Astronomical symbols

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Astronomical symbols are symbols used to represent various celestial objects, theoretical constructs and observational events in astronomy. The earliest forms of these symbols appear in Greek papyri of late antiquity. The Byzantine codices in which the Greek papyri were preserved continued and extended the inventory of astronomical symbols.[1][2] New symbols were further invented to represent many just-discovered planets and minor planets discovered in the 18th-20th centuries.

All these symbols were once commonly used by professional astronomers, amateur astronomers, and astrologers. While they are still commonly used in almanacs and astrological publications, their occurence in published research and texts on astronomy is relatively infrequent,[3] with some exceptions such as the Sun and Earth symbols appearing in astronomical constants, and certain zodiacal signs used to represent the solstices and equinoxes.

Contents

Symbols for the Sun and Moon

The use of astronomical symbols for the Sun and Moon dates to antiquity. The forms of the symbols that appear in the original papyri of Greek horoscopes are a circle with one ray () for the Sun and a crescent for the Moon.[2] The modern sun symbol, a circle with a dot (☉), first appeared in Europe in the Renaissance,[2] though it was also the ancient Chinese character for "sun", which gave rise to the modern character 日.[4]

In modern academic usage, the sun symbol is used for astronomical constants relating to the sun.[5] The luminosity, mass, and radius of stars are often represented using the corresponding solar constants as units of measurement.[6]

Sun
Name Symbol Unicode Unicode Display Symbol Represents
Sun [7][8][9] #x2609;
#9737;		 ☉ the Sun
[2] #x1f71a;
#128794;		 🜚 the Sun with one ray
[10][11] #x1f31e;
#127774;		 🌞 the face of the Sun

Moon
Name Symbol Unicode Unicode Display Symbol Represents
Moon, or first-quarter moon [12][13][14] #x263d;
#9789;		 ☽ an increscent moon
[10][15][16] #x1f31b;
#127771;		 🌛
full moon [13][14] #x1f315;
#127765;		 🌕
[10][15][16] #x1f31d;
#127773;		 🌝
Moon, or last-quarter moon [13][14] #x263e;
#9790;		 ☾ a decrescent moon
[10][15][16] #x1f31c;
#127772;		 🌜
new moon [13][14] #x1f311;
#127761;		 🌑
[10][15][16] #x1f31a;
#127770;		 🌚

Solar constants
Constant Symbol[6][17][18][19] Value
Solar luminosity L☉ 3.839×1026 W, or 3.839×1033 erg/s[20]
Solar mass M☉ 1.98892×1030 kg[6]
Solar radius R☉ 6.955×108 m [21][22]
Solar effective temperature Teff☉ 5777 K[23][24]

Symbols for the planets

Symbols for the classical planets appear in the medieval Byzantine codices in which many ancient horoscopes were preserved.[1] The written symbols for Mercury, Venus, Jupiter, and Saturn have been traced to forms found in late Greek papyri.[25] The symbols for Jupiter and Saturn are identified as monograms of the corresponding Greek names, and the symbol for Mercury is a stylized caduceus.[25] According to A. S. D. Maunder, antecedents of the planetary symbols were used in art to represent the gods associated with the classical planets; Bianchini's planisphere, produced in the 2nd century,[26] shows Greek personifications of planetary gods charged with early versions of the planetary symbols: Mercury has a caduceus; Venus has, attached to her necklace, a cord connected to another necklace; Mars, a spear; Jupiter, a staff; Saturn, a scythe; the Sun, a circlet with rays radiating from it; and the Moon, a headdress with a crescent attached.[27]

A diagram in Johannes Kamateros' 12th century Compendium of Astrology shows the Sun represented by the circle with a ray, Jupiter by the letter zeta (the initial of Zeus, Jupiter's counterpart in Greek mythology), Mars by a shield crossed by a spear, and the remaining classical planets by symbols resembling the modern ones, without the cross-mark seen in modern versions of the symbols. These cross-marks first appear around the 16th century. According to Maunder, the addition of crosses appears to be "an attempt to give a savour of Christianity to the symbols of the old pagan gods."[27]

