Eclipse Cycles

Introduction

Since ancient times astronomers have attempted to predict the occurrence of lunar and solar eclipses from the observed (or calculated) postions of the Sun and the Moon.

Entries in red denote eclipse cycles in which eclipses repeat at the same lunar node (i.e. ascending/ascending or descending/descending) while entries in magenta denote cycles in which eclipses repeat at alternating lunar nodes (i.e. ascending/descending etc.).

The average life expectancy (T) and number of members (M) in an eclipse cycle (with repeat period P) can be roughly estimated from the shift in the Moon’s orbital position with respect to the lunar node after each eclipse. As long as this shift is smaller than a certain limit (here taken to be 17.4° distant on either side of a lunar node), a new eclipse will occur.

If the eclipse cycle is of the form a I + b S (with a and b integer), then:

M = Int(34.8/abs(0.04002*a-0.47787*b)+1)

and

T ≅ (M-1)*P

As will be shown later the longitudal shift of the Moon’s orbital position with respect to a lunar node is affected by secular variations and the above relation is only valid for the epoch 2000.

The above diagram indicates how the repeat period P of an eclipse period and its expected number of members M depend on its Inex/Saros factors.

List of Eclipse Cycles

The following table gives an overview of the various eclipse cycles which have been mentioned in astronomical publications.

Eclipses in cycles with an even Inex number occur at the same lunar node and are indicated in red; eclipses in cycles with an odd Inex number occur at alternating lunar nodes and are indicated in magenta.

 Cycle Saros-Inex Combination Lunations Eclipse Seasons Period Comments Fortnight 19 I – 30½ S ½ 0 14.765 d 0.0404 y Shortest possible interval between a lunar and a solar eclipse. Synodic month (Lunation, Nova) 38 I – 61 S 1 0 29.531 d 0.0809 y Shortest possible interval between two successive lunar or solar eclipses. Short Semester (Pentalunex) 53 S – 33 I 5 1 147.65 d 0.404 y Semester 5 I – 8 S 6 1 177.18 d 0.485 y Two successive lunar or solar eclipses at alternate lunar nodes. Long Semester 43 I – 69 S 7 1 206.71 d 0.566 y Lunar year 10 I – 16 S 12 2 354.37 d 0.970 y 1 lunar year Hexon 13 S – 8 I 35 6 1033.57 d 2.830 y Hepton 5 S – 3 I 41 7 1210.75 d 3.315 y Eclipses repeat on (nearly) the same weekday. Octon 2 I – 3 S 47 8 1387.94 d 3.800 y Tzolkinex 2 S – I 88 15 2598.69 d 7.115 y Nearly 10 Tzolkins. Hibbardina 31 S – 19 I 111 19 3277.90 d 8.975 y Nearly similar pairs of central solar eclipses Sar (Half Saros) ½ S 111½ 19 3292.66 d 9.015 y Alternating lunar and solar eclipses of nearly similar character. Tritos (Saroid) I – S 135 23 3986.63 d 10.915 y Saros (Chaldean) S 223 38 6585.32 d 18.030 y Similar lunar and solar eclipses spaced about 120° apart in terrestrial longitude. Metonic Cycle 10 I – 15 S 235 40 6939.69 d 19.000 y Same date in the Julian/Gregorian and other luni-solar calendars. Semanex 3 S – I 311 53 9184.01 d 25.145 y Same weekday. Thix 4 I – 5 S 317 54 9361.20 d 25.630 y Approximately 36 Tzolkins. Inex (Lambert I Cycle, Stockwell Cycle) I 358 61 10571.95 d 28.945 y Similar eclipses at the same terrestrial longitude but at opposite latitudes. Triple Tritos (Fox, Maya, Mayan Eclipse Cycle) 3 I – 3 S 405 69 11959.89 d 32.745 y Nearly 46 Tzolkins. Double Saros 2 S 446 76 13170.64 d 36.060 y Unnamed (40) 2 I – S 493 84 14558.58 d 39.860 y Unnamed (47) I + S 581 99 17157.27 d 46.975 y Same weekday. Unnamed (51) 3 I – 2 S 628 107 18545.21 d 50.775 y Exeligmos (Triple Saros) 3 S 669 114 19755.96 d 54.090 y Similar eclipses at approximately the same terrestrial longitude. Aubrey Cycle I + 1½ S 692½ 118 20449.93 d 55.99 y Alternating lunar and solar eclipses supposedly observed from Stonehenge. Double Inex 2 I 716 122 21143.90 d 57.890 y Unnamed (61) 4 I – 3 S 763 130 22531.84 d 61.690 y McNaughton Cycle I + 2 S 804 137 23742.59 d 65.005 y 67 lunar years, nearly same date in Julian/Gregorian calendar. Unnamed (69) 3 I – S 851 145 25130.53 d 68.805 y Short Calippic Cycle 2 I + S 939 160 27729.22 d 75.920 y 4 Metonic Cycles (= Calippic Cycle) minus one month. Triad (Triple Inex) 3 I 1074 183 31715.85 d 86.835 y Quarter Palmen Cycle 4 I – S 1209 206 35702.48 d 97.750 y Mercury Cycle 2 I + 3 S 1385 236 40899.87 d 111.98 y Nearly equals 353 synodic periods of the planet Mercury. Tritrix 3 I + 3 S 1743 297 51471.82 d 140.93 y de la Hire Cycle 6 I 2148 366 63431.71 d 173.67 y 179 lunar years. Unnamed (176) 21 S – 7 I 2177 371 64288.09 d 176.01 y Nearly similar pairs of central eclipses. Unnamed (176.5) 13 S – 2 I 2183 372 64465.28 d 176.50 y Trihex 3 I + 6 S 2412 411 71227.78 d 195.02 y 201 lunar years. Half Babylonian Period 7 I + S 2729 465 80588.98 d 220.65 y Unnamed (246) 6 I + 4 S 3040 518 89772.99 d 245.79 y Lambert II Cycle 9 I + S 3445 587 101732.88 d 278.54 y Unnamed (298) 24 I – 22 S 3686 628 108849.8 d 298.02 y Macdonald Cycle 6 I + 7 S 3709 632 109529.0 d 299.88 y Nearly similar eclipses on the same day of the week. Utting Cycle 10 I + S 3803 648 112304.8 d 307.48 y Unnamed (327) 25 I – 22 S 4044 689 119421.7 d 326.97 y 337 lunar years. Unnamed (336) 11 I + S 4161 709 122876.8 d 336.43 y Hipparchus Cycle 25 I – 21 S 4267 727 126007.0 d 345.00 y Nearly similar pairs of central eclipses. Unnamed (353) 26 S – 4 I 4366 744 128930.6 d 353.00 y Same Gregorian calendar date (approximately). Square Year (Jubilee Period) 12 I + S 4519 770 133448.7 d 365.37 y Gregoriana 6 I + 11 S 4601 784 135870.2 d 372.00 y Same Gregorian calendar date and weekday (approximately). Hexdodeka 6 I + 12 S 4824 822 142455.6 d 390.03 y 402 lunar years. Grattan Guinness Cycle 16 I – 4 S 4836 824 142809.9 d 391.00 y 403 lunar years and same Gregorian calendar date (approximately). Babylonian Period (Hipparchian Period) 14 I + 2 S 5458 930 161178.0 d 441.29 y Unnamed (456) 17 I – 2 S 5640 961 166552.5 d 456.01 y Used by the Chinese astronomer Zhang Xun. Unnamed (520.5) 13 I + 8 S 6438 1097 190117.9 d 520.53 y Basic Period (Pingré Cycle, Hyper Saros) 18 I 6444 1098 190295.1 d 521.01 y 537 lunar years, same Julian calendar date and same weekday. Chalepe (Great Chaldean Cycle) 18 I + 2 S 6890 1174 203465.8 d 557.07 y Tetradia 19 I + 2 S 7248 1235 214037.7 d 586.02 y 604 lunar years and same Julian calendar date (approximately). Unnamed (595) 33 S 7359 1254 217315.6 d 594.99 y Unnamed (600) 12 I + 14 S 7418 1264 219057.9 d 599.76 y Same day of the week. Unnamed (702) 23 I + 2 S 8680 1479 256325.5 d 701.80 y Unnamed (725) 2 I + 37 S 8967 1528 264800.8 d 725.00 y Same Gregorian calendar date (approximately). Unnamed (893) 24 I + 11 S 11045 1882 326165.4 d 893.01 y Used by the Chinese astronomer Liu Hung (3rd. cent.). Hyper Exeligmos 24 I + 12 S 11268 1920 332750.7 d 911.04 y 939 lunar years. Double Basic Period 36 I 12888 2196 380590.2 d 1042.0 y 1074 lunar years, same Julian calendar date and same weekday. Unnamed (1078) 36 I + 2 S 13334 2272 393760.9 d 1078.1 y Schrader (1913). Unnamed (1154) 38 I + 3 S 14273 2432 421490.1 d 1154.0 y Same Gregorian calendar date (approximately). Unnamed (1172) 38 I + 4 S 14496 2470 428075.4 d 1172.0 y 1208 lunar years and same Julian calendar date (approximately). Unnamed (1404) 46 I + 4 S 17360 2958 512651.0 d 1403.6 y Unnamed (1418) 49 I 17542 2989 518025.6 d 1418.3 y Unnamed (1490) 49 I + 4 S 18434 3141 544366.9 d 1490.4 y Cartouche 52 I 18616 3172 549741.4 d 1505.1 y Triple Basic Period 54 I 19332 3294 570885.3 d 1563.0 y 1611 lunar years and same weekday (approximately). Unnamed (1610) 55 I + S 19913 3393 588042.6 d 1610.0 y Unnamed (1628) 55 I + 2 S 20136 3431 594627.9 d 1628.0 y 1678 lunar years and same Julian calendar date (approximately). Palaea-Horologia 55 I + 3 S 20359 3469 601213.3 d 1646.1 y Hybridia 55 I + 4 S 20582 3507 607798.6 d 1664.1 y Selenid I 55 I + 5 S 20805 3545 614383.9 d 1682.1 y Unnamed (1700) 55 I + 6 S 21028 3583 620969.2 d 1700.2 y Unnamed (1751) 58 I + 4 S 21656 3690 639514.4 d 1750.9 y Proxima 58 I + 5 S 21879 3728 646099.8 d 1769.0 y Nearly 2485 Tzolkins and same weekday. Heliotrope 58 I + 6 S 22102 3766 652685.1 d 1787.0 y Megalosaros 58 I + 7 S 22325 3804 659270.4 d 1805.0 y 95 Metonic Cycles. Immobilis 58 I + 8 S 22548 3842 665855.7 d 1823.1 y 1879 lunar years. Accuratissima 58 I + 9 S 22771 3880 672441.0 d 1841.1 y Same weekday. Mackay Cycle 76 I + 9 S 29215 4978 862736.2 d 2362.0 y Unnamed (2471) 81 I + 7 S 30559 5207 902425.3 d 2470.8 y Selenid II 95 I + 11 S 36463 6213 1076773.9 d 2948.1 y Horologia 110 I + 7 S 40941 6976 1209011.8 d 3310.2 y Same weekday (approximately).

