) months = 5923 returns in latitude
• 1 synodic month = 2931:50:08:20 days (sexagesimal 29.53059413 . days in decimals = 29 days 12 hours 44 min 3⅓ s) or 29.53 days

The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year.

Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets.

Other traces of Babylonian practice in Hipparchus' work are

• first Greek known to divide the circle in 360 degrees of 60 arc minutes.
• first consistent use of the sexagesimal number system.
• the use of the unit pechus ("cubit") of about 2° or 2½°.
• use of a short period of 248 days = 9 anomalistic months.

### Means of transmission Edit

All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BCE). According to the late classical philosopher Simplicius (early 6th century), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BCE (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BCE. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BCE a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC. [ citation needed ]

Historians have also found evidence that Athens during the late 5th century may have been aware of Babylonian astronomy. astronomers, or astronomical concepts and practices through the documentation by Xenophon of Socrates telling his students to study astronomy to the extent of being able to tell the time of night from the stars. This skill is referenced in the poem of Aratos, which discusses telling the time of night from the zodiacal signs. [7]

In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events.

## Spoiled, cancelled

Aside from fake or faked SAROs, there are also “skipping” SAROs, on account of “gaps” in the numbering sequence of SAROs. There are “spoiled/damaged” or “cancelled” SAROs as well. Many had not been defaced or marked as bad SAROs, while some others could not be produced anymore.

In 2012, most of at least 1,064 SAROs reported to be “spoilage” or “cancelled” were not marked as “cancelled” or perforated, according to procedures prescribed in DBM’s own Department Order No. 2011-12 pertaining to “Accountability for SAROs and NCA Forms and Security Paper.”

Issued on Oct. 4, 2011 by Budget Secretary Florencio ‘Butch’ Abad, it spelled out rules on “the issuance, receipt, safekeeping, and reporting” of SAROs, NCAs, and other accountable forms in DBM.

Yet when state auditors asked for copies, DBM officials said that they had destroyed some of these spoiled or cancelled SAROs.

They could not, however, produce proof they actually did so. Instead, they told COA that “due to the confidentiality of release documents, some of the spoiled SAROs were shredded, hence no longer available for inspection.”

## Are Saros series separated by &ldquo40&rdquo in numbering related in any way? - Astronomy

The Antediluvian Calendar illustrates the early Black Head Sumerian zodiac that had six astrological signs for winter and six for summer. Mayan Calendar 260 day-Tzolken-sacred-years and 360 day-Tun-years are products of the Decan stars and numbering systems. Numerically matching 364 day-Ethiopic-years with 364 year-Ethiopic-cycles demonstrates astrology in ancient religion.

The Antediluvian Calendar is similar to the classical Mayan Calendar in many respects. A 360 day-Tun-year consists of 18 Uinal periods of 20-days each. The 18 Uinal glyph names reflect an original group of 18 affiliated Mesoamerican tribes. Many Old Testament researchers relate the famous 12 tribes of Israel to 12 astrological signs of the ancient Mesopotamian zodiac. We associate zodiac names with "zoo," because most constellations aptly name animal gods. Familiar names include Leo the lion , Aries the ram , Scorpio the scorpion , Cancer the crab , Pisces the fish , Capricorn the goat and Taurus the bull. God made the heavenly bodies to show us SIGNS that serve to mark calendar time. Since ancient days, humanity has encompassed the pseudo-science of astrology to render interpretations involving motions of the sun , moon , planets and stars. Our intentions here posit archaic spiritual preoccupations against the backdrop of emerging calendar science.

Judaism recognizes a single omnipotent God without regard to any other form of idolatry, man-made or celestial. Lunar months have always been traditionally important to Jewish Calendar reckoning. Whether three 30-day months culminate in 90-day quarters or as part of Metonic 19-year lunar/solar cycles, sighting the new moon crescent is paramount to the Jewish Calendar. Jewish month names show Babylonian influence. Sumerian and Babylonian calendars also began months according to new moon crescents. Monotheism replaced polytheism for Jewish faithful living in Mesopotamia.

Sumerian cosmology is responsible for an early set of core beliefs found in the Holy Bible. Sumerians have the distinction of being among the earliest inhabitants of the Fertile Crescent region. Beginning at least 8,000-years BCE, Sumerian culture realized a priest-astronomer class, improved agrarian techniques and developed the first sexagesimal (base 60) numbering system. Sumerian language bears affinity to vocabulary and similar concepts found in the ancient tongues of India and Africa. They occasionally referred to themselves as Black Heads. The name Sudan traces the Land of the Blacks.

Biblical references may include the famous Kingdom of Kush from Northern Sudan eastward to the Nile River. One other point is worth mentioning. Etymology for the name Adam shows derivation from the Assyrian Adami or generic man. Some mention also indicates Adami was the plural form, black headed men. In light of the Ethiopic 364 day-calendar-year and full knowledge that cultural exchange took place between Northern Africa and Egypt, there is reasonable assurance that Sumerian astrology and astronomy predicates later Babylonian and Egyptian zodiacs. Astrological signs are ancient mathematical interpretations that measure time. Entire pictures decorated minds and artwork long ago. Astronomical constellations are the modern approach that purely reflect scientific observation. Many star charts contain outline diagrams depicting animal or astrological sign shapes. Egyptian, Greek, Roman, Chinese, Hindu and African people shared a 12-month zodiac.

The Sumerian zodiac had only six houses or star groups. Modern astrology includes 12 houses or sky divisions, including the hidden part beneath the horizon, and numbers the position from the east at the time of observation. The first house is rising when the seventh house is setting in the west, so six houses are visible at night. Sumerians spaced their constellation houses some 60-degrees apart or about 60-days during the course of a year instead of today’s 30-day monthly division. Doubling terms for conspicuous stellar houses from 30-days to 60-days enabled Sumerians to calculate the entire 360-days per year. Parent calendar mathematics peaked with the Sumerian 3,600-year Saros cycle. Saros cuneiform symbology meaning 3,600 applies for king lists, eclipse prediction and agriculture. The modern practice of dividing a circle into 360-degrees, of 60-minutes each hour, began with the Sumerians.

Sumerians cast the first spiritual underpinnings that relate astrological positions to governing future events. National affairs such as war, drought and a plentiful harvest were the concerns of original astrology. Priests advised the king and other ruling authorities when and how to act in order to appease the gods. Sky heaven An had a masculine nature. Mother earth Ki had a feminine nature and together An and Ki bore Enlil. Enlil was the god of the air, who ruled over the lil wind or atmosphere.

Babylonian astrology-astronomy provides clues we need to study 360 day-Tun-years in more detail and bridge the gap between Mayan and Jewish Calendars. Consider looking at the zodiac on the vernal equinox. Babylonian astronomer priests established a standard set of 18 constellations along and around the ecliptic as early as 2,000 BCE. Stars outside the zodiac belt were useful for orientation purposes. Babylonian astronomer priests later divided the year into 12 star constellations. Dawn heliacal risings for each sign were separate by about 30-days. Precision involved erecting fixed sacred pillars called Baals in the Old Testament for observation purposes. Egyptian and early Babylonian zodiacs had 36 Decan star groups which were separated by about 10-days during the year. Prior to the Roman Julian Calendar, the Romans were using a 10-month calendar with 36-day-months. Eventually 12-months stabilized more or less in their current configuration. Lunar months having 29-days or 30-days became the norm for nomadic people and expanding Greco-Roman culture into larger geographic areas. Mesoamerican Calendars are the exception to strict lunar observation. Fixed ceremonial centers encourage dividing 360 day-Tun-years into 18 Uinals of 20-days each. The Mayan lunar series or supplementary series evidences that moon glyphs tracked phases and cycles. However, the majority of lunar scripts are still unknown.

Babylonian worship divided the starry sky into three different bands around 3,000 BCE. The northern band was the Path of Anu. Winter constellations correspond primarily with the Path of Anu. Latitude limits the stars we see with respect to the Tropic of Capricorn. Extending the equator into space creates a mathematical plane that aligns with the celestial equator. Babylonians replaced mother earth Sumerian Ki with Ea. From eastern to western horizons, the central Path of Ea identifies our modern ecliptic. To the south is the Path of Enlil band. Latitude position again limits the stars seen in the summer sky with respect to the Tropic of Cancer. Calendar months reckon 30-days according to the rule of three stars each. Each Decan star of three was from a different band in the sky. Carved figurines often represented spirits for the 36 Decan stars. A new Decan star rose about every 10-days. Decans were mighty, great gods. Decan stars were companions and guides to help the deceased. Some Decan stars bestowed blessings while others were hostile or adverse.