The symbols for Uranus were created shortly after its discovery. One symbol, , invented by J. G. Köhler and refined by Bode, was intended to represent the newly discovered metal platinum; since platinum, commonly called white gold, was found by chemists mixed with iron, the symbol for platinum combines the alchemical symbols for iron, ♂, and gold, ☉.[28][29] Another symbol, , was suggested by Lalande in 1784. In a letter to Herschel, Lalande described it as "un globe surmonté par la première lettre de votre nom" ("a globe surmounted by the first letter of your name").[30]

Several symbols were proposed for Neptune to accompany the suggested names for the planet. Claiming the right to name his discovery, Le Verrier originally proposed the name Neptune[31] and the symbol of a trident,[32] while falsely stating that this had been officially approved by the French Bureau des Longitudes.[31] In October, he sought to name the planet Leverrier, after himself, and he had loyal support in this from the observatory director, François Arago,[33] who in turn proposed a new symbol for the planet ().[34] However, this suggestion met with stiff resistance outside France.[33] French almanacs quickly reintroduced the name Herschel for Uranus, after that planet's discoverer Sir William Herschel, and Leverrier for the new planet.[35] Professor James Pillans of the University of Edinburgh defended the name Janus for the new planet, and proposed a key for its symbol.[32] Meanwhile, Struve presented the name Neptune on December 29, 1846, to the Saint Petersburg Academy of Sciences.[36] In August 1847, the Bureau des Longitudes announced its decision to follow prevailing astronomical practice and adopt the choice of Neptune, with Arago refraining from participating in this decision.[37]

The International Astronomical Union discourages the use of these symbols in journal articles. In certain cases where planetary symbols might be used, such as in the headings of tables, the IAU Style Manual permits certain one- and (to disambiguate Mercury and Mars) two-letter abbreviations for the names of the planets.[38]

Planets
Name IAU
Abbrev.		 Symbol Unicode Unicode Display Symbol Interpretation
Mercury Me [7][8][39] #x263f;
#9791;		 ☿ Mercury's winged helmet and caduceus,[7] or the caduceus alone[12][39]
Venus V [7][8][39] #x2640;
#9792;		 ♀ Venus' hand mirror[7][12][39]
Earth E [7][8][39] #x1F728;
#128808;		 ⊕ Globe with equator and a meridian[7][39]
[8][12][13] #x2641;
#9793;		 ♁ a globus cruciger,[40] or an inverted symbol for Venus[12]
Mars Ma [7][8][39] #x2642;
#9794;		 ♂ Mars' shield and spear[7][12][39]
Jupiter J [7][8][39] #x2643;
#9795;		 ♃ Jupiter's thunderbolt,[12] an eagle,[7] or the letter zeta or Z for Zeus, the Greek god analogous to Jupiter[7][39]
Saturn S [7][8][39] #x2644;
#9796;		 ♄ Saturn's sickle or scythe[7][12][39]
Uranus U [28][29] #x26e2;
#9954;		 ⛢ Platinum[28][29]
[13][14][39] #x2645;
#9797;		 ♅ A globe surmounted by the letter H (for Herschel)[30]
Neptune N [7][8][14] #x2646;
#9798;		 ♆ Neptune's trident[7]
[34][39] A globe surmounted by the letters LV (for Le Verrier)[34][39]

Symbols for dwarf planets and asteroids

Following Giuseppe Piazzi's discovery of Ceres, a group of astronomers ratified the name, which Piazzi had proposed. At that time, the sickle was chosen as a symbol of the planet.[41]

The symbol for 2 Pallas, the spear of Pallas Athena, was invented by Baron Franz Xaver von Zach, and introduced in his Monatliche correspondenz zur beförderung der erd- und himmels-kunde.[42] In a letter to von Zach, discoverer Heinrich Wilhelm Matthäus Olbers (who had named the newly-discovered asteroid) expressed his approval of the proposed symbol, but wished that the handle of the sickle of Ceres had been adorned with a pommel instead of a crossbar, to better differentiate it from the sign of Venus.[42]