Comments on the Listed Cycles

Fortnight

Shortest possible interval separating a lunar and a solar eclipse. The fact that a lunar and a solar eclipse could occur within two weeks was already noted by Pliny the Elder (Naturalis Historia II.10 [57]) who reported such an event in the year A.D. 71 (lunar eclipse on 4 March, solar eclipse on 20 March).

Synodic month (Lunation, Nova)

Shortest interval separating two successive lunar or solar eclipses.

Two consecutive New Moons can each produce a solar eclipse though in nearly all cases both will be partial only (one for the North Pole region, the other for the South Pole region). Very rarely, one of both will be total somewhere near the pole: the last occurrence was in 1928 (total on 19 May, partial on 17 June), the next such pair will be not until in 2195 (partial on 7 June, total on 5 August).

The name Nova was suggested by George van den Bergh (1951, 1954).

Short Semester (Pentalunex)

The name Pentalunex was suggested by Felix Verbelen (2001).

Semester

The semester can be used for predicting short series of lunar eclipses with 5 or 6 members (penumbral eclipses excluded). The series start with one or two partial eclipses, a few total eclipses and is terminated by one or two partial eclipses.

Short series of solar eclipses can also be predicted with the semester and contain about 7 or 8 members which alternate in visibility from the northern and the southern hemisphere. A semester series of solar eclipses can commence with a total eclipse.

The name Semester was suggested by George van den Bergh (1951, 1954).

Long Semester

Very rarely, two lunar or solar eclipses can be separated by seven months.

Lunar year

Lunar and solar eclipses can reoccur after 12 lunar months or one lunar year. One lunar year is about 7.75 days longer than an ‘eclipse year’ of 346.62 days, the mean interval between two successive solar returns to the same lunar node.

It is possible to have three total lunar eclipses within one (Western) calendar year. Since the begin of the Christian era, this occurred in 307, 372, 437, 828, 893, 958, 1414, 1479, 1544, 1917 and 1982. The next trio of total lunar eclipses will not occur until 2485.

When partial and penumbral eclipses are included it is possible to have four or even five lunar eclipses within one (Western) calendar year. Since the introduction of the Gregorian Calendar quartets occurred in 1582, 1593, 1600, 1611, 1615, 1629, 1633, 1637, 1640, 1651, 1658, 1669, 1680, 1684, 1687, 1698, 1702, 1705, 1709, 1712, 1716, 1720, 1723, 1727, 1734, 1738, 1741, 1745, 1752, 1756, 1763, 1767, 1774, 1781, 1785, 1792, 1803, 1806, 1810, 1814, 1821, 1828, 1832, 1839, 1843, 1846, 1850, 1857, 1861, 1864, 1868, 1886, 1890, 1897, 1908, 1915, 1926, 1933, 1944, 1951, 1973, 1991, 2009 and 2020. The next quartets will be in 2038, 2056, 2085 and 2096.