Mesoamerican Calendars distinguish a visible nighttime sky that divides the 260 day-Tzolken-sacred-year zodiac into 13 animal constellations. The ecliptic subsequently determines the sacred Tzolken part of the Mayan Calendar. Babylonian and Egyptian zodiacs concentrate upon the entire 36 Decan star array during the year with a similar three stars each notion. Half of 36 Decan stars empower the visible 18 Decan stars during 6-months of winter or summer. The other 18 Decan stars belong to the opposing 6-months and are below the horizon. Sumerians first noted six 60-degree houses that later evolved into the earliest Babylonian 18 astrological signs. By 1,200 BCE, Mesoamerican Olmecs concerned themselves with 13 visible astrological signs in a 260 day-Tzolken-sacred-year. The 360 day-Tun-year and 365 day-Haab-solar-year are later additions to Mesoamerican Calendars. The ecliptic pathway eventually replaced the central Path of Ea as reference to divide the Semitic sky by a factor of three. Reducing the Sumerian-Babylonian numbering system from sexagesimal (base 60) to the later Mesoamerican vigesimal (base 20), infers that Mesoamerican 360 day-Tun-years were using 20-degree houses for their astrological signs. Astrological Uinals continued to have major Decan stars in the tribal Tun schema of 18 Uinals. Mesoamerican zodiacs supplant the 12-house Babylonian zodiac that had three Decan stars each.

Semitic 360-day Midpoint length of years are equal to 36 Decan stars multiplied by 10-days each (Eqn. 1). The Mayan 260 day-Tzolken-sacred-year results from 13 Tzolken sacred zodiac signs of 20-days each (Eqn. 2). Mayan 360 day-Tun-years tabulate 18 ancestral tribe Uinals that multiply by 20-days each (Eqn. 3). Compared with Semitic cosmology, the Mayan moon goddess seems like the Venus Ishtar goddess of rebirth and fertility. As the moon goddess moved through 13 sacred signs and 18 star groups coincident with 18 tribes, she held the fertility profile of a Rabbit in the Moon.

Mesoamerican culture may have alternatively adapted the direct predecessor Babylonian 18 Stars Path of the Moon to the ecliptic that marks apparent motions of the sun and moon. The Greek zodiac further adjusts 12 astrological sign names to become the accepted 12 astronomical constellations. Greco-Roman zodiacs consistently lay along the ecliptic. Concordance with the Egyptian zodiac has shown the ecliptic was the main focus of astral worship. Today, there are several different permutations of the animal zodiac and personal horoscopes are an outgrowth resource once reserved for kings and leaders.

Get_More_Time in printable pdf format and help support timeemits for less than $1. Sumerian_6_Sign_Zodiac_and_Mayan_Calendar_360-Day-Tun-Years The Antediluvian Calendar in Genesis 5 illustrates the early Black Head Sumerian zodiac that had six astrological signs. Sumerian and Babylonian animal zodiacs stipulate the vernal equinox began the New Year. Mayan Calendar 260-day-Tzolken-sacred-years and 360-day-Tun-years are products of the Decan stars and numbering systems. Egyptian, Greek, Roman, Chinese, Hindu and African people shared a 12-month zodiac. Numerically matching 364-day-Ethiopic-years with 364-year-Ethiopic-cycles demonstrates astrology in ancient religion. Cart Item S6SZMC360 Get PDF Download Only .99 cents from Paypal-Payloadz 116 kb 0.99 Semitic 360 day Midpoint length of year 1. 36 Decan stars x 10-days = 360 day Midpoint length of year Mayan 260 day-Tzolken-sacred-year with 13 animal gods related to 13 zodiac constellations 2. 13 animal gods x 20-days = 260 day-Tzolken-sacred-year Mayan 360 day-Tun-year with 18 Uinals related to early Babylonian 18 zodiac constellations 3. 18 Uinals 20-days = 360 day-Tun-year Are you a pastor, educator or a student of the Holy Bible ? Timeemits.com seeks anointed people to review and contribute to the Ages_of_Adam ministry. Ancient lunar/solar calendars like the Jewish and Mayan calendars provide the background to understanding early time. Ancient calendars of the Holy Bible use differences between the moon and sun, numerical matching and a 364-day calendar year to describe X-number of days that match with X-number of years. Ages_of_Adam is a free read at timeemits. tags Antediluvian, Genesis, Sumerian, zodiac, astrology, signs, house, Decan, stars, Babylon, Egypt, Hindu ## External links Saros cycles: 110 · 111 · 112 · 113 · 114 · 115 · 116 · 117 · 118 · 119 · 120 · 121 · 122 · 123 · 124 · 125 · 126 · 127 · 128 · 129 · 130 · 131 · 132 · 133 · 134 · 135 · 136 · 137 · 138 · 139 · 140 · 141 · 142 · 143 · 144 · 145 · 146 · 147 · 148 · 149 · 150 · 151 · 152 · 153 · 154 · 155 · 156 · 157 · 158 · 159 · 160 · 161 · 162 ## This Month's Big Lunar Eclipse If you live in North or South America, the sky will put on a very fine show on the night of January 20/21. Lunar eclipses are not rare, but ones that coincide with a so–called "Super Moon" are a lot more unusual. And that's exactly what you will be seeing, provided that no clouds get in the way: a particularly big Full Moon going dark, maybe even turning coppery–red in the process. Caveat: absolutely guaranteed, the media is going to oversell it, leading to lots of disappointment among people who've been jaded by special effects in movies. I can see the hyperbolic Yahoo! headlines now: GIGANTIC MEGA-MOON ECLIPSES ENTIRE SKY! And of course somebody somewhere will have their fifteen minutes of fame by proclaiming some grand governmental conspiracy to conceal the fact that the Moon will collide with the Earth, probably due to some alleged malfeasance on the part of Hillary Clinton. Ignore the hyperbole, but please, if you possibly can, have a look at this sky–show! Just keep your expectations somewhere south of seeing a real–life Star Wars up there that night. Lunar Eclipses are languorous affairs, to be savored like long, slow winter sunsets or your last piece of chocolate. Totality, for example – the period of total lunar eclipse – lasts about an hour. Compare that with the frantic few minutes of a total solar eclipse. That's an entirely different beast, and admittedly a lot more spectacular. January's Moon–show, from the first, nearly–unnoticeable "penumbral" contact of the outer edges of Earth's shadow with the Moon to the final " not–with–a–bang–but–a–whimper" end of it all, runs about five hours. The part you really don't want to miss is Totality. That begins at 11:41 PM–EST and ends at 12:43 AM–EST – and if you are in the Pacific Zone, lucky you: it's a far more convenient 8:41–9:43 PM on January 20. Starting maybe an hour earlier, it will be worth a peek – that's when the umbral period of the eclipse begins. So make a thermos of hot tea and bring a blanket . . . unless you're in South America, of course. Then just kick back and enjoy. Total lunar eclipses happen frequently, and unlike solar eclipses, you can see them from anywhere on our planet so long as the Moon is in the sky at the time. We'll have another one, for example, on May 26, 2021, then again on May 15, 2022 and yet another on November 8, 2022. What makes this particular lunar eclipse special is the fact that it coincides with a "Super Moon." The term is unfortunate because of the way it hypes the reality of the thing. But the Super Moon effect is real – and the idea behind it is simple. The Moon orbits Earth in an ellipse rather than in a circle. Sometimes it's closer to us – and thus looks bigger – and sometimes it's further away, and so it appears smaller. The variation in the Moon's apparent size is significant – a "perigee" Full Moon looks about 14% bigger than an "apogee" one. For two reasons, people generally don't notice the difference: first, Full Moons only happen once a month, so it's a long time to wait between comparisons. Secondly, and more importantly, most Full Moons don't coincide with apogee or perigee, so their size is somewhere in between maximum diameter and minimum. For those of you listening to this as a podcast, just trust me. For those of you who are reading, have a look at this diagram on the right. It graphically represents the size–contrast between a perigee and an apogee Full Moon. You'll see that it's pretty dramatic, actually. Here's the point of this astronomy lesson: on January 20, we get the double–whammy: a nice, big perigee Full Moon that just happens to go into total lunar eclipse. That combo–platter is obviously rare. I bet even aliens will be setting up their lawn chairs. Switch your perspective for a moment: what if you were looking at this event from the surface of the Moon rather than from here on Earth? Well, lunar eclipses occur when Earth lies directly between the Sun and the Moon – so Earth's shadow is cast on the lunar surface. But if you were watching from the Moon, something more like a solar eclipse would occur, as Earth blocked out the face of the Sun. It would actually be a magnificent thing to behold. You would see Earth as black disk with a brilliant flickering ring of orange, red, and crimson light surrounding it. If you think about what you would be contemplating, it'll give you goose–bumps. That flickering ring of orange, red, and crimson light is actually all of the sunsets and sunrises happening on the Earth at that particular moment, combined. Pretty amazing, huh? But you'll need to catch the next bus to the Moon if you want to see it. Our next step is closer to Earth, and it builds on what we just learned. What you are seeing projected onto the surface of the Moon during a lunar eclipse is actually the light of all those sunsets and sunrises. That's why a lunar eclipse is generally more "coppery" than black. Of course we all know that sunsets and sunrises come in a variety of shades, ranging from Ho–Hum to Oh My God. This is why the color of each total lunar eclipse is so unpredictable. Can you predict whether tonight's sunset will be a memorable one? Probably not. Really, what you will be looking at on January 20 is Earth's weather, and even the weatherman gets that wrong a lot. Less romantically, a lunar eclipse also reflects the level of pollution in our atmosphere. The volcano, Mount Pinatubo, blew its top in June 1991. A year and a half later, a lot of that dust was still in the air – and the next lunar eclipse was nearly black. What will the eclipsed Moon look like on January 20? No one knows . . . not anymore than anyone can predict the weather that night. Here we get a bit more technical. Read on anyway! For reasons that lie on the other side of a short science class, we just might possibly also be close to a real technical breakthrough in evolutionary astrology – one pioneered by an Australian fellow named Murray Beauchamp. We will meet Murray in a moment. There is a Sun–Moon opposition every month – that's just a simple Full Moon. Why then is there no lunar eclipse every month? Simple: Earth's shadow typically misses the Moon entirely. The Moon lies a bit above it or a bit below it. There may be a nearly–invisible penumbral eclipse, as the Moon passes through the faint edges of Earth's shadow. Another possibility is that the darker umbra of Earth's shadow might graze the Moon, creating a partial eclipse. Or it might be the Real Deal – a Total eclipse – like what's in store for us this month. For a lunar eclipse to occur, the Moon must lie fairly close to the north node or south node. That assures that the Moon and the Sun are lined up not only in terms of their sign positions, but also in terms of their declinations. That's the critical ingredient. (The same is true for solar eclipses.) Each eclipse, whether solar or lunar, has unique properties. How long does it last? Is it total or partial? How big does the face of the Sun or the Moon look? Is Moon lined up with the north node or the south node? Well over two millennia ago, Chaldean astrologer–astronomers discovered that these identical eclipse–producing conditions repeat like clockwork. This enabled them to predict eclipses with great accuracy. They called this cycle the Saros. Its length is 18 years, 11 days, 8 hours. After that precise interval, Sun, Earth, and Moon return to approximately the same relative geometry. They are lined up the same way, and a nearly identical eclipse happens. That last phrase – a nearly identical eclipse – is critical here. Earlier we saw that after this January's lunar eclipse, we will have another one in May 2021. That's only two years and four months later – way short of a Saros cycle. But it will be a different kind of event in terms of length, the visual size of the Moon, and so on. So all of the eclipses linked to a specific Saros cycle are like a family–line, with strands of astronomical DNA held in common. Together, they are called a Saros Series. There are separate solar and lunar Saros series, by the way. All of them are assigned numbers. Currently, for example, there are 41 active lunar Saros series happening. But each Saros series evolves, and eventually dies. Their life spans vary a lot, but you can think in terms of a Saros series lasting a very long time – say, a thousand years. Are you getting dizzy yet? Obviously this is complicated territory. Space and format mercifully prevent me from getting "book length–technical" in this newsletter. If you want to learn more, there is a fine article about the Saros cycle in Wikipedia – just Google "Saros (astronomy)" and it will take you directly to Virgo paradise. You may be wondering what any of this has to do with astrology. Fair enough. "Not much," is a good initial answer. Your mileage may vary, but in my experience lunar eclipses, while visually captivating, have not impacted me much more than the monthly Full Moon – like you, I just grow a coat of fur, sharp fangs, and a compelling jones for human blood. But, taken as a Saros series, these same lunar eclipses might provide a powerful missing link in the foundational logic of evolutionary astrology. The key is to remember that the nodes of the Moon are critical to eclipses – and that the nodes of the Moon are also the heart of what makes evolutionary astrology a unique discipline within the field. They are what links your chart to reincarnation – the long journey of your soul through human history. And just maybe lunar eclipses – and the Saros seris – can focus our attention on certain specific periods in history, perhaps periods which feel inexplicably familiar and real to you. Earlier, I mentioned Murray Beauchamp. He has been part of my Australian apprenticeship program pretty much from the beginning, and he has developed some intriguing ideas about the lunar Saros series. His book, The Cryptic Cycle: Astrology and the Lunar Saros is unfortunately currently listed as "Out of Print – Limited Availability" on Amazon. You can still get it via the American Federation of Astrologers . You can also contact Murray directly at [email protected] He can mail you copies of his book for$20 Australian, plus postage.