Karl Ludwig Harding created the symbol for 3 Juno. Harding, who discovered this asteroid, proposed the name Juno and the use of a scepter topped with a star as its astronomical symbol.[43]

The symbol for 4 Vesta was invented by German mathematician Carl Friedrich Gauss. Dr. Olbers, having previously discovered and named 2 Pallas, gave Gauss the honor of naming his newest discovery. Gauss decided to name the new asteroid for the goddess Vesta, and also designed the symbol ⚶ (): the altar of the goddess, with the sacred fire burning on it.[44][45] Other contemporaneous writers use a more elaborate symbol () instead.[46][47]

The next two asteroids, 5 Astraea and 6 Hebe, were both discovered by Karl Ludwig Hencke. Hencke requested that the symbol for 5 Astraea be an upside-down anchor;[48] however, a pair of balances was sometimes used instead.[9][49] Gauss named 6 Hebe at Hencke's request, and chose a wineglass as the symbol.[50][51]

As more new asteroids were discovered, astronomers continued to assign symbols to them. Thus, 7 Iris had for its symbol a rainbow with a star;[52] 8 Flora, a flower;[52] 9 Metis, an eye with a star;[53] 10 Hygiea, an upright snake with a star on its head;[54] 11 Parthenope, a standing fish with a star;[54] 12 Victoria, a star topped with a branch of laurel;[55] 13 Egeria, a buckler;[56] 14 Irene, a dove carrying an olive branch with a star on its head;[57] 15 Eunomia, a heart topped with a star;[58] 16 Psyche, a butterfly wing with a star;[59] 17 Thetis, a dolphin with a star;[60] 18 Melpomene, a dagger over a star;[61] and 19 Fortuna, a star over Fortuna's wheel.[61]

Johann Franz Encke made a major change in the Berliner Astronomisches Jahrbuch (BAJ, Berlin Astronomical Yearbook) for the year 1854, published in 1851. He introduced encircled numbers instead of symbols, although his numbering began with Astraea, the first four asteroids continuing to be denoted by their traditional symbols. This symbolic innovation was adopted very quickly by the astronomical community. The following year (1852), Astraea's number was bumped up to 5, but Ceres through Vesta would be listed by their numbers only in the 1867 edition. The circle later became a pair of parentheses, and the parentheses sometimes omitted altogether over the next few decades.[9]

A few asteroids were given symbols by their discoverers after the encircled-number notation became widespread. 26 Proserpina, 28 Bellona, 35 Leukothea, and 37 Fides, all discovered by R. Luther, were assigned, respectively, a pomegranate with a star inside;[62] a whip and spear;[63] an antique lighthouse;[64] and a cross.[65] 29 Amphitrite, discovered by Albert Marth, was assigned a shell for its symbol.[66]

Pluto's name and symbol were announced by the discoverers on May 1, 1930.[67] The symbol, a monogram of the letters PL, could be interpreted to stand for Pluto or for Percival Lowell, the astronomer who initiated Lowell Observatory's search for a planet beyond the orbit of Neptune.[7]

Dwarf planets
Name Symbol Unicode Unicode Display Symbol Represents
Ceres [9][13][39] #x26b3;
#9907;		 ⚳ a handle-down sickle;[39] cf. the handle-up sickle symbol of Saturn
Pluto [7][8] #x2647;
#9799;		 ♇ PL monogram for Pluto and Percival Lowell[7]