Quintets are of course much rarer and since the introduction of the Gregorian calendar they have only occurred in 1676, 1694, 1749 and 1879. The next quintet will not occur until 2132.

For eclipses of any kind (but excluding penumbral lunar eclipses) it is even possible to have seven in one (Western) calendar year. Since the introduction of the Gregorian Calendar this occurred in 1591, 1656, 1787, 1805, 1917, 1935 and 1982. The next septet will be in 2094.

N.B. This list is based on Von Oppolzer’s tables and does not include penumbral lunar eclipses.

Hexon

Third convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. As its length of duration lasts six eclipse seasons, the name Hexon would seem to be appropriate.

Hepton

The hepton can be used for predicting series of solar eclipses with some 13 or 14 members which alternate in visibility between the northern and the southern hemisphere. The name was introduced by George van den Bergh (1951) and reflects its length of duration (i.e. seven eclipse seasons).

Octon

The name was introduced by George van den Bergh (1951) and reflects its length of duration (i.e. eight eclipse seasons). Fourth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Tzolkinex

First studied by George van den Bergh (1951). The name Tzolkinex was suggested by Felix Verbelen (2001) as its length is nearly 10 Tzolkins (260-day periods).

Hibbardina

Nearly half of the Saros period. First identified by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses. The name Hibbardina was suggested by George van den Bergh (1957).

Sar (Half Saros)

Half of the Saros period, equal to 111.5 synodic, 121 draconic and 119.5 anomalistic months. Solar and lunar eclipses of the same character repeat after this cycle; i.e. a solar eclipse visible in the northern (southern) hemisphere is followed by a lunar eclipse at which the Moon passes through the northern (southern) part of the Earth’s umbral cone. A long solar eclipse (when the Moon is near the perigee of its orbit) is followed by a deep lunar eclipse (when the Moon is near the apogee of its orbit). According to Jean Meeus (1965) this cycle was first discussed by Paul Ahnert in his Kalender für Sternfreunde 1965. The name Sar was suggested by Jean Meeus (1965).

Tritos (Saroid)

This eclipse cycle was known to Chinese astronomers as the shuò wàng zhī huì 朔望之會 [“New and Full Moons Coincidence Cycle”] and appears to have been developed in the first century B.C. (Needham, 1959). During each cycle 23 lunar eclipses were predicted to occur. The name Tritos was introduced by George van den Bergh (1951, 1954). Robert Wheeler Willson (1924), who named it the Saroid, believed that it was also known to Maya astronomers.

The Tritos can be used for predicting series of solar eclipses with more than 60 members which alternate in visibility between the northern and the southern hemisphere. At the begin and the end of a solar Tritos series it is possible to have a few “missing” eclipses.

Saros (Chaldean)

Fifth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Strictly speaking, the name Saros for this eclipse cycle is a misnomer as it was derived from an ancient Babylonians term to indicate the number 3600 (šār). As demonstrated by William Thynne Lynn (1889) and again by Otto Neugebauer (1938, 1952, 1975), the name was first coined in 1691 by the English astronomer Edmond Halley, who extracted it from a 10th-century Byzantine lexicon (q.v. Σάροι in Suda Σ 148) which identified it as a 222-month Babylonian cycle and then erroneously linked it to a (unnamed) 223-month Babylonian eclipse cycle mentioned by Pliny the Elder (Naturalis Historia II.10 [56]). Ancient Babylonian texts simply referred to this cycle as the “18-Year Cycle” while Ptolemy of Alexandria (Almagest IV.2) referred to it as the περιοδικὸϲ χρόνοϲ (“Periodic Interval”). Some have therefore argued that it would be better to name this cycle the Chaldean but the name Saros has now become so familiar that it will be difficult to supplant it.

The Saros cycle is a successful eclipse series as its period of 223 synodic months not only closely approximates 242 draconic months but also because the number of anomalistic returns of the Sun (18.029) and the Moon (238.992) are nearly whole numbers. Successive eclipses in a Saros series are therefore very similar in character. The main drawback of the cycles lies in the fact that after each eclipse the time of maximum obscuration is shifted by nearly 8 hours so that successive eclipses are about 120° apart in longitude and thus often not visible from a fixed position on Earth.

The Saros series number SNS of a solar eclipse (introduced by George van den Bergh in the 1950’s) can be derived from the lunation number LN with the following algorithm first given by Charles Kluepfel (1985):

ND=LN+105
NS=136+38*ND
NX=-61*ND
NC=FLOOR(NX/358+0.5-ND/(12*358*358))
SNS=MODULO(NS+NC*223-1,223)+1

with:

LN = Lunation number (0 on 6 January 2000)
N.B.: LN = Brown Lunation Number - 953
= Islamic Lunation Number - 17038
= Goldstine Lunation Number - 37105

Solar eclipses in an odd-numbered Saros series occur near the ascending node of the lunar orbit: they start with a small partial eclipse in the northern polar regions and slowly progress southwards, ending with a small partial eclipse in the southern polar regions. Solar eclipses in an even-numbered Saros series occur near the descending node of the lunar orbit: they start with a small partial eclipse in the southern polar regions and slowly progress northwards, ending with a small partial eclipse in the northern polar regions.

Solar Saros series can be as short as 1226 years (with 69 members) and as long as 1550 years (with 87 members). An average solar Saros series lasts about 1388 years and contains about 78 members of which some 48 are central. At the moment 40 solar Saros series are active (nrs. 117 to 156). Series 117 will terminate on 3 August 2054, dus decreasing the number of active series to 39 but a new series (nr. 157) will commence on 21 June 2058 raising the number of active series again to 40.

For lunar eclipses the Saros series number SNL is defined by Bao-Lin Liu & Fiala (1992) as:

SNL=MODULO(LN+60,223)+1

For a different method of obtaining the Saros series number of a solar or a lunar eclipse, cf. Verbelen (2001).

In contrast with the solar Saros numbers, the parity (the even- or oddness) of SNL does not correlate with eclipses at either the ascending or the descending node of the lunar orbit. Of the current Lunar Saros series, numbers 2, 14, 26, 38, 49, 61, 73, 85, 96, 108, 120, 132, 143, 155, 167, 178, 179, 190, 202 and 214 take place at the ascending node of the lunar orbit: they start with a penumbral eclipse at the southern limb of the lunar disk and slowly progress northwards, ending with a penumbral eclipse at the northern limb of the lunar disk.

Of the current Lunar Saros series, numbers 8, 20, 32, 43, 44, 55, 67, 79, 90, 91, 102, 114, 126, 137, 149, 161, 173, 184, 196, 208 and 220 take place at the descending node of the lunar orbit: they start with a penumbral eclipse at the northern limb of the lunar disk and slowly progress southwards, ending with a penumbral eclipse at the southern limb of the lunar disk.