Murray has lectured quite a lot in Australia and New Zealand, but his work is pretty much unknown in the northern hemisphere. His ideas are still formative, but I already find them extremely intriguing.

Here is his technique in a nutshell:

Look for the lunar eclipse immediately prior to your birth. It does not have to be Total it can be umbral, or even penumbral. Find out which Lunar Saros series that pre–natal lunar eclipse belongs to. Then look for the first umbral eclipse in the series. That is the birth of the series. Murray says make sure it's the first umbral eclipse – not the first eclipse of the series, which is always penumbral and does not count.

By the way, The Cryptic Cycle contains tables and Internet links that will help you with all this.

Proof of the pudding? Well, it's early to use the word "proof," but here's what got me hooked:

The lunar eclipse that immediately preceded my own birth was part of Lunar Saros Series #116. That cycle began with an umbral lunar eclipse on June 16, 1155 A.D.

What follows is totally subjective and quite possibly meaningless. All I can say in defense of what I am about convey is that the inevitable first test of all astrological techniques lies in one's own personal experience. I would never teach anything that failed to illuminate my own life. We must of course eventually go beyond our narrow ego–world in order to make sure we are not turning a personal quirk into a cosmology. Before we open our mouths, we need to be sure that what we conjecture will be helpful to people in general.

But everything begins with your own personal astrological experience, and that's natural. No one should be ashamed of it.

The 12th century, when my own Saros series began, is the High Middle Ages. For what it is worth, I have always related in a strong, visceral way to that time. The Gothic cathedrals were rising. A kind of humanism entered Christianity, and with it, the onset of many of the very battles that I am still fighting in this lifetime, publicly and personally. When, many years ago, reading Rodney Collin's The Theory of Celestial Influence, I first heard of the Christian monastery at Cluny, I got chills. Was I once there as a literate monk? I thought so – and Cluny was in active upheaval around the time of the lunar eclipse that started "my" series. I did not know about my specific astrological connection to that time until I met Murray Beauchamp

In common with many Westerners, my knowledge of Chinese history is pitiful, although it has improved somewhat since I began teaching there a decade ago. There is a weird familiarity about China for me, which leaves me with no doubt that I've had lifetimes there. For some previously inexplicable reason, I lit up the first time I encountered the architecture, style and romantic history of the Song Dynasty – which I had never heard of before I began visiting that country. I felt sure that I'd had a lifetime in that period.

You guessed it: the fingerprints of Saros Series #116 are all over it. A quote from Wikipedia: "The Southern Song dynasty (1127–1279) refers to the period after the Song lost control of its northern half (of China) . . . During this time, the Song court retreated south of the Yangtze and established its capital at Lin'an (now Hangzhou)." That line gave me goosebumps too. I've spent many happy days in Hangzhou, and felt a compelling sense of deja vu there, especially in the Buddhist temples in the hills above the city.

My heart is telling me that Murray Beauchamp is onto something with his research into the lunar Saros series. Did I live in one or both of those times? If both, were my incarnations separated by some multiple of the Saros cycle?

If I had to formulate a hypothesis, it would be this: that a lifetime or lifetimes spent around the beginning of the lunar Saros cycle reflected in the lunar eclipse just before your birth represent the roots of the karmic issues with which you are reckoning today.

I would also like to pursue the obvious conjecture that we might tend to take birth around other subsequent lunar eclipses in "our" Saros series. I've not yet explored that possibility.

Will time prove this hypothesis to be helpful or not?

