Procyon

The position of Procyon
Observation data
Epoch J2000      Equinox J2000
Constellation Canis Minor
Pronunciation /ˈproʊsi.ɒn/ PROH-see-on[1]
Right ascension 07h 39m 18.11950s[2]
Declination +05° 13′ 29.9552″[2]
Apparent magnitude (V) 0.34[3] (A) / 10.7[4] (B)
Characteristics
Spectral type F5 IV–V[3] + DQZ[5]
U−B color index +0.00[6]
B−V color index +0.42[6]
Variable type suspected[7] (A)
Astrometry
Radial velocity (Rv)−3.2[8] km/s
Proper motion (μ) RA: −714.590[2] mas/yr
Dec.: −1036.80[2] mas/yr
Parallax (π)284.56 ± 1.26 mas[2]
Distance11.46 ± 0.05 ly
(3.51 ± 0.02 pc)
Absolute magnitude (MV)2.66/13.0[4]
Details
Procyon A
Mass1.499±0.031[9] M☉
Radius2.048±0.025[3] R☉
Luminosity6.93[3] L☉
Surface gravity (log g)3.96[3] cgs
Temperature6,530±50[3] K
Metallicity [Fe/H]−0.05±0.03[3] dex
Rotation23 days[10]
Rotational velocity (v sin i)3.16±0.50[3] km/s
Age1.87±0.13[9] Gyr
Procyon B
Mass0.602±0.015[5] M☉
Radius0.01234±0.00032[5] R☉
Luminosity0.00049[11] L☉
Surface gravity (log g)8.0[5] cgs
Temperature7,740±50[5] K
Age1.37[11] Gyr
Orbit[12]
CompanionProcyon B
Period (P)40.840 ± 0.022 yr
Semi-major axis (a)4.3075 ± 0.0016″
Eccentricity (e)0.39785 ± 0.00025
Inclination (i)31.408 ± 0.050°
Longitude of the node (Ω)100.683 ± 0.095°
Periastron epoch (T)1,968.076 ± 0.023
Argument of periastron (ω)
(secondary)		89.23 ± 0.11°
Other designations
Elgomaisa[13], α Canis Minoris, 10 Canis Minoris, BD+05°1739, GJ 280, HD 61421, HIP 37279, HR 2943, SAO 115756, LHS 233[14]
Database references
SIMBADThe system
A
B

Procyon (/ˈproʊsi.ɒn/)[15] is the brightest star in the constellation of Canis Minor and usually the eighth-brightest star in the night sky, with an apparent visual magnitude of 0.34.[3] It has the Bayer designation α Canis Minoris, which is Latinized to Alpha Canis Minoris, and abbreviated α CMi or Alpha CMi, respectively. As determined by the European Space Agency Hipparcos astrometry satellite,[16] this system lies at a distance of just 11.46 light-years (3.51 parsecs),[2] and is therefore one of Earth's nearest stellar neighbors.

A binary star system, Procyon consists of a white-hued main-sequence star of spectral type F5 IV–V, designated component A, in orbit with a faint white dwarf companion of spectral type DQZ,[5] named Procyon B. The pair orbit each other with a period of 40.84 years and an eccentricity of 0.4.

Observation

Procyon (top left), Betelgeuse (top right) and Sirius (bottom) form the Winter Triangle. Orion is to the right. Viewed from Northern Hemisphere

Procyon is usually the eighth-brightest star in the night sky, culminating at midnight on 14 January.[17] It forms one of the three vertices of the Winter Triangle asterism, in combination with Sirius and Betelgeuse.[18] The prime period for evening viewing of Procyon is in late winter in the Northern Hemisphere.[17]

It has a color index of 0.42, and its hue has been described as having a faint yellow tinge to it.[18]

Stellar system

Procyon is a binary star system with a bright primary component, Procyon A, having an apparent magnitude of 0.34,[3] and a faint companion, Procyon B, at magnitude 10.7.[4] The pair orbit each other with a period of 40.84 years along an elliptical orbit with an eccentricity of 0.4,[12] more eccentric than Mercury's. The plane of their orbit is inclined at an angle of 31.1° to the line of sight with the Earth.[19] The average separation of the two components is 15.0 AU, a little less than the distance between Uranus and the Sun, though the eccentric orbit carries them as close as 8.9 AU and as far as 21.0 AU.[20]