Of the complete lunar Saros series contained in the catalogue of Bao-Lin Liu & Fiala (1992) the shortest lasted 1262 years (with 71 members) while the longest lasted nearly 1551 years (with 87 members). However, the length distribution of lunar Saros series is strongly skewed to short values resulting in a most likely lunar Saros length of about 1280 years with 72 members of which the number of total eclipses ranges from 40 to 58. At the moment 41 lunar Saros series are active. A new series (nr. 3) will commence on 25 May 2013 after which 42 lunar Saros series will be active until 18 August 2016 with the demise of series nr. 43.

Metonic Cycle

As the Octon (a fifth part of the Metonic Cycle), the Metonic Cycle can be used for predicting short series of lunar or solar eclipses with only 4 or 5 members which nearly fall on the same calendar day. Cuneiform sources indicate that this cycle was used by Babylonian astronomers (perhaps as early as the 6th century B.C.) for predicting lunar eclipses (Koch, 2001). The cycle was also briefly mentioned as an eclipse cycle by Stockwell (1895).

Semanex

First studied by Colton & Martin (1967). Felix Verbelen (2001), who suggested the name, discovered that eclipses repeat on the same day of the week.

Thix

The name Thix was suggested by Charles H. Smiley (1973) as its length is equal to thirty-six Tzolkins.

Inex (Lambert I Cycle, Stockwell Cycle)

Although the cycle was already described by J.H. Lambert in 1765 and rediscovered at the end of the 19th century (first mentioned by Necomb in 18?? and Stockwell and Crommelin in 1901), the name Inex (sometimes erroneously referred to as Index) was first introduced by George van den Bergh in 1951.

According to Van den Bergh an average solar Inex series lasts about 22 600 years and contains about 780 members. At the moment some 70 solar Inex series are active.

At the begin and the end of an Inex series there are several long gaps during which no eclipses take place.

Triple Tritos (Fox, Mayan Eclipse Cycle)

The Mayan Eclipse Cycle (often abbreviated as MEC or Mec). Van den Bergh (1951) calls this cycle the Maya. The name Fox was suggested by Charles H. Smiley (1973) as its length is equal to forty-six Tzolkins.

According to Colton & Martin (1967) this cycle was employed by ancient Chinese astronomers to predict eclipses.

???

Unnamed (40)

Mentioned in Colton & Martin (1967).

Unnamed (47)

Mentioned in Colton & Martin (1967).

Unnamed (51)

Mentioned in Colton & Martin (1967).

Exeligmos (Triple Saros)

Similar eclipses follow approximately similar paths on the Earth’s surface.

According to Geminus of Rhodes (Elementa Astronomiae XVIII) and Claudius Ptolemy of Alexandria (Almagest IV.2), who named this cycle the Exeligmos (ἐξελιγμός, “Revolution [of the Celestial Bodies]”), this cycle was already known to Hipparchus of Nicaea and the “most ancient astronomers” (i.e. the Babylonians). The cycle is also featured on the calendar scale of the Antikythera mechanism.

Aubrey Cycle

Alternating lunar and solar eclipses supposedly predicted by means of the Aubrey holes at Stonehenge.

Double Inex

This cycle was intensively studied by Torroja Menéndez (1941). Sixth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month.

Unnamed (61)

Mentioned in Colton & Martin (1967).

McNaughton Cycle

Mentioned in Colton & Martin (1967) and studied in more detail in McNaughton (1995).

Unnamed (69)

Mentioned in Colton & Martin (1967).

Short Calippic Cycle

Mentioned in Colton & Martin (1967). Also known in China, cf. Sivin (1969).

???

???

Mercury Cycle

The length of this cycle is very nearly equal to 353 synodic periods of the planet Mercury. The cycle and its name was suggested by Peter Nockolds (SE Newsletter February 1999).

Tritrix

Briefly mentioned by George van den Bergh (19??).

de la Hire Cycle

Adopted by Philippe de la Hire in the luni-solar tables in his Tabularum Astronomicarum (1687).

Unnamed (176)

Briefly mentioned by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses.

Unnamed (176.5)

Karl Palmen (2001, unpublished) has suggested to name this cycle the Half Tropicana.

Trihex

Briefly mentioned by George van den Bergh (19??).

Half Babylonian Period

Plutarch of Chaeronea (De facie in orbe lunae 20 [933E]) states that 465 eclipse seasons are made up of 404 six-month eclipse seasons and 61 five-month eclipse seasons. As its period is half of that of the Babylonian Period, I suggest to name it the Half Babylonian Period.

Unnamed (246)

Briefly mentioned by Torroja Menéndez (1941) and George van den Bergh (1951).

Lambert II Cycle

First mentioned by J.H. Lambert (1765) as a cycle in which eclipses repeat in nearly identical circumstances.

Unnamed (298)

Briefly mentioned by George van den Bergh (1951).

Macdonald Cycle

Briefly mentioned by A.C.D. Crommelin (1905), Torroja Menéndez (1941) and George van den Bergh (1951). Macdonald (2000) noted that solar eclipses of long duration visible from the British Isles between +1 and +3000 tend to occur in pairs separated by this period.

Utting Cycle

Seventh convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. First(?) discussed by James Utting (1827).

Unnamed (327)

Briefly mentioned by George van den Bergh (1951, 1954).

Unnamed (336)

Briefly mentioned by George van den Bergh (1951, 1954).

Hipparchus Cycle

According to Hipparchus of Nicaea (Ptolemy, Almagest, IV.2), the Moon makes 4573 complete returns in lunar anomaly within this period. Briefly mentioned by William B. Hibbard (1956) as a period that produces close pairs of central solar eclipses when the nodal position is evenly “bracketed” by both eclipses. The name Hipparchus Cycle was suggested by Tom Peters (2003, unpublished).

Unnamed (353)

Karl Palmen (2001, unpublished) has suggested to name this cycle the Tropicana.

Square Year (Jubilee Period)

Introduced by George van den Bergh (1951), who initially called it the Jubilee Period but later changed the name to Square Year as its length in years was nearly equal to the number of days in a year. Eighth convergent in the continued fractions development of the ratio between the eclipse year and the synodic month. This cycle has an exceptionally long life expectancy.

Gregoriana

Briefly mentioned by Stockwell (1901), Schrader (1913) and by Torroja Menéndez (1941). The name Gregoriana was suggested by George van den Bergh (1954). Combined with the Accuratissima this cycle also gives good predictions for the latitudinal position of the central line of a solar eclipse on the Earth’s surface; for details, cf. Van den Bergh (1954). The greatest accuracy is achieved for eclipse pairs centred on –600.

Hexdodeka

Introduced by George van den Bergh (1954). Combined with the Palaea-Horologia, this cycle can be employed for giving accurate predictions of the time of luni-solar syzygies.

Grattan Guinness Cycle

Shortest cycle that predicts lunar or solar eclipses with the same date (more or less) in both the Gregorian calendar as in a 12-month lunar calendar. Discovered by Henry Grattan Guinness (1896) from a speculative reading of Revelation 9:15.