Like almost everything of lasting value in astrology, the answer will not come from one person, but rather from marrying the idea and the entire astrological community in the alchemical cauldron of time. We may know the answer in a generation or two, in other words – but only if we ask the question.

In any case, it is something to ponder as the big–as–it–can–get Super Moon turns to copper on the night of January 20.

One last thought – the Lunar Saros series of which this upcoming eclipse is a member began on July 7, 1694. As time goes by, it will be interesting see if events around that historical period have any apparent karmic relevance to some of our friends who are in utero at the moment. I also note that The Bank of England was founded in that year and it is the model on which most modern central banks are based. I find this intriguing, especially in light of Uranus crossing back into Taurus on March 6 and the world's economy seeming to be on the verge of major evolution or even revolution as we face what people are increasingly calling "late stage Capitalism." Is something about our relationship with money that began in 1694 with the founding of the Bank of England coming to a time of karmic reckoning? We'll see . . .

## The Number 83

83 is the atomic number of bismuth (symbol Bi).

In Judaism, when someone reaches 83 years old they may celebrate a second bar mitzvah. The Torah says that a normal lifespan is 70 years, so an 83-year-old person can be considered 13 years old in a second lifetime.

83 is the highest UHF channel on older televisions made before the late 1970s (newer televisions only go up to channel 69, due to the frequency spectrum previously assigned to channels 70–83 in the USA being reassigned to cellular phone service there in the late 1970s–early 1980s).

The 83rd day of the year in the Gregorian calendar is March 24 in non-leap years, March 23 in leap years.

The Bell XP-83 (later redesignated ZXF-83) was a United States prototype escort fighter designed by Bell Aircraft during World War II. It first flew in 1945. As an early jet fighter, its limitations included a lack of power and it was soon eclipsed by more advanced designs.

The B83 thermonuclear bomb is a variable-yield gravity bomb developed by the United States in the late 1970s, entering service in 1983. With a maximum yield of 1.2 megatonnes of TNT (75 times the yield of the atomic bomb “Little Boy” dropped on Hiroshima on August 6, 1945, which had a yield of 16 kilotonnes of TNT), it is the most powerful nuclear free-fall weapon in the United States arsenal. The first underground test detonation of the production B83 took place on December 15, 1984.

HLA-B*83 (B83) is an HLA-B allele-group composed of a single allele, B*8301. There is no useful serology associated with this allele. It is found in a single Mbenzele Pygmy tribe of the Central Africa Republic.

Interstate 83 (abbreviated I-83) is an Interstate Highway in the Eastern United States that runs from Baltimore, Maryland to Harrisburg, Pennsylvania.

83 is the ISBN Group Identifier for books published in Poland. The International Standard Book Number (ISBN) is a unique numeric commercial book identifier assigned to each edition and variation (except reprintings) of a book. For example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 10 digits long if it was assigned on or before December 31, 2006 and 13 digits long if assigned on or after January 1, 2007.

83 is slang for a bisexual person. It is derived from the atomic number of bismuth which has the symbol Bi.

83 is a glasses-wearing variation of the :3 emoticon. The :3 emoticon represents the cat face made by anime characters when they say something clever or sarcastic, or are commenting on something cute.

### Prime Numbers

83 is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

83 is the 23rd prime number. 23 is also a prime number. The previous prime number is 79 and the next prime number is 89.

79 and 83 are cousin primes. Cousin primes are prime numbers that differ by four. Twin primes are pairs of prime numbers that differ by two, and sexy primes are pairs of prime numbers that differ by six. The term “sexy prime” stems from the Latin word for six: sex.

83 is the sum of three consecutive prime numbers: 23 + 29 + 31.

83 is the sum of five consecutive primes: 11 + 13 + 17 + 19 + 23.

### Astronomy

Messier object M83, also known as the Southern Pinwheel galaxy, is a magnitude 8.5, barred spiral galaxy, 15 million light-years away in the constellation Hydra. M83 is classified as a barred spiral galaxy due to the bar-like pattern of stars that run through its center, very similar in structure to our own Milky Way galaxy. More info.

New General Catalogue object NGC 83 is a magnitude 14.2, a lenticular galaxy, 285–330 million light-years away in the constellation Andromeda. NGC 83 was discovered by John Herschel on August 17, 1828. More info.

Solar eclipse saros series 83 contained 71 solar eclipses over a period of 1,262.11 years, beginning on May 5, 210 BCE and ended on May 30, 1052. More info.

Lunar eclipse saros series 83 contained 84 lunar eclipses over a period of 1,496.50 years, beginning on August 22, 197 BCE and ended on February 5, 1300. More info.

The saros is a period of approximately 223 synodic months (approximately 6,585.3211 days, or 18 years, 11 days, 8 hours), that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros. A series of eclipses that are separated by one saros is called a saros series.

### In Other Number Systems

83 in Roman numerals is LXXXIII.

83 in binary (base 2) is 10100112.

83 in ternary (base 3) is 100023.

83 in quaternary (base 4) is 11034.

83 in quinary (base 5) is 3135.

83 in senary (base 6) is 2156.

83 in octal (base 8) is 1238.

83 in duodecimal (base 12) is 6B12.

83 in hexadecimal (base 16) is 5316.

83 in vigesimal (base 20) is 4320.

83 in base 36 is 2B36.

### Mathematics

83 is both a Sophie Germain prime and a safe prime. A prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime.
As a Sophie Germain prime, 2 × 83 + 1 = 167 (167 is the safe prime).
As a safe prime, 2 × 41 + 1 = 83 (41 is the Sophie Germain prime)

83 is a Chen prime. A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen’s theorem. The lower member of a pair of twin primes is by definition a Chen prime.

83 is an Eisenstein prime with no imaginary part and real part of the form 3n – 1. An Eisenstein prime is an Eisenstein integer

that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units (±1, ±ω, ±ω 2 ), a + bω itself and its associates. The associates (unit multiples) and the complex conjugate of any Eisenstein prime are also prime.

83 is a highly cototient number. A highly cototient number is a positive integer k which is above one and has more solutions to the equation

than any other integer below k and above one. Here, φ is Euler’s totient function.

### In Other Languages

In Afrikaans eighty-three is drie en tagtig.

In Albanian eighty-three is tetëdhjetë e tre.

In Amharic eighty-three is የሰማንያ ሦስት (_____).

In Arabic eighty-three is ثلاث وثمانون (thlath wathamanun).

In Armenian eighty-three is ութսուներեք (ut’sunerek’).

In Azerbaijani eighty-three is səksən üç.

In Basque eighty-three is laurogeita hiru.

In Belarusian eighty-three is восемдзесят тры (vosiemdziesiat try).

In Bengali eighty-three is তিরাশি (tirāśi).

In Bosnian eighty-three is osamdeset i tri.

In Bulgarian eighty-three is осемдесет и три (osemdeset i tri).

In Catalan eighty-three is vuitanta-tres.

In Cebuano eighty-three is kawaloan ug tulo ka.

In Chichewa eighty-three is eyite atatu.

In Chinese (Simplified) eighty-three is 八十三 (bāshísān).

In Chinese (Traditional) eighty-three is 八十三 (bāshísān).

In Corsican eighty-three is ottanta-di trè.

In Croatian eighty-three is osamdeset tri.

In Czech eighty-three is osmdesát tři.

In Danish eighty-three is treogfirs.

In Dutch eighty-three is drieëntachtig.

In Esperanto eighty-three is okdek tri.

In Estonian eighty-three is kaheksakümmend kolm.

In Filipino eighty-three is may walong pu’t tatlong.

In Finnish eighty-three is kahdeksankymmentäkolme.

In French eighty-three is quatre vingt trois.

In Frisian eighty-three is trijentachtich.

In Galician eighty-three is oitenta e tres.

In Georgian eighty-three is ოთხმოცდასამი (ot’khmots’dasami).

In German eighty-three is dreiundachtzig.

In Greek eighty-three is ογδόντα τρία (ogdónta tría).

In Gujarati eighty-three is એંસી ત્રણ (ēnsī traṇa).

In Haitian Creole eighty-three is katreven-twa.

In Hausa eighty-three is tamanin da uku.

In Hawaiian eighty-three is kanawalu-ekolu.

In Hebrew eighty-three is שמונים ושלוש (_____).

In Hindi eighty-three is तिरासी (tiraasee).

In Hmong eighty-three is eighty-peb.

In Hungarian eighty-three is nyolcvanhárom.

In Igbo eighty-three is iri-na-atọ.