Procyon A

The primary has a stellar classification of F5IV–V, indicating that it is a late-stage F-type main-sequence star. Procyon A is bright for its spectral class, suggesting that it is evolving into a subgiant that has nearly fused its hydrogen core into helium, after which it will expand as the nuclear reactions move outside the core.[3] As it continues to expand, the star will eventually swell to about 80 to 150 times its current diameter and become a red or orange color. This will probably happen within 10 to 100 million years.[21]

The effective temperature of the stellar atmosphere is an estimated 6,530 K,[3] giving Procyon A a white hue. It is 1.5 times the solar mass (M☉), twice the solar radius (R☉), and has seven times the Sun's luminosity (L☉).[3][22] Both the core and the envelope of this star are convective; the two regions being separated by a wide radiation zone.[9]

Oscillations

In late June 2004, Canada's orbital MOST satellite telescope carried out a 32-day survey of Procyon A. The continuous optical monitoring was intended to confirm solar-like oscillations in its brightness observed from Earth and to permit asteroseismology. No oscillations were detected and the authors concluded that the theory of stellar oscillations may need to be reconsidered.[23] However, others argued that the non-detection was consistent with published ground-based radial velocity observations of solar-like oscillations.[24][25] Subsequent observations in radial velocity have confirmed that Procyon is indeed oscillating.[26][27]

Photometric measurements from the NASA Wide Field Infrared Explorer (WIRE) satellite from 1999 and 2000 showed evidence of granulation (convection near the surface of the star) and solar-like oscillations.[28] Unlike the MOST result, the variation seen in the WIRE photometry was in agreement with radial velocity measurements from the ground. Additional observations with MOST taken in 2007 were able to detect oscillations.[29]

Procyon B

Orbit of Procyon B seen from above its plane

Like Sirius B, Procyon B is a white dwarf that was inferred from astrometric data long before it was observed. Its existence had been postulated by German astronomer Friedrich Bessel as early as 1844, and, although its orbital elements had been calculated by his countryman Arthur Auwers in 1862 as part of his thesis,[30] Procyon B was not visually confirmed until 1896 when John Martin Schaeberle observed it at the predicted position using the 36-inch refractor at Lick Observatory.[31] It is more difficult to observe from Earth than Sirius B, due to a greater apparent magnitude difference and smaller angular separation from its primary.[20]

At 0.6 M☉, Procyon B is considerably less massive than Sirius B; however, the peculiarities of degenerate matter ensure that it is larger than its more famous neighbor, with an estimated radius of 8,600 km, versus 5,800 km for Sirius B.[5][32] The radius agrees with white dwarf models that assume a carbon core.[5] It has a stellar classification of DQZ,[5] having a helium-dominated atmosphere with traces of heavy elements. For reasons that remain unclear, the mass of Procyon B is unusually low for a white dwarf star of its type.[9] With a surface temperature of 7740 K, it is also much cooler than Sirius B; this is a testament to its lesser mass and greater age. The mass of the progenitor star for Procyon B was about 2.59+0.22
−0.18 M☉ and it came to the end of its life some 1.19±0.11 billion years ago, after a main-sequence lifetime of 680±170 million years.[9]

X-ray emission

Attempts to detect X-ray emission from Procyon with nonimaging, soft X-ray-sensitive detectors prior to 1975 failed.[33] Extensive observations of Procyon were carried out with the Copernicus and TD-1A satellites in the late 1970s.[34] The X-ray source associated with Procyon AB was observed on 1 April 1979, with the Einstein Observatory high-resolution imager (HRI).[35] The HRI X-ray pointlike source location is ~4″ south of Procyon A, on the edge of the 90% confidence error circle, indicating identification with Procyon A rather than Procyon B which was located about 5″ north of Procyon A (about 9″ from the X-ray source location).[34]

Etymology and cultural significance

α Canis Minoris (Latinized to Alpha Canis Minoris) is the star's Bayer designation.