Asteroids
Name Symbol Unicode Unicode Display Symbol Represents
2 Pallas [42] #x26b4;
#9908;		 ⚴ a spear[42][49]
3 Juno [43][68] #x26b5;
#9909;		 ⚵ a scepter topped with a star[43]
[39][69]
4 Vesta [44] #x26B6;
#9910;		 ⚶ an altar with fire on it[44]
[9][49][69]
5 Astraea [48][49] an anchor[48]
[70] a pair of balances[39][49]
6 Hebe [50][71][72] a wineglass[50]
[9][39][49] #x1f377;
#127863;		 🍷
7 Iris [9][39] a rainbow with a star inside it[52]
8 Flora [9][49] #x2698;
#9880;		 ⚘ a flower[52]
9 Metis [9][39][49] an eye with a star above it[53]
10 Hygeia [54][61] a serpent with a star[54]
[9][49] #x2695;
#9877;		 ⚕ Rod of Asclepius
11 Parthenope [9][54] a fish with a star[54]
[70] a harp[49]
12 Victoria [9][49] a star with a branch of laurel[55]
13 Egeria [61] a buckler[56]
14 Irene [70] a dove carrying an olive-branch in its mouth and a star on its head[57]
15 Eunomia [9][49] a heart with a star on top[58]
16 Psyche [61] a butterfly's wing and a star[59]
17 Thetis [60] a dolphin and a star[60]
18 Melpomene [61] a dagger over a star[61]
19 Fortuna [61] a star over a wheel[61]
26 Proserpina [62] a pomegranate with a star inside it[62]
28 Bellona [63] Bellona's whip and spear[63]
29 Amphitrite [73] a shell[66]
35 Leukothea [64] an ancient lighthouse[64]
37 Fides [65] a cross[65][73]

Symbols for zodiac constellations and signs

The zodiac symbols have several astronomical interpretations. Depending on context, a zodiac symbol may denote a constellation, a sign, or a point on the ecliptic plane.

Lists of astronomical phenomena published by almanacs sometimes included conjunctions of stars and planets or the Moon; rather than print the full name of the star, a Greek letter and the symbol for the constellation of the star was sometimes used instead.[74][75] In modern academic usage, all the constellations, including the twelve of the zodiac, have dedicated three-letter abbreviations.[76]

In astronomy, a sign was a unit of arc measurement, now obsolete, equal to 30 degrees.[77][78] Ecliptic longitude was thus measured in signs, degrees, minutes, and seconds. The sign component of this measurement was expressed either with a number from 0 to 11[79] or with the corresponding zodiac symbol.[78]

The zodiac symbols are also sometimes used to represent points on the ecliptic, each symbol representing the "first point" of each sign. Thus, ♈ is the vernal equinox, ♋ is the summer solstice, etc.[80][81]

Zodiac
Name IAU
Abbrev.		 Signs Degrees Symbol Translation Unicode Display Unicode
Aries Ari 0 0° ram ♈ #x2648;
#9800;
Taurus Tau 1 30° bull ♉ #x2649;
#9801;
Gemini Gem 2 60° twins ♊ #x264a;
#9802;
Cancer Cnc 3 90° crab ♋ #x264b;
#9803;
Leo Leo 4 120° lion ♌ #x264c;
#9804;
Virgo Vir 5 150° virgin ♍ #x264d;
#9805;
Libra Lib 6 180° scale ♎ #x264e;
#9806;
Scorpius Sco 7 210° scorpion ♏ #x264f;
#9807;
Sagittarius Sgr 8 240° archer ♐ #x2650;
#9808;
Capricornus Cap 9 270° sea-goat ♑ #x2651;
#9809;
Aquarius Aqr 10 300° waterbearer ♒ #x2652;
#9810;
Pisces Psc 11 330° fish ♓ #x2653;
#9811;

Other symbols

Symbols for aspects and nodes appear in medieval texts, although medieval and modern usage of the node symbols differ; ☊ formerly stood for the descending node, and ☋ for the ascending node.[2] In describing the Keplerian elements of an orbit, ☊ is sometimes used to denote the ecliptic longitude of the ascending node, although it is more common to use Ω (capital omega), which was originally a typographical substitute for the old symbol.[82]