In Indonesian eighty-three is delapan puluh tiga.

In Irish eighty-three is ochtó is trí.

In Italian eighty-three is ottantatre.

In Japanese eighty-three is 八十三 (yasomi).

In Javanese eighty-three is wolung puluh telu.

In Kannada eighty-three is ಎಂಬತ್ಮೂರು (embatmūru).

In Kazakh eighty-three is сексен үш (seksen üş).

In Khmer eighty-three is ប៉ែតសិប​បី (betseb​ bei).

In Korean eighty-three is 여든세 (yeodeunse).

In Kurdish (Kurmanji) eighty-three is heştê-sê.

In Kyrgyz eighty-three is сексен үч (seksen üç).

In Lao eighty-three is eighty ສາມ (eighty sam).

In Latin eighty-three is octoginta trium.

In Latvian eighty-three is astoņdesmit trīs.

In Lithuanian eighty-three is aštuoniasdešimt trys.

In Luxembourgish eighty-three is uechtzeg-dräi.

In Macedonian eighty-three is осумдесет и три (osumdeset i tri).

In Malagasy eighty-three is amby valo-telo.

In Malay eighty-three is lapan puluh tiga.

In Malayalam eighty-three is എണ്പത്തിമൂന്ന് (eṇpattimūnn).

In Maltese eighty-three is tlieta u tmenien (tlieta “three” u “and” tmenien “eighty”). More info.

In Maori eighty-three is e waru tekau-toru.

In Marathi eighty-three is त्र्याऐंशी (tryā’ainśī).

In Mongolian eighty-three is наян гурав (nayan gurav)

In Myanmar (Burmese) eighty-three is ရှစ်ဆယ့်သုံး (shit s y sone).

In Navajo eighty-three is tseebídiin dóó ba’ąą táá’ (tseebídiin “eighty” dóó ba’ąą “and in addition to it” táá’ “three”). More info.

In Nepali eighty-three is असी तीन (asī tīna).

In Norwegian eighty-three is åttitre.

In Pashto eighty-three is اتيا درې (_____).

In Persian eighty-three is هشتاد و سه (_____).

In Polish eighty-three is osiemdziesiąt trzy.

In Portuguese eighty-three is oitenta e três.

In Punjabi eighty-three is ਅੱਸੀ-ਤਿੰਨ (asī-tina).

In Romanian eighty-three is optzeci și trei.

In Russian eighty-three is восемьдесят три (vosem’desyat tri).

In Samoan eighty-three is valusefulu-tolu.

In Scots Gaelic eighty-three is ceithir fichead ’sa trì.

In Serbian eighty-three is осамдесет три (osamdeset tri).

In Sesotho eighty-three is mashome a robeli e meraro.

In Shona eighty-three is makumi masere nematatu.

In Sindhi eighty-three is اسي-ٽي (_____).

In Sinhala eighty-three is අසු තුන (asu tuna).

In Slovak eighty-three is osemdesiat tri.

In Slovenian eighty-three is tri in osemdeset.

In Somali eighty-three is siddeetan iyo saddex.

In Spanish eighty-three is ochenta y tres (ochenta “eighty” y “and” tres “three”).

In Sundanese eighty-three is dalapan puluh tilu.

In Swahili eighty-three is themanini na mitatu.

In Swedish eighty-three is _____.

In Tajik eighty-three is ҳаштоду се (_____).

In Tamil eighty-three is எண்பத்தி மூன்று (eṇpatti mūṉṟu).

In Telugu eighty-three is ఎనభై మూడు (enabhai mūḍu).

In Thai eighty-three is แปดสิบสาม (pæd s̄ib s̄ām).

In Turkish eighty-three is seksen üç.

In Ukrainian eighty-three is вісімдесят три (visimdesyat try).

In Urdu eighty-three is تراسی (_____).

In Uzbek eighty-three is sakson uch.

In Vietnamese eighty-three is tám mươi ba.

In Welsh eighty-three is wyth deg tri o.

In Xhosa eighty-three is asibhozo anesithathu.

In Yiddish eighty-three is _____ (_____). (אַכציק “eighty” דרײַ “three”). More info.

In Yoruba eighty-three is ọgọrin-mẹta.

In Zulu eighty-three is ayisishiyagalombili nantathu.

## Lunar eclipse

A lunar eclipse occurs when the Moon passes directly behind the Earth into its umbra (shadow). This can occur only when the Sun, Earth, and Moon are aligned (in "syzygy") exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a full moon. The type and length of an eclipse depend upon the Moon's location relative to its orbital nodes.

Unlike a solar eclipse, which can only be viewed from a certain relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of the Earth. A lunar eclipse lasts for a few hours, whereas a total solar eclipse lasts for only a few minutes at any given place, due to the smaller size of the Moon's shadow. Also unlike solar eclipses, lunar eclipses are safe to view without any eye protection or special precautions, as they are dimmer than the full Moon.

The umbra is the portion of the Earth's shadow that does not contain any direct radiation from the Sun. Likewise, the penumbra is the region of space where the Earth is only partially blocking the light from the Sun.

In order to classify what kind of lunar eclipse is occurring a scale known as the Danjon scale was developed by André-Louis Danjon.

• L=0 - the darkest eclipse, one most people imagine when they think of a lunar eclipse.
• L=1 - while still very dark, there is a grey or brown hue to the Moon. However, details of the Moon are still difficult to identify.
• L=2 - the Moon will appear dark red, possibly with a slight hint of orange. The Moon still appears very dark at this value.
• L=3 - the Moon is brick-red and noticeably lighter than L=2. Also, the edges can appear lighter, possibly with a yellowish hue.
• L=4 - the Moon appears bright red or orange, while the edge of the Moon appears almost bluish

The timing of total lunar eclipses are determined by its contacts.

• P1 (First contact)
Beginning of the penumbral eclipse. The Earth's penumbra touches the Moon's outer limb.
• U1 (Second contact)
Beginning of the partial eclipse. The Earth's umbra touches the Moon's outer limb.
• U2 (Third contact)
Beginning of the total eclipse. The Moon's surface is entirely within the Earth's umbra.
• Greatest eclipse
The peak stage of the total eclipse. The Moon is at its closest to the center of the Earth's umbra.
• U3 (Fourth contact)
End of the total eclipse. The Moon's outer limb exits the Earth's umbra.
• U4 (Fifth contact)
End of the partial eclipse. The Earth's umbra leaves the Moon's surface.
• P4 (Sixth contact)
End of the penumbral eclipse. The Earth's penumbra no longer makes contact with the Moon.
• Total
the Earth's umbra – the central, dark part of its shadow – obscures all of the Moon's visible surface.
• Partial
only part of the Moon's visible surface is obscured by the Earth’s umbra.
• Penumbral
the Moon travels through the faint penumbral portion of the Earth’s shadow.

### Lunation number

A number given to each lunation beginning from a certain one in history. Several conventions are in use.

The most commonly used is the Brown Lunation Number (BLN), which defines lunation 1 as beginning at the first new moon of 1923, the year when Ernest William Brown's lunar theory was introduced in the major national astronomical almanacs. Lunation 1 occurred at approximately 02:41 UTC, January 17, 1923. New moons occur on Julian Dates.

2449128.59 + 29.53058867 * (BLN - 871) +/- 0.25

with the given uncertainty due to varying torques from the Sun

### Dynamical time (TD)

Dynamical Time (TD) of Greatest Eclipse, the instant when the distance between the center of the Moon and the axis or Earth's umbral shadow cone reaches a minimum.

TD was introduced by the IAU in 1979 as the coordinate time scale for an observer on the surface of Earth. It takes into account relativistic effects and is based on International Atomic Time (TAI), which is a high-precision standard using several hundred atomic clocks worldwide. As such, TD is the atomic time equivalent to its predecessor ET and is used in the theories of motion for bodies in the solar system. To ensure continuity with ET, TD was defined to match ET for the date 1977 Jan 01. In 1991, the IAU refined the definition of TD to make it more precise. It was also renamed Terrestrial Time (TT), although on this Web site, the older name Terrestrial Dynamical Time is preferred and used.

### Saros

A period of approximately 223 synodic months (approximately 6585.3211 days, or 18 years and 11 days and 8h), that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros.

For a lunar eclipse to occur, the Earth must be located between the Sun and Moon. This can happen only when the Moon is full, and repeat occurrences of these lunar phases result from solar and lunar orbits producing the Moon's synodic period of 29.53059 days.

During most full and new moons, however, the shadow of the Earth or Moon falls to the north or south of the other body. Eclipses occur when the three bodies form a nearly straight line.