The name Procyon comes from the Ancient Greek Προκύων (Prokyon), meaning "before the dog", since it precedes the "Dog Star" Sirius as it travels across the sky due to Earth's rotation. (Although Procyon has a greater right ascension, it also has a more northerly declination, which means it will rise above the horizon earlier than Sirius from most northerly latitudes.) In Greek mythology, Procyon is associated with Maera, a hound belonging to Erigone, daughter of Icarius of Athens.[36] In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN)[37] to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016[38] included a table of the first two batches of names approved by the WGSN; which included Procyon for the star α Canis Minoris A.

The two dog stars are referred to in the most ancient literature and were venerated by the Babylonians and the Egyptians, In Babylonian mythology, Procyon was known as Nangar (the Carpenter), an aspect of Marduk, involved in constructing and organizing the celestial sky.[39]

The constellations in Macedonian folklore represented agricultural items and animals, reflecting their village way of life. To them, Procyon and Sirius were Volci "the wolves", circling hungrily around Orion which depicted a plough with oxen.[40]

Rarer names are the Latin translation of Procyon, Antecanis, and the Arabic-derived names Al Shira and Elgomaisa. Medieval astrolabes of England and Western Europe used a variant of this, Algomeiza/Algomeyza.[41] Al Shira derives from الشعرى الشامية aš-ši‘ra aš-šamiyah, "the Syrian sign" (the other sign being Sirius; "Syria" is supposedly a reference to its northern location relative to Sirius); Elgomaisa derives from الغميصاء al-ghumaisa’ "the bleary-eyed (woman)", in contrast to العبور "the teary-eyed (woman)", which is Sirius. (See Gomeisa.)

In Chinese, 南河 (Nán Hé), meaning South River, refers to an asterism consisting of Procyon, ε Canis Minoris and β Canis Minoris.[42] Consequently, Procyon itself is known as 南河三 (Nán Hé sān, the Third Star of South River).[43] It is part of the Vermilion Bird.

The Hawaiians see Procyon as part of an asterism Ke ka o Makali'i ("the canoe bailer of Makali'i") that helps them navigate at sea.[44] In Hawaiian language, this star is called Puana ("blossom"), which is a new Hawaiian name based on the Māori name Puangahori. It forms this asterism (Ke ka o Makali'i) with the Pleiades (Makali'i), Auriga, Orion, Capella, Sirius, Castor and Pollux.[45] In Tahitian lore, Procyon was one of the pillars propping up the sky, known as Anâ-tahu'a-vahine-o-toa-te-manava ("star-the-priestess-of-brave-heart"), the pillar for elocution.[46] Māori astronomers know the star as Puangahori ("False Puanga") which distinguishes it from its pair Puanga or Puanga-rua ("Blossom-cluster") which refers to a star of great importance to Māori culture and calendar, known by its western name Rigel.[47]

Procyon appears on the flag of Brazil, symbolizing the state of Amazonas.[48] The Kalapalo people of Mato Grosso state in Brazil call Procyon and Canopus Kofongo ("Duck"), with Castor and Pollux representing his hands. The asterism's appearance signified the coming of the rainy season and increase in food staple manioc, used at feasts to feed guests.[49]

Known as Sikuliarsiujuittuq to the Inuit, Procyon was quite significant in their astronomy and mythology. Its eponymous name means "the one who never goes onto the newly formed sea ice", and refers to a man who stole food from his village's hunters because he was too obese to hunt on ice. He was killed by the other hunters who convinced him to go on the sea ice. Procyon received this designation because it typically appears red (though sometimes slightly greenish) as it rises during the Arctic winter; this red color was associated with Sikuliarsiujuittuq's bloody end.[50]

View from this system

Were Sol to be observed from this star system, it would appear to be a magnitude 2.55 star in the constellation Aquila with the exact opposite coordinates at right ascension 19h 39m 18.11950s, declination −05° 13′ 29.9552″. It would be as bright as β Scorpii is in our sky. Canis Minor would obviously be missing its brightest star.

