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The Flamsteed designation is a convention to name stars introduced by British astronomer John Flamsteed in his work, Historia coelestis Britannica, published in 1712, without Flamsteed's approval. It consists number, followed by the genitive form of the name of the constellations (exemples: 4 Aurigae, 8 Orionis, etc.). The system is often abbreviated by writing the corresponding number with the three letters abbreviation of the constellation (exemples: 61 Cyg, 82 Eri).
The system gained in popularity in the 18th century, and nowadays, is only when a star doesn't have a Bayer designation. 61 Cygni and 51 Pegasi are such exemples of well-known stars with a Flamsteed designation name.
The observations having been made from England, only the stars visible from that country do have a Flamsteed designation. Only two exceptions exist, them being 47 Tucanae, a globular cluster mistook for a single star, and 82 Eridani; those two are the result of Benjamin Gould's seldom used catalogue, Uranometria Argentina. Also, the star 37 Tauri doesn't denote a star at all, but well planet Uranus, which Flamsteed did observe in 1690, nearly a century before William Hershell, but failed to identify as a planet.