After one saros, the Moon will have completed roughly an integer number of lunar orbit cycles and synodic, draconic, and anomalistic periods (241, 223, 242, and 239) and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase and be at the same node and the same distance from the Earth. In addition, because the saros is close to 18 years in length (about 11 days longer), the earth will be nearly the same distance from the sun, and tilted to it in nearly the same orientation.

### Gamma

Gamma (denoted as γ) of an eclipse describes how centrally the shadow of the Moon or Earth strikes the other. The distance, when the axis of the shadow cone passes closest to Earth or Moon's center, is stated as a fraction of the equatorial radius of the Earth.

The sign of gamma defines for a lunar eclipse whether the axis of the Earth's shadow passes north or south of the Moon a positive value means south.

### Magnitude

The magnitude of an eclipse is the fraction of the diameter of the eclipsed body which is in eclipse. During a lunar eclipse, the eclipsed body is the Moon and the eclipsing 'body' is the Earth's shadow. Since the Earth's shadow at the Moon's distance always is considerably larger than the Moon, a lunar eclipse can never be annular but is always partial or total. The Earth's shadow has two components: the dark umbra and the much brighter penumbra. A lunar eclipse will have two geometric magnitudes: the umbral magnitude and the penumbral magnitude. If the maximum value of the umbral magnitude is negative, the Moon doesn't reach into the Earth's umbra - it may still pass through the Earth's penumbra though, and such an eclipse is called a penumbral eclipse.

#### Penumbral

Penumbral magnitude is the fraction of the Moon's diameter immersed in the penumbra at the instant of greatest eclipse (equal to the distance measured from the edge of the penumbral shadow to the edge of the Moon deepest in the penumbra).

#### Umbral

Umbral magnitude is the fraction of the Moon's diameter immersed in the umbra at the instant of greatest eclipse (equal to the distance measured from the edge of the umbral shadow to the edge of the Moon deepest in the umbra).

### Duration

#### Penumbral Eclipse Phase Duration

The time interval between first and last contact of the Moon with the penumbral shadow (= P4 - P1).

#### Parial Eclipse Phase Duration

The time interval between first and last contact of the Moon with the umbral shadow (= U4 - U1).

#### Total Eclipse Phase Duration

The time interval between second and third contact of the Moon with the umbral shadow (= U3 - U2).

## Voyages of the Saros

Is anybody out there? Can anyone still be faithfully tuning in to look for this long-overdue update on our progress? Well, whoever you are, this update is for you, and I hope you will accept our sincerest thanks for hanging in this long. You have demonstrated unusual determination and strength of character. Send us email some time ([email protected]) so we'll know who you are!

I will now proceed to tell you everything worth telling, and some things not, starting from where we last left off in French Polynesia and ending up (happily) in New Zealand. I should mention, though, that while our adventures are not yet over, our circumnavigation is on hold for an indefinite period, possibly years, making this the final "Voyage of the Saros" update for now. (Though we are considering a spin-off along the lines of "Auckland: the Adventure Ashore.") The reasons will become apparent as you read on, but here's a brief summary: a) New Zealand strikes us so far as a beautiful country with a high standard of living (thanks in large part to a peculiarly rational government) which we'd be crazy to leave in a hurry b) by a wonderful stroke of luck, we've arrived at a time when our professional fields are both growing rapidly here and our skills in great demand and c) we've had quite enough of passage-making for a while, thank you!

### Raiatea & Tahaa

These two islands are nested together within a single surrounding coral reef. This arrangement makes for fantastic sailing conditions: a large and breezy but protected lagoon with numerous scattered islets (motus) to meander among, and nary an ocean swell to be seen (or felt). In Raiatea, we caught up with our friends aboard Danza and spent a couple of very pleasant days docked at the marina where they were planning to spend the season. We then circumnavigated Tahaa and, just before moving on, anchored near a boat yard to arrange for some minor repairs. An aluminum cleat at the starboard bow had cracked while we were anchored in heavy swells at Puerto Ayora in the Galapagos, and we were finally able to replace it here. We also hired a marine radio expert named Jean-Yves to figure out why we were having trouble being heard on our SSB (single side-band) radio.

The very next day, Jean-Yves paid us a house call, as it were. I can't say much about the technical particulars of what he did--I tried not to pay too much attention lest I should get anxious and try to tell him what to do, which would surely have defeated the purpose of hiring an expert in the first place--but Jean-Yves left an impression nonetheless. He spoke French, like almost everyone else, and indeed looked French enough, but there was something decidedly un-French about him: he idled at a distinctly higher rpm than other ex-pats. About once a minute he would issue apparently involuntary outbursts of sentiment toward assorted products and manufacturers ("Copper wire c'est MERDE!" "Icom radios--TRES BON!" "Vinyl electrical tape ees SHEEET!") and it took all our concentration to catch the key words in the steady stream of French he muttered the rest of the time. But he was cheerful and good-humored, and nothing if not entertaining. Having had little success on this first visit, he arranged to return the next day with more equipment, and announced that he would be at the dock waiting for us at eight a.m.. John, to whom the concept of punctuality meant little or nothing after two years of cruising, tried to confirm the arrangement by repeating it, but when he said it it came out like this: "OK, so we'll expect you some time after eight--you can call us on the marina's VHF radio when you're ready to be picked up at the dock." To which Jean-Yves replied, "I weel be ready at eight I yam Suisse."

### Bora Bora

On September 15 we left Raiatea in the morning and arrived at Bora Bora in the evening. Bora Bora is a beautiful island, thought by many in fact to be the most beautiful in all of French Polynesia, though its praises are frequently followed by a lament for what its beauty might have been were it not for the heavy tread of tourism and the hotel industry. Not having seen it before the fall, I won't comment on this except to say that there's still plenty of magic left. Had it been the first Polynesian island we'd seen, I think we would have found it irresistible, swum and snorkeled for days in its magnificent lagoon, and hiked and explored the interior thoroughly. We would have staked out its serenest anchorage. And we would most definitely have sniffed out the best buys in French cuisine. We would probably not, on the other hand, have gone to any great effort to get to know the locals, as it is widely rumored that the French and islanders alike have grown quite crabby on this island, in no small part because of all those tourists, I'll bet.

But as it happened, Bora Bora was among the last French Polynesian islands we visited. Like the majority of American cruising sailors heading west with the Trades, we'd landed first in the exotic Marquesas in the northeast corner of French Polynesia. More rugged than the Society Islands, and accustomed to far fewer visitors, the Marquesas made a luscious yet wild and other-worldly landfall for us. Naturally, we would have welcomed the sheltered lagoon and creature comforts of an island like Bora Bora, but in many ways I'm glad we arrived at these only obliquely, and had occasion to get to know the essential, uncut version of a tropical island first.

From the Marquesas, which are craggy, high volcanic islands without reefs, we passed (without stopping) through the Tuamotus--low, flat, ring-shaped islands (atolls) whose reefs have expanded and central land masses have receded, leaving behind the pale green-blue lagoons of travel brochure fame--and on to the Societies. The Societies (this is by way of a recap, if you're asking yourself why it all sounds so familiar) are high volcanic islands coupled with lagoon and reef, and as such could be said to combine the other two island groups' best features. All the same, because this is the island type we got to know best--we spent two months in the Societies--we found ourselves growing less susceptible to its charms over time. There are, after all, only so many possible variations on the basic arrangement of reef, lagoon, mountainous interior, and French Polynesian culture, and we figured we "got" the concept. This would be sacreligious talk to many a cruiser, of course. Some sailors cruise west through Polynesia for one season, summer in New Zealand or Fiji, and then cycle through again via eastern Polynesia once more in what can become an endless loop. Or they pick a single island group--Tonga's Vava'u is a favorite--and spend months in search of the most beautiful or remote anchorages. But our own unique brand of wanderlust demands a different sort of diet: we must feed it new experiences with some regularity. Also, we feel the need to get out of the sun once in a while! This, then, will make clear our state of mind (living together in such close quarters, we frequently find ourselves having to share a single state of mind) upon arriving in Bora Bora: we could see that it was lovely, we were obliged to stay for a few days, and we could hardly wait to leave again.

What we did accomplish in Bora Bora: John went scuba diving for the second time in ten years (the first was at Huahine, where he was joined by me in what was to be my first and last diving trip--don't ask me to explain why I just didn't like it) and swam with giant manta rays and had a grand old time and I briefly went snorkeling at a recommended spot in front of a resort hotel and saw lots of pretty fish.