Procyon's closest neighboring star is Luyten's Star, about 1.12 light-years (0.34 parsecs) away.[51] Procyon would be the brightest star in the night sky of an exoplanet orbiting Luyten's Star, with an apparent magnitude of -4.68.[lower-alpha 1]

See also

Notes

  1. ↑ The absolute magnitude Mv of Procyon is 2.66, so the apparent magnitude m is given by 2.66 − 5 + (5*log10(0.34)) = -4.68.[52]

References

  1. ↑ "Procyon". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  2. 1 2 3 4 5 6 van Leeuwen, F. (November 2007), "Validation of the new Hipparcos reduction", Astronomy and Astrophysics, 474 (2): 653–664, arXiv:0708.1752, Bibcode:2007A&A...474..653V, doi:10.1051/0004-6361:20078357, S2CID 18759600
  3. 1 2 3 4 5 6 7 8 9 10 11 12 13 Kervella, P.; et al. (January 2004), "The diameter and evolutionary state of Procyon A. Multi-technique modeling using asteroseismic and interferometric constraints", Astronomy and Astrophysics, 413 (1): 251–256, arXiv:astro-ph/0309148, Bibcode:2004A&A...413..251K, doi:10.1051/0004-6361:20031527, S2CID 8840932
  4. 1 2 3 Schroeder, Daniel J.; Golimowski, David A.; Brukardt, Ryan A.; Burrows, Christopher J.; Caldwell, John J.; Fastie, William G.; Ford, Holland C.; Hesman, Brigette; Kletskin, Ilona; Krist, John E.; Royle, Patricia; Zubrowski, Richard. A. (February 2000), "A Search for Faint Companions to Nearby Stars Using the Wide Field Planetary Camera 2", The Astronomical Journal, 119 (2): 906–922, Bibcode:2000AJ....119..906S, doi:10.1086/301227
  5. 1 2 3 4 5 6 7 8 9 Provencal, J. L.; et al. (2002), "Procyon B: Outside the Iron Box", The Astrophysical Journal, 568 (1): 324–334, Bibcode:2002ApJ...568..324P, doi:10.1086/338769
  6. 1 2 Mermilliod, J.-C (1986). "Compilation of Eggen's UBV data, transformed to UBV (unpublished)". Catalogue of Eggen's UBV Data. Bibcode:1986EgUBV........0M.
  7. ↑ Samus, N. N.; Durlevich, O. V.; et al. (2009). "VizieR Online Data Catalog: General Catalogue of Variable Stars (Samus+ 2007–2013)". VizieR On-line Data Catalog: B/GCVS. Originally Published in: 2009yCat....102025S. 1: 02025. Bibcode:2009yCat....102025S.
  8. ↑ Wilson, Ralph Elmer (1953). "General catalogue of stellar radial velocities". Washington. Bibcode:1953GCRV..C......0W.
  9. 1 2 3 4 5 Liebert, James; et al. (May 2013), "The Age and Stellar Parameters of the Procyon Binary System", The Astrophysical Journal, 769 (1): 10, arXiv:1305.0587, Bibcode:2013ApJ...769....7L, doi:10.1088/0004-637X/769/1/7, S2CID 118473397, 7
  10. ↑ Koncewicz, R.; Jordan, C. (January 2007), "OI line emission in cool stars: calculations using partial redistribution", Monthly Notices of the Royal Astronomical Society, 374 (1): 220–231, Bibcode:2007MNRAS.374..220K, doi:10.1111/j.1365-2966.2006.11130.x
  11. 1 2 Giammichele, N.; Bergeron, P.; Dufour, P. (April 2012), "Know Your Neighborhood: A Detailed Model Atmosphere Analysis of Nearby White Dwarfs", The Astrophysical Journal Supplement, 199 (2): 29, arXiv:1202.5581, Bibcode:2012ApJS..199...29G, doi:10.1088/0067-0049/199/2/29, S2CID 118304737 Age is for the white dwarf stage.
  12. 1 2 Bond, Howard E.; et al. (November 2015), "Hubble Space Telescope Astrometry of the Procyon System", The Astrophysical Journal, 813 (2): 19, arXiv:1510.00485, Bibcode:2015ApJ...813..106B, doi:10.1088/0004-637X/813/2/106, S2CID 55163606, 106