The symbols for aspects first appear in Byzantine codices.[2] Of the symbols for the five Ptolemaic aspects, only the three displayed here—for conjunction, opposition, and quadrature—are used in astronomy.[83]

Symbols for a comet (☄) and a star () have been used in published astronomical observations of comets. In tables of these observations, ☄ stood for the comet being discussed and for the star of comparison relative to which measurements of the comet's position were made.[84]

Other symbols
Name Symbol Unicode Unicode Display Symbol Represents
ascending node [8][13] #x260a;
#9738;		 ☊
descending node [8][13] #x260b;
#9739;		 ☋
conjunction [13][14] #x260c;
#9740;		 ☌
opposition [13][14] #x260d;
#9741;		 ☍
quadrature [13][14] #x25a1;
#9633;		 □
comet [13][73][84] #x2604;
#9732;		 ☄
star [13][73][84]

See also

References

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  51. ^ Steger, Franz (1847). Ergänzungs-conversationslexikon, Volume 3. p. 442. http://books.google.com/books?id=aZyhQWSEjhoC&pg=PA442. "Hofrath Gauß gab auf Hencke's Ansuchen diesem neuen Planetoiden den Namen Hebe mit dem Zeichen (ein Weinglas)." 
  52. ^ a b c d "Report of the Council to the Twenty-eighth Annual General Meeting". Monthly notices of the Royal Astronomical Society 8: 82. 1848. Bibcode 1848MNRAS...8...82.. http://books.google.com/books?id=GOA3AAAAMAAJ&pg=PA82. "The symbol adopted for [Iris] is a semicircle to represent the rainbow, with an interior star and a base line for the horizon....The symbol adopted for [Flora's] designation is the figure of a flower." 
  53. ^ a b >"Extract of a Letter from Mr. Graham". Monthly notices of the Royal Astronomical Society 8: 147. 1848. http://books.google.com/books?id=GOA3AAAAMAAJ&pg=PA147. "I trust, therefore, that astronomers will adopt this name [viz. Metis], with an eye and star for symbol." 
  54. ^ a b c d e f de Gasparis, Annibale (1850). "Letter to Mr. Hind, from Professor Annibale de Gasparis". Monthly notices of the Royal Astronomical Society 11: 1. Bibcode 1850MNRAS..11....1D. http://books.google.com/books?id=_uw3AAAAMAAJ&pg=RA1-PA1. "The symbol of Hygeia is a serpent (like a Greek ζ) crowned with a star. That of Parthenope is a fish crowned with a star." 
  55. ^ a b Hind (1850). "Letter from Mr. Hind". Monthly notices of the Royal Astronomical Society 11: 2. Bibcode 1850MNRAS..11....2H. http://books.google.com/books?id=87cRAAAAYAAJ&pg=RA1-PA2. "I have called the new planet Victoria, for which I have devised, as a symbol, a star and laurel branch, emblematic of the Goddess of Victory." 
  56. ^ a b (France), Académie des Sciences (1851). "Correspondance". Comptes rendus des séances de l'Académie des sciences 32: 224. http://books.google.com/books?id=eXcbAAAAMAAJ&pg=RA1-PA244. "M. De Gasparis adresse ses remerciments à l'Académie, qui lui a décerné, dans la séance solennelle du 16 décembre 1850, deux des médailles de la fondation Lalande, pour la découverte des planètes Hygie, Parthénope et Egérie. M. de Gasparis annonce qu'il a choisi, pour symbole de cette dernière planète, la figure d'un bouclier." 