### Maupiti

There were two other boats anchored not far off. On the day we arrived, soon after we dropped anchor, a single-hander on one of the boats radioed us to ask if we'd gone aground. Certainly not! We'd sailed well out of the channel--entirely on purpose--and had followed the charted depths till we were right where we wanted to be. But we only thanked him politely for his concern, and spared him our self-congratulatory reflection on how long it had been since we'd been aground (a year), and indeed on how far our sailing abilities had progressed in general. Though careful never to become complacent, we do permit ourselves the occasional pat on our own backs.

To return to the subject at hand, Maupiti is best known by cruisers for two things: the scary entry channel I've already mentioned and the high, sheer natural rock formation that juts out to one side of the port town and forms the backdrop of the port itself. The tiny town itself does not offer much--no internet access, for example, or not the day we asked, anyway--and if there was a restaurant or hotel, we never saw them. But John took the pleasant two-hour walk around the base of the island, at the end of which he declared himself to be an object of some fascination for the island's younger female population. Frankly, that's about all I remember of the place.

### Mopelia

I've already spilled our secret that we were by this point restless to head off for new sights, and you may imagine we were long past seeking out secluded anchorages in paradisiacal (usage note: my dictionary--American Heritage, 3rd ed.--offers no fewer than five different ways to form the adjective from "paradise" I chose this one at random, but was impressed at all the options) locales in the now too-familiar French Polynesia. But that was before Mopelia.

The entrance to Maupiti had nothing on Mopelia's. There was so much swirling surface commotion in the waters outside the reef break at Mopelia that it was obvious we would be sucked down some sort of gigantic bathtub drain if we went any closer. We had timed it badly and now faced the ebbing tide the prudent thing would be to stand off and wait for the tide to turn. On the other hand, we were sleepy after sailing all night to get there and the prospect of a restful nap at anchor merited serious consideration. While I was still deliberating, John began to get this squinty-eyed look on his face like the proverbial action-adventure hero about to throw common sense to the wind and in the next frame we were plowing ahead at full throttle. I'm sure we looked like a sock in a washing machine from overhead but from our vantage point things didn't go too badly. We did work the engine a bit hard, and our subsequent discovery of a hole in the engine's exhaust elbow suggested we'd achieved new heights in exhaust pressure. But the experience nevertheless represented a milestone in that it vindicated our decision not to throw the engine overboard all those innumerable times we'd wanted to.

We hadn't heard anything about Mopelia except that it was practically uninhabited and that the only people we'd be likely to run into would be pearl divers from Maupiti and the occasional French military representative. There were no other boats in the lagoon when we arrived, and only a couple of small houses away in the distance. We snaked our way between the coral heads and anchored in a clear spot over white sand. Gradually we took in our surroundings and it dawned on us that a) we were effectively alone here, a hundred miles from the next nearest island, and b) a more idyllic place to be stranded for a while would be hard to imagine.

Mopelia was one big, wonderful beach, miles and miles long. Beach along the ocean separated by a wide strip of palm trees from more beach along the lagoon. The ocean beach was wild and the going was difficult. The shore consisted of hard, packed sand under a dense cover of hearty bushes and plants and weirdly shaped pieces of driftwood. The surf, crashing and roaring with abandon, was separated from the accessible areas by slippery expanses of rock and scattered tidal pools. We saw miniature sharks in the pools and tried unsuccessfully to photograph them. On the lagoon side, all was calm and the hermit crab was king. This was a great beach for shell-hunting, though John will never forgive me for inadvertantly bringing home two shells not yet vacated (the sound of the shells migrating precipitately from my pocketbook to the floor brought us running to the aft cabin, where we found them wandering anxiously). I brought my camera to the beach several days in row and took dozens of photos I was sure would all be of National Geographic quality. They weren't that, exactly, but they did preserve the place for me nicely.

We spent almost a week at Mopelia, ostensibly waiting for the passing of some bad weather we kept hearing about on the SSB radio, but any excuse would have done we wanted to stay. When we did leave, it was only for fear of running out of water (it hadn't rained in weeks and there was, of course, no tap to connect our hose to). Then again, it may have been the French military invasion that forced our hand. The day before we left, two unrelated military units showed up out of nowhere. One sizable group patrolled around noisily in half a dozen speedboats--the mothership that appeared to have spawned them stayed outside the reef and hovered there stealthily for some time before moving off--and before long we were politely interrogated and offered assistance (we said we were fine, which we were). This group would be staying at a military facility at the far end of the island. We didn't ask their intent and they didn't volunteer it. The second group--the informal guys--also paid us a visit. They'd come to Mopelia to assist the Maupitian pearl divers, which seemed rather nice of them, and were planning to camp out in tents on the beach. Nobody suggested we should be moving along, though we'd technically cleared out of French Polynesia two weeks earlier, but we took our cue all the same.

### Rarotonga, Cook Islands

Sadly, John's stepfather died during this period. John flew home to be with his mother we agreed that I should stay with the boat. He was gone for about two weeks, and the time passed slowly.

There was, in addition to John's return, another occasion I had to look forward to in two weeks' time, only this one had the opposite effect on the clock: cyclone season would begin on November 1. As you may recall, Saros had faced similar circumstances once before, lingering dangerously for more two months of the 1999 North Atlantic hurricane season in that hurricane magnet, the western Caribbean. With the help of weatherfaxes, careful planning (careful otherwise, I mean--if we'd really been thinking, we would have been somewhere else entirely), and some old-fashioned good luck, we safely reached the Panama Canal just as the first big tropical storm systems were showing up. The situation we now faced in the South Pacific, though reminiscent of that experience, differed in some interesting ways. In both regions, Caribbean and South Pacific, the probability of a tropical cyclone in the first month of the season is about thirty percent. In the second month (July and December, respectively), this increases to forty and fifty percent. But while the odds of a cyclone occurring in the South Pacific in the third month--January--are still a measly seventy percent, in the Caribbean in August they soar to one hundred and fifty percent, or three cyclones every two years. That's one difference. A second is that the South Pacific is a vast body of water the Caribbean is, comparatively speaking, tiny. There is a downside to this for the Pacific cruiser: it takes longer to sail anywhere from anywhere else--should you want to be ashore when the big one hits, for example. On the other hand, it is comforting to consider how much of that enormous ocean will not be in the path of any one cyclone.

The other difference has to do with the danger of heading out of the South Pacific cyclone belt too early, and straight into the teeth of the higher latitudes' late-spring gale season the two different storm seasons overlap inconveniently for a period of several weeks. We couldn't allow ourselves to be caught unawares by an early cyclone, and yet neither did we relish the significant odds of encountering fifty-knot winds and battering seas in the famously unpredictable southern thirties. I will revisit this troublesome problem later, but I am just trying to give you an idea what went on in my head as November approached: it was not as if the official start of cyclone season represented an acute increase in risk (I did appreciate this) and even if we left for Tonga immediately, we'd only wind up waiting around till the end of gale season (I appreciated this, too) besides, if the first cyclone did come early, it was a big ocean and we would probably be okay (here's where I'd become highly agitated).

While I waited for John and the cyclones, I kept busy in various ways. First, I simply took in my surroundings, and the following is a sampling of what I noticed. The inhabitants spoke English, not French (you would have noticed this, too). They spoke it with a funny accent--the New Zealand accent. When I first started hearing it, I found it so interesting that I jotted some notes down, and came up with a phonetic guide to speaking Kiwi. But after a while, I heard so much of that it now sounds about the same to me as an Ohio accent. Which is to say, if you can't recall hearing an Ohio accent, no accent at all. Unfortunately, I've lost the phonetic guide and somehow can't seem to reproduce it.

It would be silly for me to describe the Rarotongan personality--silly because I would be tempted to remark on how friendly, charming and helpful everyone was, and clearly not all Rarotongans are this way all the time, nor would I want to imply that the French Polynesians are, by comparison, not this way. Still, there is something to this impression I got, something stemming from the colonial pasts of the two regions or their present-day political status (French Polynesians still resent their subjugation by the French, many voicing bitterness about past abuses, even if the majority would not for the moment choose independence, having long since become financially dependent on France Cook Islanders, "independent in free association with" New Zealand, are to outward appearances a more contented people, though I can't say I heard their opinions first-hand), or some other influences I am unaware of. The atmosphere throughout the island is a congenial one, and if the climate has something to do with this--it is hot but not too hot, and the nights dry and cool--the people, and the well-designed civic infrastructure, surely do as well. Anecdotal evidence doesn't count for much, I know, but if you should require an example of what I'm talking about, the following may serve: one day while wandering through the woods in search of a particular path, a hiking companion and I sought the guidance of a local resident. She didn't know of the path herself, but insisted on phoning another area resident for us to ask. The second woman knew less than the first, but asked me lots of questions (she clearly thought me very confused and hoped to discover the root cause of my misapprehensions) and in the end steered me on a course back to town. We found the path on our second attempt--it was more or less where we'd thought. The point is, these two women were genuinely concerned about our well-being, and went out of their way to be helpful.