Babylonian Period (Hipparchian Period)

According to Hipparchus of Nicaea (Ptolemy, Almagest IV.2) the Moon makes 5923 complete returns in latitude within this period. The name was introduced by George van den Bergh (1951, 1954), who called it the Long Babylonian Period and the Old Babylonian Period, although there is no evidence that this cycle was known to ancient Babylonian astronomers. In the earlier literature, this cycle is also known as the Hipparchian Period.

Unnamed (520.5)

Briefly mentioned by George van den Bergh (19??).

Basic Period (Pingré Cycle, Hyper Saros)

Achieves a nearly integer number of calendar years (521 years + 4 days) and anomalistic years (521 years – 5 days). According to Lalande (Astronomie, 3rd ed., vol. II, 195) this cycle was first discovered by A.G. Pingré. Also mentioned by A. Mackay (18??). It was rediscovered by Monck (1902), Schrader (1913) and named Hyper Saros by Alexander Pogo (1935). Also mentioned by Torroja Menéndez (1941) and in Barlow et al. (1944). Van den Bergh lists it as the Basic Period.

Chalepe (Great Chaldean Cycle)

Introduced by George van den Bergh (19??). Discussed earlier by James Utting (1827). Also known in the earlier literature as the Great Chaldean Cycle although there is no evidence that this cycle was known to Babylonian astronomers.

Tetradia

Rules the regularity of lunar eclipse tetrads (four successive lunar eclipses that are all total and occur at intervals of six lunations) and solar eclipse duos (two solar eclipses at an interval of one lunation). The change in lunar anomaly is too large for the cycle to be useful in predicting the character of solar eclipses.

Unnamed (595)

Briefly mentioned by George van den Bergh (19??).

Unnamed (600)

Briefly mentioned by A.C.D. Crommelin (1905) and George van den Bergh (1951).

Unnamed (702)

Briefly mentioned by George van den Bergh (19??).

Unnamed (725)

Briefly mentioned by George van den Bergh (19??).

Hyper Exeligmos

Equals twelve Short Calippic Periods. First mentioned by Alexander Pogo (1935).

Double Basic Period

Briefly mentioned by George van den Bergh (19??).

Unnamed (1078)

Briefly mentioned by Schrader (1913).

Unnamed (1154)

Briefly mentioned by George van den Bergh (19??).

Unnamed (1172)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1404)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1418)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1490)

Briefly mentioned by George van den Bergh (1951).

Cartouche

Introduced by George van den Bergh (19??).

???

Unnamed (1610)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1628)

Briefly mentioned by George van den Bergh (1951).

Palaea-Horologia

Introduced by George van den Bergh (19??). Combined with the Hexdodeka, this cycle can be employed for giving accurate predictions of the time of luni-solar syzygies; for details, cf. Van den Bergh (1954).

Hybridia

Introduced by George van den Bergh (19??).

Selenid I

Introduced by George van den Bergh (19??). Gives good predictions for the magnitudes of lunar eclipses in the third millennium A.D.

Unnamed (1700)

Briefly mentioned by George van den Bergh (1951).

Unnamed (1751)

Briefly mentioned by George van den Bergh (1951).

Proxima

Introduced by George van den Bergh (1951).

Heliotrope

Introduced by George van den Bergh (19??). Gives good predictions for the longitudinal position of the central line of a solar eclipse on the Earth’s surface. The greatest accuracy is achieved for eclipse pairs encompassing the period +500 to +1100.

Megalosaros

Eclipse cycle first studied by Julius Oppert (1873) who claimed that it was known by Chaldaean astronomers as early as 2517 B.C. The name was suggested by A.C.D. Crommelin (1901, 1903). Gives accurate predictions of the time of syzygies in the third millennium B.C.; for details, cf. Van den Bergh (1954).

Immobilis

Introduced by George van den Bergh (19??).

Accuratissima

Gives good predictions for the magnitudes of lunar eclipses and the character of solar eclipses. According to George van den Bergh (1954), the errors in the predicted magnitudes of lunar eclipses are less than 10% during the third millennium B.C.

Combined with the Gregoriana this period also gives good predictions for the latitudinal position of the central line of a solar eclipse on the Earth’s surface; for details, cf. Van den Bergh (1954). The greatest accuracy is achieved for eclipse pairs centered on –600.

Mackay Cycle

Mentioned by A. Mackay (18??).

Unnamed (2471)

Briefly mentioned by George van den Bergh (19??).

Selenid II

Introduced by George van den Bergh (1951). Gives good predictions for the magnitudes of lunar eclipses in the third millennium A.D.

Horologia

Introduced by George van den Bergh (1951). Gives accurate predictions for the time of ecliptic conjunctions (solar eclipses) and oppositions (lunar eclipses).

References (chronological)

