Front Page Titles (by Subject) 12.: THE COMET OF 531 — ( P. 292-3 ) - The History of the Decline and Fall of the Roman Empire, vol. 7
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12.: THE COMET OF 531 — ( P. 292-3 ) - Edward Gibbon, The History of the Decline and Fall of the Roman Empire, vol. 7 
The History of the Decline and Fall of the Roman Empire, ed. J.B. Bury with an Introduction by W.E.H. Lecky (New York: Fred de Fau and Co., 1906), in 12 vols. Vol. 7.
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THE COMET OF 531 — (P. 292-3)
The identity of the comet of 1680 with the comets of 1106, 531, 44, &c., is merely an ingenious speculation of Halley. See his Synopsis of the Astronomy of Comets, at end of Whiston’s “Sir Isaac Newton’s mathematick Philosophy more easily demonstrated” (1716), p. 440 sqq. The eccentricity of the comet of 1680 was calculated by Halley (Philosophical Transactions, 1705, p. 1882), and subsequently by Encke, Euler, and others, — on the basis, of course, of the observations of Flamsteed and Cassini. Newton regarded its orbit as parabolic (Principia, 3, Prop. 41); but it has been calculated that the eccentricity arrived at by Encke, combined with the perihelion distance, would give a period of 8813.9 years (J. C. Houzeau, Vademecum de l’Astronome, 1887, p. 762-3). The observations were probably not sufficiently accurate or numerous to establish whether the orbit was a parabola, or an ellipse with great eccentricity; but in any case there is nothing in the data to suggest 575 years, nor have we material for comparison with the earlier comets which Halley proposed to identify.
For the Chinese observations to which Gibbon refers, see John Williams, Observations of Comets from Chinese Annals, 1871: for comet of 44, p. 9, for a doubtful comet (?) of 532, p. 33, for comet of 1106, p. 60.