  57. ^ a b Hind (1851). "On the Discovery of a Fourth New Planet, at Mr. Bishop's Observatory, Regent's Park". Monthly notices of the Royal Astronomical Society 11: 171. http://books.google.com/books?id=87cRAAAAYAAJ&pg=RA1-PA171. "Sir John Herschel, who kindly undertook the selection of a name for this, the fourteenth member of the ultra-zodiacal group, has suggested Irene as one suitable to the present time, the symbol to be a dove carrying an olive-branch with a star on the head; and since the announcement of this name, I have been gratified in receiving from all quarters the most unqualified expressions of approbation." 
  58. ^ a b de Gasparis, Annibale (1851). "Beobachtungen und Elemente der Eunomia". Astronomische Nachrichten: 174. http://books.google.com/books?id=D6EEAAAAQAAJ&pg=RA2-PA174. "J'ai proposé le nom Eunomia pour la nouvelle planète. Le symbole serait un coeur surmonté d'une étoile." 
  59. ^ a b Sonntag, A. (1852). "Elemente und Ephemeride der Psyche". Astronomische Nachrichten 34 (20): 283. Bibcode 1852AN.....34..283.. doi:10.1002/asna.18520342010. http://books.google.com/books?id=fWM_AAAAcAAJ&pg=PA283. "(in a footnote) Herr Professor de Gasparis schreibt mir, in Bezug auf den von ihm März 17 entdeckten neuen Planeten: "J'ai proposé, avec l'approbation de Mr. Hind, le nom de Psyché pour la nouvelle planète, ayant pour symbole une aile de papillon surmontée d'une étoile."" 
  60. ^ a b c Luther, R. (1852). "Beobachtungen der Thetis auf der Bilker Sternwarte". Astronomische Nachrichten 34 (16): 243–244. doi:10.1002/asna.18520341606. http://books.google.com/books?id=fWM_AAAAcAAJ&pg=PA243. "Herr Director Argelander in Bonn, welcher der hiesigen Sternwarte schon seit längerer Zeit seinen Schutz und Beistand zu Theil werden lässt, hat die Entdeckung des April-Planeten zuerst constatirt und mir bei dieser Gelegenheit dasür den Namen Thetis und das Zeichen [symbol pictured] vorgeschlagen, wodurch der der silberfüssigen Göttinn geheiligte Delphin angedeutet wird. Indem ich mich hiermit einverstanden erkläre, ersuche ich die sämmtlichen Herren Astronomen, diesen Namen und dieses Zeichen annehmen und beibehalten zu wollen." 
  61. ^ a b c d e f g h i Hind, J. R. (1852). An astronomical vocabulary. pp. v. http://books.google.com/books?id=_DgDAAAAQAAJ&pg=PR5. 
  62. ^ a b c Luther, R. (1853). "Beobachtungen des neuesten Planeten auf der Bilker Sternwarte". Astronomische Nachrichten 36 (24): 349–350. doi:10.1002/asna.18530362403. http://books.google.com/books?id=o2M_AAAAcAAJ&pg=RA1-PA37. 
  63. ^ a b c Encke, J. F. (1854). "Beobachtung der Bellona, nebst Nachrichten über die Bilker Sternwarte". Astronomische Nachrichten 38 (9): 143. doi:10.1002/asna.18540380907. http://books.google.com/books?id=1mM_AAAAcAAJ&pg=PA19-IA6128. 
  64. ^ a b c Rümker, G. (1855). "Name und Zeichen des von Herrn R. Luther zu Bilk am 19. April entdeckten Planeten". Astronomische Nachrichten 40 (24): 373. doi:10.1002/asna.18550402405. http://books.google.com/books?id=_GM_AAAAcAAJ&pg=PA59. 
  65. ^ a b c Luther, R. (1856). "Schreiben des Herrn Dr. R. Luther, Directors der Sternwarte zu Bilk, an den Herausgeber". Astronomische Nachrichten 42 (7): 107. Bibcode 1855AN.....42..107L. doi:10.1002/asna.18550420705. http://books.google.com/books?id=1KEEAAAAQAAJ&pg=RA1-PA107. 