• Halley, Edmond, “Emendationes & Notæ in tria loca vitiose edita in Textu vulgato Naturalis Historiæ C. Plinii”, Philosophical Transactions of the Royal Society of London, 16 (1691), 535-540 [doi link] – reprinted in Acta Eruditorum anno M DC XCII publicata (Leipzig: Johann Grosse & Johann Friedrich Gleditsch, 1692), 529-534 [GDZ link].
• Struyck, Nicolaas, Inleiding tot de algemeene geographie, benevens eenige sterrekundige en andere verhandelingen (Amsterdam: Isaak Tirion, 1740), second part, pp. 78-81 [E-RARA link].
• Fréret, Nicolas, “Observations sur les années employées à Babylone, avant & depuis la conquête de cette ville par Alexandre”, Histoire de l’Académie Royale des Inscriptions et Belles-Lettres, avec les Mémoires de Littérature tirés des Registres de cette Académie, depuis l’année M. DCCXLI. jusques & compris l’anné M. DCCXLIII., 16 (1751), Mémoires, 205-232 [Google Books link] – reprinted in Œuvres complètes de Fréret, (Paris: ???, 1796-1799), vol. 12, ???-???.
• Struyck, Nicolaas, Vervolg van de beschryving der staartsterren, en nader ontdekkingen omtrent den staat van ’t menschelyk geslagt, benevens eenige sterrekundige, aardrykskundige en andere aanmerkingen (Amsterdam: Isaak Tirion, 1753), pp. 130-132 [Google Books link].
• le Gentil de la Galaisière, Guillaume J., “Remarques sur un Mémoire de M. Halley, inséré dans les Transactions philosophiques de l’année 1692, No. 194, page 535, dans lequel M. Halley parle du Saros des Chaldéens”, Histoire et Mémoires de l’Académie Royale des Sciences [pour] l’année M.DCCLVI (Paris: l’Imprimerie Royale, 1762), pp. 55-69 [Gallica link].
• le Gentil de la Galaisière, Guillaume J., “Addition au Mémoire précédent, sur le Saros des Chaldéens; & Remarques sur l’Éclipse de Soleil prédite par Thalès”, Histoire et Mémoires de l’Académie Royale des Sciences [pour] l’année M.DCCLVI (Paris: l’Imprimerie Royale, 1762), pp. 70-81 [Gallica link].
• Lambert, Johann Heinrich, Beschreibung und Gebrauch einer neuen und allgemeinen eccliptischen Tafel worauf alle Finsternisse des Mondes und der Erde in ihrer natürlichen Gestalt vorgestellt werden, nebst der leichtesten Art dieselbe und die dabey vorkommenden Umstände zu berechnen und zu entwerfen (Berlin: Verlag der Realschulbuchhandlung, 1765) [E-RARA link].
• Ideler, Ludwig, Handbuch der mathematischen und technischen Chronologie, aus den Quellen bearbeitet (Berlin: August Rücker, 1825-1826), 2 vols. [E-RARA link] – vol. I, pp. 205ff discuss cycles such as the Saros, Neros and Sossos ascribed to the ancient Babylonians.
• Utting, James, “On a New Period of Eclipses”, Memoirs of the Astronomical Society of London, 3 (1827), 89-92 [ADS link] – summary in Monthly Notices of the Astronomical Society of London, 1 (1831), 33 [ADS link].
• Oppert, Julius, “Sur une date préhistorique”, in: Congrès International d’Anthropologie & d’Archéologie Préhistoriques: Compte rendu de la 6e Session, Bruxelles, 1872 (Brussels: C. Muquardt, Éditeur, 1873), 162-164 [Google Books link].
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• Peters, Carl Friedrich Wilhelm, “Ueber die Sonnenfinsterniss des Thales”, Astronomische Nachrichten, 120 (1889), 231-232 [ADS link].
• Lynn, William Thynne, “The Chaldæan Saros”, The Observatory: A Monthly Review of Astronomy, 12 (1889), 261-262 [ADS link].
• Maunder, Edward Walter, “The Life-History of a Solar Eclipse”, Knowledge: An Illustrated Magazine of Science, 16 [= New Series, 8] (1893), 181-184 [Internet Archive link].
• Epping, Joseph & Strassmaier, Johann Nepomuk, “Der Saros-Canon der Babylonier nach der Keilschrift-Tafel Sp. II, 71 des Britischen Museums, nebst dem entsprechenden babylonischen und julianischen Kalender vom Jahre 13 Artaxerxes' II. bis zum jahre 34 des Seleukos, d. i. von 392 bis 278 v. Chr.”, Zeitschrift für Assyriologie und verwandte Gebiete, 8 (1893), 149-178 [MENAdoc link].
• Stockwell, John Nelson, “On the Law of Recurrence of Eclipses on the Same Day of the Tropical Year”, The Astronomical Journal, 15 (1895), 73-75 [ADS link].
• Flammarion, Camille, “Le cycle des éclipses de soleil”, Bulletin de la Société Astronomique de France et revue mensuelle d’astronomie, de météorologie et de physique du globe, 10 (1896), 248-257 [Gallica link].
• Manitius, Karl, Gemini Elementa Astronomiae: Ad codicum fidem recensuit, Germanica interpretatione et commentariis instruxit (Leipzig: B.G. Teubner Verlag, 1898) [Internet Archive link] – chapter XVIII discusses the Exeligmos eclipse cycle.
• Johnson, Samuel Jenkins, “Three Lunar Eclipses in a Year”, The Observatory: A Monthly Review of Astronomy, 22 (1899), 235-236 [ADS link].
• Whitmell, Charles Thomas, “The Maximum Duration Possible for a Total Solar Eclipse”, Monthly Notices of the Royal Astronomical Society, 60 (1900), 435-441 [ADS link].
• Stockwell, John Nelson, “Eclipse-Cycles”, The Astronomical Journal, 21 (1901), 185-191 [ADS link] – errata in ibid., 24 (1904), 42 [ADS link].
• Crommelin, Andrew Claude de la Cherois, “The 29-Year Eclipse-Cycle”, The Observatory: A Monthly Review of Astronomy, 24 (1901), 379-382 [ADS link].
• Monck, William Henry Stanley, “An Eclipse Cycle”, Popular Astronomy, 10 (1902), 240-242 [ADS link].
• Crommelin, Andrew Claude de la Cherois, “Cycles of Eclipses”, Knowledge: An Illustrated Magazine of Science, Literature & Art, 26 [= New Series, 18] (1903), 202-206 & 224-227 [Internet Archive link].
• Cowell, P.H., “An Eclipse in the Reign of Nero”, The Observatory: A Monthly Review of Astronomy, 30 (1907), 408-409 [ADS link].
• Monck, William Henry Stanley, “Eclipse Cycles”, The Observatory: A Monthly Review of Astronomy, 34 (1911), 52-53 [ADS link].
• Monck, William Henry Stanley, “Eclipse Cycles”, The Journal of the Royal Astronomical Society of Canada, 5 (1911), 117-124 [ADS link].
• Seagrave, Frank Evans, “The Completing of an Eclipse Cycle”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 22 (1914), 405-407 [ADS link].
• Whitmell, Charles Thomas, “Lunar Penumbral Eclipses”, Journal of the British Astronomical Association, 25 (1915), 225-228 [ADS link].
• Pannekoek, Anton, “The Origin of the Saros”, Proceedings of the Section of Sciences of the Koninklijke Akademie van Wetenschappen te Amsterdam, 20 (1918), 943-955 [ADS link / Internet Archive link / KNAW link].
• Rigge, William Francis, “The Lunar Saros”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 26 (1918), 85-95 [ADS link].
• Seagrave, Frank Evans, “The Recurrence of Solar Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 26 (1918), 308-310 [ADS link].
• Auric, André, “Sur le cycle des éclipses”, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, 169 (1919), 1026-1027 [Gallica link] – reprinted in Bulletin de la Société Astronomique de France et revue mensuelle d’astronomie, de météorologie et de physique du globe, 34 (1920), 163 [ADS link] and Bulletin de l’Observatoire de Lyon, 4 (1920), 4.