A number of things impressed me about Rarotonga's main town, Avarua: its lovely, unobstructed waterfront the flower-lined and well-shaded path running the length of town down the median strip the large weekly farmers' market featuring the freshest, sweetest corn I'd ever tasted, and other such rarities (to a cruising sailor) as watercress and arugula a movie theater showing three different movies nightly, cleverly rotated so as to bring back the popular ones interittently for weeks on end yet allow for variety throughout the week a great public library, open for use to resident and visitor alike the Telecom-operated telephone/internet center open 24/7 a nice, cheap laundromat accessible restrooms, without the usual "Customers Only" restriction a reliable bus service running clockwise and counterclockwise around the island, morning till night and--I've saved the best for last--good, affordable restaurants. (What made them affordable, I should explain, was the exchange rate: the U.S. dollar buys 2.2 New Zealand dollars.)

Oh, and one more thing: rental bikes for about US\$18--per week. While John was away, I took my camera and cycled around the island and into the interior a bit. The center was mountainous, but in the farm country between mountain and ocean were good roads for biking. I also found subjects galore for my animal portraits. (This may be a phase I'm going through--John thinks so--but I think of it more as a niche I'm in the process of cornering.) There were pigs everywhere--pleasant, clean & wholesome-looking pigs. Also, goats. I must say, I'm exceedingly proud of the goat series I shot.

I went walking, too. Once. I took a four-mile walk in a big loop starting from the harbor, going along the ocean road past the airport and the golf course, and then turning inland to take the rural back road ("Ara Tapu") back toward the harbor. After the airport buildings, there was a lonely stretch of road at the end of which I was chagrined to see a trio of large, hairy dogs eyeing me. I carried a crude walking stick for protection, but at fifty feet I was overcome with shyness (I haven't yet come to terms with this as frank dog-phobia) and hung back. I tried hitching a ride past them but no cars stopped. Then a kind man on a motorbike pulled over, sympathized with my plight and graciously offered to carry me safely past the beasts. This was only the second time I'd been on a non-enclosed motorized vehicle, and, climbing on to it, I tried to remember what I'd learned the other time, with John on the island of Providencia. With my feet, I located the little passenger foot rests, and with my arms I reached around the man's ample middle and clung tightly. A second's reflection, though, and the discovery of the hand-hold behind me, revealed the gratuitousness of this embrace--mortified, I withdrew my arms to their rightful position, but not before spying the happy grin on my chauffeur's face. The remainder of my walk was an anti-climax, and I grew bolder with the dogs, but after that I stuck to biking.

Before John left, we were working out our itinerary in the sand at Rarotonga's best beach--Muri Beach--when we met a German couple, Annette & Thomas, who'd just arrived in the Cooks and were beginning a six-month travel vacation, to include New Zealand and Thailand. We spent time together while John was away--biking and eating, mostly--and I was extremely grateful for their company together we summoned a good amount of hilarity. When John returned, we four rented kayaks and paddled out to the reef, whereupon both couple's kayaks immediately got stuck on the reef. This happened repeatedly, and before long we could see we were not acting in the best interests of the reef (nor the kayaks) and turned back before we could do any more damage. (Whose idea was that, anyway?). We have since heard from Annette and Thomas by email, and if we ever get as far as Europe, maybe we will see them there.

I made another interesting acquaintance on Rarotonga. But first I must tell you about the engine problem. The day John left for Ohio, we started up the engine in order to charge the batteries, but no sooner had it sprung to life when there was a strange noise followed by a dreadful burning smell. We turned it off immediately and warily looked it over, always at these moments expecting to see something as dramatic as the time, in the Cayman Islands, we discovered the engine several inches from the engine mounts. This time, however, there was nothing grossly evident, only the bad smell which was strongest in the vicinity of the blower (which removes hot air from the engine compartment). We tried to restart the engine, for diagnostic purposes, but now it wouldn't start--giving me some idea about the prognosis, at least. John had no choice but to leave for his flight, and I was left scratching my head and blinking at the miserable hunk of iron that was our engine.

The blower was the place to start, we'd reasoned as John was leaving, because it was electrical--this smelled, literally and figuratively, like an electrical problem--and was wired into the ignition switch in such a way that perhaps, if it had shorted, its malfunction might interfere with starting the engine. Also, the blower had been making other strange noises intermittently for weeks, which up until now we'd ignored. So the first thing I did was to clip the blower wires and turn the ignition key again, but there was no response. Not even a "click." Then I disassembled the blower to see if there had ever been anything wrong with it--there hadn't--and spent part of an afternoon putting it back together and reconnecting the severed wires.

Next I checked the starter battery, which is usually kept on a separate circuit from the house bank so we don't accidentally run both down together, but which for about a day had been connected in parallel with the others--we sometimes do this briefly when the house bank is low and we can't bear to run the engine yet. It was low-ish, though I didn't think this was the problem, but to be certain I borrowed a battery charger from the powerboat next door and fully charged all the batteries. Still, the engine refused to start.

My final effort, an attempt to test the various components of the starter circuit, was too much of a stretch for my nascent engine-repair skills, and I knew I was licked. John no longer required the assistance of a professional mechanic when he tackled such problems, but I was new at this and not above asking for help (actually, the thought hadn't occurred to me until that point, or I might have given up sooner). I found an auto parts & repairs center up the road that looked like it got plenty of business, and I told them my troubles. The following morning, the owner, who I'd spoken with, showed up with one of his mechanics, a tall young Rarotongan man wearing company overalls. They made arrangements for the trip back--the mechanic would call the owner when he was ready to be picked up--and the owner drove off. The mechanic followed me aboard and listened without interruption while I detailed the steps I had taken. I must have indicated that I hoped to solve the problem by means of discussion alone because he smiled, finally, and said he thought perhaps he should have a look at the engine himself. A minute later, the starter was on the table, its blackened, twisted innards speaking for themselves.

Slowly it came back to me: we'd left the old, repaired starter in place when we bought that spare in Costa Rica, and that meant there was a new starter somewhere on the boat. I tracked it down--we keep all heavy, clunky items together where they can do no harm, in the water heater locker--and the mechanic had it installed in no time. The engine, of course, started up on the first try. There was just one thing, he said: we still didn't know what had triggered the failure. He made a few suggestions, which I privately dismissed my own, unexamined belief was that the ancient starter with its well-worn brushes had long outlived its intended life span. I thanked him heartily for the job he had done and told him we would likely bring more business his way when John returned and we replaced the ruptured exhaust elbow (the new one was on order from New Zealand).

He turned to go, then paused. "I have a surprise to tell you," he said. I was all ears. "I'm not just a mechanic: I'm a prisoner!" What was there to say to this? I asked a few polite questions about prison--Have you been there long? Is it nearby? Are the other prisoners nice? (Well, maybe that isn't quite how I phrased the last question.)--and he supplied answers to these and one of my unspoken ones (it was murder, or more likely manslaughter or negligent homicide I'm fairly certain he said "murder," though the story he told suggested it wasn't, technically). He was part of a work release program (a very liberal one, from the looks of it) but had two more years to serve. He was married and was, by degrees, building a house to live in with his wife and child upon release. Oh, and he wasn't planning on being a mechanic anymore once he got out that was just something to do in prison. Well he could have fooled me a skilled mechanic with a talent for listening, who can tell a good yarn about life on the inside--if that's not a marketable commodity, what is?

At long last, John returned and we were off once again. We left on the second of November, and in spite of the season, I allowed John to persuade me to stop at the island of Niue for a few days.

Niue is larger than Rarotonga, yet its population is tiny. It, too, is closely associated with New Zealand and shares the same currency. It has not, however, been developed to nearly the same degree, for three reasons that we could see: it has no harbors (Niue wisely provides free moorings for cruisers, though they are effectively out in the ocean) no beaches and it is linked to New Zealand, 1800 miles to the southwest, by a single, overpriced airline. Its principal road is the requisite loop road around the perimeter, but with hardly any view whatsoever you could circuit the island and mistake it for central Florida, says John who has experience of such things. And it's hot--damn hot.