  13. ↑ von Littrow, Karl (1866). J. J. von Littrow's Atlas des gestirnten Himmels für Freunde der Astronomie (in German). Stuttgart: Gustav Weise. p. 9.
  14. ↑ "PROCYON AB -- Spectroscopic binary", SIMBAD, Centre de Données astronomiques de Strasbourg, retrieved 23 November 2011
  15. ↑ Kunitzsch, Paul; Smart, Tim (2006). A Dictionary of Modern star Names: A Short Guide to 254 Star Names and Their Derivations (2nd rev. ed.). Cambridge, Massachusetts: Sky Pub. ISBN 978-1-931559-44-7.
  16. ↑ Perryman, Michael (2010), The Making of History's Greatest Star Map (PDF), Astronomers’ Universe, Heidelberg: Springer-Verlag, Bibcode:2010mhgs.book.....P, doi:10.1007/978-3-642-11602-5, ISBN 978-3-642-11601-8
  17. 1 2 Schaaf 2008, p. 257.
  18. 1 2 Schaaf 2008, p. 166.
  19. ↑ Girard, T. M.; et al. (May 2000), "A Redetermination of the Mass of Procyon", The Astronomical Journal, 119 (5): 2428–2436, Bibcode:2000AJ....119.2428G, doi:10.1086/301353
  20. 1 2 Kaler, James B., "Procyon", Stars, University of Illinois, retrieved 23 November 2011
  21. ↑ Schaaf 2008, p. 168.
  22. ↑ Gatewood, G.; Han, I. (February 2006), "An Astrometric Study of Procyon", Astronomical Journal, 131 (2): 1015–1021, Bibcode:2006AJ....131.1015G, doi:10.1086/498894
  23. ↑ Matthews, Jaymie M.; et al. (2004), "No stellar p-mode oscillations in space-based photometry of Procyon", Nature, 430 (921): 51–3, Bibcode:2004Natur.430...51M, doi:10.1038/nature02671, PMID 15229593, S2CID 4420705
  24. ↑ Bouchy, François; et al. (2004), "Brief Communications Arising: Oscillations on the star Procyon", Nature, 432 (7015): 2, arXiv:astro-ph/0510303, Bibcode:2004Natur.432....2B, doi:10.1038/nature03165, PMID 15568216, S2CID 593117
  25. ↑ Bedding, T. R.; et al. (2005), "The non-detection of oscillations in Procyon by MOST: Is it really a surprise?", Astronomy and Astrophysics, 432 (2): L43, arXiv:astro-ph/0501662, Bibcode:2005A&A...432L..43B, doi:10.1051/0004-6361:200500019, S2CID 53350078
  26. ↑ Arentoft, Torben; et al. (2008). "A Multisite Campaign to Measure Solar-like Oscillations in Procyon. I. Observations, Data Reduction, and Slow Variations". The Astrophysical Journal. 687 (2): 1180–1190. arXiv:0807.3794. Bibcode:2008ApJ...687.1180A. doi:10.1086/592040. hdl:2152/34819. S2CID 15693672.
  27. ↑ Bedding, Timothy R.; et al. (2010). "A Multi-Site Campaign to Measure Solar-Like Oscillations in Procyon. Ii. Mode Frequencies". The Astrophysical Journal. 713 (2): 935–949. arXiv:1003.0052. Bibcode:2010ApJ...713..935B. doi:10.1088/0004-637X/713/2/935. hdl:2152/34818. S2CID 118470468.
  28. ↑ Bruntt, H.; et al. (2005), "Evidence for Granulation and Oscillations in Procyon from Photometry with the WIRE Satellite", The Astrophysical Journal, 633 (1): 440–446, arXiv:astro-ph/0504469, Bibcode:2005ApJ...633..440B, doi:10.1086/462401, S2CID 1812152
  29. ↑ Huber, Daniel; et al. (2011). "Solar-like Oscillations and Activity in Procyon: A Comparison of the 2007 MOST and Ground-based Radial Velocity Campaigns". The Astrophysical Journal. 731 (2): 94. arXiv:1102.2894. Bibcode:2011ApJ...731...94H. doi:10.1088/0004-637X/731/2/94. S2CID 56123076.
  30. ↑ Auwers, Arthur (1868), "Untersuchungen uber veranderliche eigenbewegungen", Leipzig (in German), Leipzig: W. Engelmann, Bibcode:1868uuve.book.....A
  31. ↑ Burnham Jr., Robert (1978), Burnham's Celestial Handbook, vol. 1, New York: Dover Publications Inc., p. 450, ISBN 0-486-23567-X