• Crombie, William Thomas Berger, “The Saros”, The Journal of the Royal Astronomical Society of Canada, 16 (1922), 313-318 [ADS link].
• Comrie, Leslie John, “The Prediction of Eclipses”, Nature, 119 (1927), 73-75 [Nature link].
• Lewis, Isabel Martin, “The Maximum Duration of a Total Solar Eclipse”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 38 (1930), 23-24 [ADS link] – reprinted in Publications of the American Astronomical Society, 6 (1931), 265-266 [ADS link].
• Gleißberg, Wolfgang & Zimmermann, Günter, “Tzolkin-Periode und Finsternisse”, Astronomische Nachrichten, 241 (1931), 309-312 [ADS link].
• Way, Breading G., “An Unusual Eclipse Year”, Publications of the Astronomical Society of the Pacific, 46 (1934), 346-347 [ADS link].
• Pogo, Alexander, “The Saros Cycle Ending with the Partial Eclipse of January 5, 1935”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 7-14 [ADS link].
• Pogo, Alexander, “The Eclipse of February 3, 1935: A Partial Solar Eclipse Visible in Central America”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 95-99 [ADS link].
• Pogo, Alexander, “Lunar Saros Series”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 207-213 [ADS link].
• Pogo, Alexander, “Solar Saros Series”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 335-344 [ADS link].
• Pogo, Alexander, “Calendar Years with Five Solar Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 412-423 [ADS link].
• Pogo, Alexander, “Calendar Years with Three Lunar Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 549-557 [ADS link].
• Pogo, Alexander, “The Eclipse of 1935 December 25: An Umbral Eclipse of the Midnight Sun in the Antarctic”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 43 (1935), 617-627 [ADS link].
• Pogo, Alexander, “The Lunar Appulses of 1882 and their Exeligmos Returns in 1936”, Publications of the Astronomical Society of the Pacific, 47 (1935), 187-190 [ADS link].
• Pogo, Alexander, “The Lunar Saros Series of the Columbus Eclipse of 1504 February 29-March 1”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 44 (1936), 353-363 [ADS link].
• Pogo, Alexander, “The Lunar Appulse of 1936 December 28”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 44 (1936), 481-483 [ADS link].
• Pogo, Alexander, “The Classification of Solar and Lunar Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 45 (1937), 540-549 [ADS link].
• Neugebauer, Otto E., “Untersuchungen zur antiken Astronomie: III. Die babylonische Theorie der Breitenbewegung des Mondes”, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B: Studien, 4 (1938), 193-346 [pdf link].
• Neugebauer, Otto E., “Untersuchungen zur antiken Astronomie: V. Der Halleysche ,,Sarosʻʻ und andere Ergänzungen zu UAA III”, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B: Studien, 4 (1938), 407-411 [pdf link].
• Pogo, Alexander, “The Solar Eclipse of 1938 May 29: The First Umbral Eclipse of its Saros Series”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 46 (1938), 256-259 [ADS link].
• Pogo, Alexander, “The Lunar Eclipse of 1938 May 14 and its Saros Series”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 46 (1938), 385-389 [ADS link].
• Pogo, Alexander, “Limits of Umbral Runs in Lunar Saros Series”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 46 (1938), 456-461 [ADS link].
• Pogo, Alexander, “The Eclipse of 1938 November 22: A Partial Solar Eclipse Visible in the Tropics”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 46 (1938), 565-567 [ADS link].
• Couder, André, “Du saros”, L’Astronomie: Bulletin de la Société Astronomique de France et revue mensuelle d’astronomie, de météorologie et de physique du globe, 54 (1940), 3-15 [ADS link].
• Pogo, Alexander, “The Penumbral Lunar Eclipses of 1940”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 48 (1940), 6-9 [ADS link].
• Menéndez, José Maria Torroja, “Contribución al estudio general del problema de la repetición de los eclipses”, Memorias del Observatorio del Ebro, nr. 8 (1941) [ADS link].
• Pogo, Alexander, “The Four Penumbral Lunar Eclipses of 1944”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 51 (1943), 354-358 [ADS link].
• Bell, Raymond M., “Recurrence of Total Solar Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 59 (1951), 22-24 [ADS link].
• Grant, Gordon, “A Graphical Representation of Eclipses”, Popular Astronomy: A Review of Astronomy and Allied Sciences, 59 (1951), 419-428 [ADS link].
• van den Bergh, George, “Reeksen totale maansverduisteringen”, Hemel en Dampkring, 49 (1951), 142-146.
• Pannekoek, Anton, “Periodicities in Lunar Eclipses”, Proceedings of the Section of Sciences of the Koninklijke Nederlandse Akademie van Wetenschappen, Series B [Physical Sciences], 54 (1951), 30-41 [pdf link] = Circulars of the Astronomical Institute of the University of Amsterdam, nr. 2.
• van den Bergh, George, Regelmaat en wisseling bij zonsverduisteringen, met een aanhangsel over maansverduisteringen (Haarlem: H.D. Tjeenk Willink & Zoon N.V., 1951), 2 vols. [HathiTrust link].
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• van den Bergh, George, “Zichtbaarheid van totale maansverduisterings-tetraden”, Hemel en Dampkring, 51 (1953), 8-9.
• van den Bergh, George, “Merkwaardige opeenvolging van zonsverduisteringen”, Hemel en Dampkring, 52 (1954), 232-234.
• van den Bergh, George, Eclipses in the Second Millennium B.C. (–1600 to –1207) and how to Compute them in a Few Minutes (Haarlem: H.D. Tjeenk Willink & Zoon N.V., 1954) [HathiTrust link].
• Meeus, Jean, “Calcul de la grandeur maximum d’une éclipse partielle de soleil”, Ciel et Terre: Bulletin de la Société Belge d’Astronomie, de Météorologie et de Physique du Globe, 71 (1955), 415-425 [ADS link].
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• van den Bergh, George, Periodicity and Variation of Solar (and Lunar) Eclipses (Haarlem: H.D. Tjeenk Willink & Zoon N.V., 1955), 2 vols. [HathiTrust link].
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• van den Bergh, George, “De Hibbardina of “Halve Saros””, Hemel en Dampkring, 55 (1957), 101-103.
• Geneslay, Éloi Henri, “Le saros et la succession des éclipses”, L’Astronomie: Bulletin de la Société Astronomique de France et revue mensuelle d’astronomie, de météorologie et de physique du globe, 74 (1960), 329-335 [ADS link].
• Couderc, Paul, “Eclipses and their Sequences”, Leaflets of the Astronomical Society of the Pacific, 8 (1961), 263-270 [nr. 384] [ADS link].
• Meeus, Jean, “Is een niet-centrale ringvormig-totale zonsverduistering mogelijk?”, Hemel en Dampkring, 59 (1961), 18-24 – English version in Meeus (2002), chapter 19.
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• Meeus, Jean, “Quelques périodes de récurrence des éclipses”, Ciel et Terre: Bulletin de la Société Belge d’Astronomie, de Météorologie et de Physique du Globe, 78 (1962), 265-270 [ADS link].
• Meeus, Jean, “De halve Saros”, Hemel en Dampkring, 63 (1965), 141-143 – English version in Meeus (1997), chapter 18.