  66. ^ a b Marth, A. (1854). "Elemente und Ephemeride des Marz 1 in London entdeckten Planeten Amphitrite". Astronomische Nachrichten 38 (11): 167. doi:10.1002/asna.18540381103. http://books.google.com/books?id=1mM_AAAAcAAJ&pg=PA19-IA73. 
  67. ^ Chambers, George Frederick (1877). A handbook of descriptive astronomy. Clarendon Press. pp. 920–921. ISBN 1108014755. http://books.google.com/books?id=n8sJAAAAMAAJ&pg=PA920. 
  68. ^ a b Olmsted, Dennis (1855). Letters on astronomy. Harper. p. 288. http://books.google.com/books?id=BYoXAAAAYAAJ&pg=PA288. 
  69. ^ a b c Wilson, John (1899). A treatise on English punctuation. p. 302. ISBN 1425536425. http://books.google.com/books?id=oIICAAAAYAAJ&pg=PA302. 
  70. ^ Hencke, Karl Ludwig (1847). "Schreiben des Herrn Hencke an den Herausgeber". Astronomische Nachrichten (610): 155-156. http://books.google.com/books?id=-qAEAAAAQAAJ&pg=RA2-PA157. 
  71. ^ Austria: Oesterreichischer Universal-Kalender für das gemeine Jahr 1849.. 1849. p. xxxix. http://books.google.com/books?id=6H0AAAAAcAAJ&pg=PR63. 
  72. ^ a b c d Webster, Noah; Goodrich, Chauncey Allen (1884). Webster's Complete Dictionary of the English Language. p. 1780. http://books.google.com/books?id=ql4IAAAAQAAJ&pg=PA1780. 
  73. ^ Admiralty, T.H.E. Board O.F. (1831). The Nautical Almanac and Astronomical Ephemeris for the Year 1833. p. 1. http://books.google.com/books?id=3fMNAAAAQAAJ&pg=PR1. 
  74. ^ The American Almanac and Repository of Useful Knowledge, for the Year 1835. 1834. p. 47. http://books.google.com/books?id=P3QFAAAAQAAJ&pg=PA47. 
  75. ^ The IAU Style Manual. 1989. p. 34. http://www.iau.org/static/publications/stylemanual1989.pdf. 
  76. ^ Encyclopædia Britannica, Edition 6. 3. 1823. p. 155. http://books.google.com/books?id=a8QnAAAAMAAJ&pg=PA155. "...observe, that 60 seconds make a minute, 60 minutes make a degree, 30 degrees make a sign, and 12 signs make a circle." 
  77. ^ a b Joyce, Jeremiah (1866). Scientific dialogues for the instruction and entertainment of young people. p. 109. ISBN 1145492444. http://books.google.com/books?id=h8AAAAAAMAAJ&pg=PA109. 
  78. ^ The Nautical Alamanac and the Astronomical Ephemeris for the year 1834. 1833. p. xiii. http://books.google.com/books?id=Bf8NAAAAQAAJ&pg=PR13.  The 1834 edition of the Nautical Almanac and Astronomical Ephemeris abandoned the use of numerical signs (among other innovations); compare the representation of (ecliptic) longitude in the editions for the years 1834 and 1833.
  79. ^ Roy, Archie E.; David, Clarke (2003). Astronomy: principles and practice. p. 73. ISBN 9780750309172. http://books.google.com/books?id=v2S6XV8dsIAC&pg=PA73. 
  80. ^ King-Hele, Desmond (1992). A tapestry of orbits. p. 16. ISBN 9780521393232. http://books.google.com/books?id=hiPuoBZBpRwC&pg=PA16. 
  81. ^ Covington, Michael A. (2002). Celestial objects for modern telescopes, volume 2. pp. 77–78. 
  82. ^ Ridpath, John Clark, ed (1897). The standard American encyclopedia, volume 1. p. 198. http://books.google.com/books?id=1GMMAAAAYAAJ&pg=PA198. 
  83. ^ a b c Tupman, G. L. (1877). "Observations of Comet I 1877". Astronomische Nachrichten 89 (11): 169–170. Bibcode 1877AN.....89..169T. doi:10.1002/asna.18770891103. http://books.google.com/books?id=46MEAAAAQAAJ&pg=PA67. Retrieved 2011-03-24.