  32. ↑ Holberg, J. B.; et al. (2 April 1998), "Sirius B: A New, More Accurate View", The Astrophysical Journal, 497 (2): 935–942, Bibcode:1998ApJ...497..935H, doi:10.1086/305489
  33. ↑ Mewe, R.; et al. (1 December 1975), "Detection of X-ray emission from stellar coronae with ANS", Astrophysical Journal Letters, 202: L67–L71, Bibcode:1975ApJ...202L..67M, doi:10.1086/181983
  34. 1 2 Schmitt, J. H. M. M.; et al. (15 January 1985), "The X-ray corona of Procyon", Astrophysical Journal, Part 1, 288: 751–755, Bibcode:1985ApJ...288..751S, doi:10.1086/162843
  35. ↑ Giacconi, R.; et al. (1979), "The Einstein /HEAO 2/ X-ray Observatory", Astrophysical Journal, 230: 540–550, Bibcode:1979ApJ...230..540G, doi:10.1086/157110, S2CID 120943949
  36. ↑ Wendy Doniger, ed. (1999), "Erigone", Merriam-Webster's encyclopedia of world religions, Merriam-Webster, p. 333, ISBN 0-87779-044-2
  37. ↑ "IAU Working Group on Star Names (WGSN)". Retrieved 22 May 2016.
  38. ↑ "Bulletin of the IAU Working Group on Star Names, No. 1" (PDF). Retrieved 28 July 2016.
  39. ↑ Kelley, David H.; Milone, Eugene F.; Aveni, A. F. (2011). Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy. New York City: Springer. p. 217. ISBN 978-1441976239.
  40. ↑ Cenev, Gjore (2008). "Macedonian Folk Constellations". Publications of the Astronomical Observatory of Belgrade. 85: 97–109. Bibcode:2008POBeo..85...97C.
  41. ↑ Gingerich, O. (1987). "Zoomorphic Astrolabes and the Introduction of Arabic Star Names into Europe". Annals of the New York Academy of Sciences. 500 (1): 89–104. Bibcode:1987NYASA.500...89G. doi:10.1111/j.1749-6632.1987.tb37197.x. S2CID 84102853.
  42. ↑ (in Chinese) 中國星座神話, written by 陳久金. Published by 台灣書房出版有限公司, 2005, ISBN 978-986-7332-25-7.
  43. ↑ (in Chinese) 香港太空館 – 研究資源 – 亮星中英對照表 Archived 30 January 2011 at the Wayback Machine, Hong Kong Space Museum. Accessed on line 23 November 2010.
  44. ↑ "Hawaiian Star Lines". archive.hokulea.com. Retrieved 21 October 2020.
  45. ↑ Brosch, Noah (2008). Sirius Matters. Springer. p. 46. ISBN 978-1-4020-8318-1.
  46. ↑ Henry, Teuira (1907). "Tahitian Astronomy: Birth of Heavenly Bodies". The Journal of the Polynesian Society. 16 (2): 101–04. JSTOR 20700813.
  47. ↑ Best, Elsdon (1922). Astronomical Knowledge of the Maori: Genuine and Empirical. Wellington, New Zealand: Dominion Museum. p. 33.
  48. ↑ MacDonald, Ian (9 August 2009), Astronomy of the Brazilian Flag, FOTW Flags of the World website, archived from the original on 28 June 2009, retrieved 23 November 2011
  49. ↑ Basso, Ellen B. (1987). In Favor of Deceit: A Study of Tricksters in an Amazonian Society. Tucson, Arizona: University of Arizona Press. pp. 360. ISBN 978-0-8165-1022-1.
  50. ↑ MacDonald, John (1998). The Arctic sky: Inuit astronomy, star lore, and legend. Toronto, Ontario/Iqaluit, NWT: Royal Ontario Museum/Nunavut Research Institute. pp. 72, 231–33. ISBN 9780888544278.
  51. ↑ "Annotations on LHS 33 object", SIMBAD, Centre de Données astronomiques de Strasbourg, retrieved 21 April 2010
  52. ↑ Tayler, Roger John (1994). The Stars: Their Structure and Evolution. Cambridge University Press. p. 16. ISBN 978-0-521-45885-6.

Sources

  • Schaaf, Fred (2008). The Brightest Stars: Discovering the Universe through the Sky's Most Brilliant Stars. Hoboken, New Jersey: John Wiley & Sons. ISBN 978-0-471-70410-2.
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