• Offroy, C., “Sur la périodicité des éclipses”, L’Astronomie: Bulletin de la Société Astronomique de France et revue mensuelle d’astronomie, de météorologie et de physique du globe, 79 (1966), 319-326 [ADS link].
• Smiley, Charles Hugh, “Solar Eclipse Intervals in the Dresden Codex”, The Journal of the Royal Astronomical Society of Canada, 59 (1965), 127-131 [ADS link].
• Sadler, Donald Harry, “Prediction of Eclipses”, Nature, 211 (1966), 1119-1121 [Nature link].
• Colton, R. & Martin, R.L., “Eclipse Cycles and Eclipses at Stonehenge”, Nature, 213 (1967), 476-478 [Nature link].
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• Können, Gunther P. & Meeus, Jean, “Periodicities of Eclipses”, The Journal of the Royal Astronomical Society of Canada, 70 (1976), 81-83 [ADS link].
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• Bao-Lin Liu, “On the Number of Lunar Eclipses in a Year”, Acta Astronomica Sinica, 21 (1980), 64 – in Chinese; English translation in Chinese Astronomy and Astrophysics, 5 (1981), 376 [ADS link].
• Hostetter, H. Clyde. “A 56-Year Eclipse Prediction System”, Archaeoastronomy: The Bulletin of The Center for Archaeoastronomy, Volume III, Number 2 (April-June 1980), 29-30.
• Kluepfel, Charles, “What Saros Number?”, Sky & Telescope, 70 (1985), 366-367 [ADS link / pdf link].
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• Perozzi, Ettore, Roy, Archie E., Steves, Bonnie A. & Valsecchi, Giovanni B., “Significant High Number Commensurabilities in the Main Lunar Problem. I: The Saros as a Near-Periodicity of the Moon’s Orbit”, Celestial Mechanics and Dynamical Astronomy, 52 (1991), 241-261 [ADS link].
• Steves, Bonnie A., Valsecchi, Giovanni B., Perozzi, Ettore & Roy, Archie E., “Significant High Number Commensurabilities in the Main Lunar Problem. II: The Occurrence of Saros-Like Near Periodicities”, Celestial Mechanics and Dynamical Astronomy, 57 (1993), 341-358 [ADS link].
• Kollerstrom, Nick, “A Reintroduction of Epicycles: Newton’s 1702 Lunar Theory and Halley’s Saros Correction”, Quarterly Journal of the Royal Astronomical Society, 36 (1995), 357-368 [ADS link].
• McNaughton, David L., “Eclipses during Ramadhan”, Journal of the British Astronomical Association, 105 (1995), 160 [ADS link].
• Cook, Alan, “Halley and the Saros”, Quarterly Journal of the Royal Astronomical Society, 37 (1996), 349-353 [ADS link].
• Cullen, Christopher, Astronomy and Mathematics in Ancient China: The Zhou bi suan jing (Cambridge: Cambridge University Press, 1996 [= Needham Research Institute Studies, nr. 1]).
• McNaughton, David L., “Eclipses during Ramaḍān”, Hamdard Islamicus: Quarterly Journal of Studies and Research in Islam, 19 (1996), No. 1, 81-86 [pdf link].
• Meeus, Jean, Mathematical Astronomy Morsels (Richmond: Willmann-Bell, 1997), chapters 8-18 & 22-24.
• Meeus, Jean, Astronomical Algorithms. Second Edition (Richmond: Willmann-Bell, 1998).
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• Steele, John M., “Eclipse Prediction in Mesopotamia”, Archive for History of Exact Sciences, 54 (2000), 421-454 [JSTOR link].
• Buus, Jens, “A Simple Estimate of the Relative Frequencies of Different Types of Solar Eclipses”, Journal of the British Astronomical Association, 112 (2002), 153-155 [ADS link].
• de Meis, Salvo, Eclipses: An Astronomical Introduction for Humanists (Rome: Istituto Italiano per l’Africa e l’Oriente, 2002 [= Serie Orientale Roma, vol. XCVI]).
• Meeus, Jean, More Mathematical Astronomy Morsels (Richmond: Willmann-Bell, 2002), chapters 8-25.
• Beard, Darren, “Why there cannot be Two Successive Pure Total Solar Eclipses”, The Journal of the British Astronomical Association, 113 (2003), 220-224 [ADS link].
• Meeus, Jean, “The Maximum Possible Duration of a Total Solar Eclipse”, Journal of the British Astronomical Association, 113 (2003), 343-348 [ADS link].
• Rawlings, Dennis, “Vast Eclipse Cycles: Stabilities & Gaps” DIO: The International Journal of Scientific History, 13 (2003), nr. 1, 12-18 [DIO link].
• Meeus, Jean, Mathematical Astronomy Morsels III (Richmond: Willmann-Bell, 2004), chapter 21.
• McCurdy, Bruce, “Orbital Oddities: Fading Foursome”, The Journal of the Royal Astronomical Society of Canada, 98 (2004), 202-206 [ADS link].
• Buus, Jens, “A New Type of Solar Eclipse”, Journal of the British Astronomical Association, 116 (2006) 333 [ADS link].
• Evans, James & Berggren, J. Lennart, Geminos’s Introduction to the Phenomena: A Translation and Study of a Hellenistic Survey of Astronomy (Princeton/Oxford: Princeton University Press, 2006) – chapter XVIII discusses the Exeligmos eclipse cycle.
• McCurdy, Bruce, “Orbital Oddities: Saros Subtleties I”, The Journal of the Royal Astronomical Society of Canada, 101 (2007), 168-170 [ADS link].
• Beard, Darren, “Total Penumbral Lunar Eclipses”, Journal of the British Astronomical Association, 118 (2008), 157-160 [ADS link].
• Beard, Darren & Meeus, Jean, “Interesting Patterns from Umbral Lunar Eclpses”, Journal of the British Astronomical Association, 119 (2009), 29-30 [ADS link].
• Sivin, Nathan, Granting the Seasons: The Chinese Astronomical Reform of 1280, With a Study of Its Many Dimensions and an Annotated Translation of Its Records (New York: Springer, 2009 [= Sources and Studies in the History of Mathematics and Physical Sciences, nr. ??]).
• McCurdy, Bruce, “Orbital Oddities: Saros Start”, The Journal of the Royal Astronomical Society of Canada, 105 (2011), 120-122 [ADS link].
• Nickiforov, Michael G., “On the Discovery of the Saros”, Bulgarian Astronomical Journal, 16 (2011), 72-90 [ADS link].
• West, Tony, “Isolated Total Lunar Eclipses”, Journal of the British Astronomical Association, 122 (2012) 227-228 [ADS link].
• Carman, Christián C. & Evans, James, “On the Epoch of the Antikythera Mechanism and its Eclipse Predictor”, Archive for History of Exact Sciences, 68 (2014), 693-774 [JSTOR link].
• West, Tony, “Central and Non-Central Total Lunar Eclipses”, Journal of the British Astronomical Association, 124 (2014) 35-37 [ADS link].
• Buus, Jens, “Latitude Dependency of the Maximum Duration of a Total Solar Eclipse”, Journal of the British Astronomical Association, 124 (2014) 151-153 [ADS link].
• Macdonald, Peter, “The Maximum Duration of a Total Solar Eclipse at Various Latitudes”, Journal of the British Astronomical Association, 124 (2014) 230 [ADS link].
• Fischetti, Mark M., “1,000 Years of Solar Eclipses”, Scientific American, 317 (2017), nr. 2, 62-65 [Scientific American link].
• Brown, Todd & Brown, Katrina, “Looking for Patterns in Eclipses: Saros Series”, The Physics Teacher, 56 (2018), 564-565 [doi link].
• Iwaniszewski, Stanislaw, “Remarks on the Lunar Series and Eclipse Cycles in Late Classic Maya Records”, in: E. Boutsikas, S.C. McCluskey & J. Steele (eds.), Advancing Cultural Astronomy: Studies In Honour of Clive Ruggles (Cham: Springer International Publishing, 2021), pp. 237-249 [ADS link].