Eclipse Cycles

• Introduction
• List of Eclipse Cycles
• References

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.

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 Johann H. Lambert in 1765 and rediscovered at the end of the 19th century (first mentioned by von Oppolzer in 1881 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 can be 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.

Double Saros

???

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).

Triad (Triple Inex)

???

Quarter Palmen Cycle

???

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??).

Triple Basic Period

???

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].
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• 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].
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• 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].
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• 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].
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• 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].
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