Flamsteed's Alleged Measurement of Annual Parallax for the Pole Star

Hooke Robert , “An attempt to prove the movement of the Earth” (London, 1674), reproduced in Gunther's R. T. Early science in Oxford, viii (Oxford, 1931), 1–28.

Picard Jean , “Voyage d'Uranibourg” (1680) in Auzout A. , Lettres du M. Auzout sur les grandes lunettes (Paris, 1736).

Cassini submitted an account of these observations to the Académie des Sciences in 1693 in a letter entitled “S'il est arrivé du changement dans la hauteur du Pole, ou dans la cours du Soleil”, published in Mémoires de l'Académie royale des Sciences depuis 1666 jusqu'à 1699, x (Paris, 1730), 360–75.

Picard's and Cassini's observations have been analysed in detail in a paper by Peters C. A. F. : “Recherches sur la parallaxe des étoiles fixes” in Mémoires de l'Académie impériale des Sciences de Saint-Petersbourg, 6 série, tome v (St Petersbourg, 1853), 1–180, p. 13.

Wallis John , Opera mathematica, iii (Oxford, 1699), 701–8.

For a detailed account of the early years of the observatory, see Forbes Eric G. , Greenwich Observatory: Its origins and early history (London, 1975).

An account of these methods is given in Forbes Eric G. , “The origins of the Greenwich Observatory”, Vistas in astronomy, xx (1976), 39–50.

Letter from Flamsteed to Ward, first published in Baily F. , An account of the Rev'd John Flamsteed (hereafter cited as Baily, Account) (London, 1835), 118–23. Professor Forbes kindly let me see a transcript of this letter from the copy belonging to the Royal Greenwich Observatory (P.R.O. 42, f. 12^v–17^r).

According to Forbes, in Greenwich Observatory, 38, this method was similar to one used earlier by Johannes Hevelius.

Baily , Account, 120.

This is the interpretation of Flamsteed's letter to Ward put forward by Forbes in Greenwich Observatory, 38.

On Flamsteed's arc 5” would be approximately 50 microns, which he measured by means of an endless screw with micrometer head attached. For an account of the mural arc see Howse Derek , Royal Observatory, Greenwich: The buildings and instruments (London, 1975), 19–21.

See Forbes , Greenwich Observatory, 38.

Wallis , Opera mathematica, iii, 703 (“animadverti, non aliunde has provenire posse, quam ex Parallaxi”).

Letter from Flamsteed to Caswell, 5 February 1697–8. Professor Forbes also kindly let me see his transcript of this letter from the copy belonging to the Royal Greenwich Observatory (P.R.O. 42, ff. 82^r,v, 83^r).

These letters are reproduced together with Flamsteed's replies in Baily , Account, 160–8.

Wallis , Opera mathematica, iii, 702.

The effect of precession is due to the motion of the Earth's axis, causing a movement of the fundamental reference point from which all stellar positions are measured. The value Flamsteed took for the apparent movement of the Pole Star because of precession is very close to the one accepted today. For an account of precession, and the formulae giving its effect on right ascension and declination, see Smart W. M. , A textbook on spherical astronomy (Cambridge, 1931), chap. X. All subsequent definitions are taken from Smart unless otherwise stated.

Wallis , Opera mathematica, iii, 705.

When the minimum distance is being measured, the star is between the vertical and the Pole, and as the effect of precession is such that the star appears to be moving towards the Pole, in this case the precession effect must be added. For the maximum distance the Pole is between the star and the vertical, so the precession effect must be subtracted.

This effect is due to a slight shift of the Earth's axis brought about mainly through the gravitational attraction of the Sun and Moon. For a detailed account see Smart , op. cit., section 134.

Whiston William , Praelectiones astronomicae (Cambridge, 1707).

Ibid., 33–39. Whiston uses Flamsteed's figure for the annual parallax of the Pole Star to estimate stellar distances by first calculating the maximum parallax possible (which would be for a star at the pole of the ecliptic) from the value for the Pole Star, and then using a simple trigonometric relationship between the diameter of the Earth's orbit and the distance he wishes to calculate.

Gregory David , Astronomiae physicae et geometricae elementa (Oxford, 1702), 274–6.

Ibid., 276.

Ibid., 275.

Whiston William , Praelectiones physico-mathematicae (Cambridge, 1710), 194–202.

Baily , Account, 208–9.

For Roemer's attempts to measure parallax, see Pedersen K. M. , “Roemer, Flamsteed and the search for a stellar parallax”, in Vistas in astronomy, xx (1976), 165–9.

Letter from Roemer to Flamsteed, from the printed copy in P. N. Horrebow's Operum mathematico-physicorum tomus tertius (Copenhagen, 1741), 80–81. Professor Forbes kindly sent me a copy of his transcript and translation of this letter.

Cassini Jacques , “Réflexions sur une lettre de M. Flamsteed à M. Wallis touchant la parallaxe annuelle de l'étoile Polaire”, in Mémoires de l'Académie royale des Sciences pour 1699 (Paris, 1702), 177–83.

Ibid., 183.

I should like to thank Dr Dennis Rawlins for the help he gave me in the preparation of the mathematical section of this paper.

Letter from Flamsteed to Sir Christopher Wren, 19 November 1702, reproduced in Wren Stephen , Parentalia, or memoirs of the family of the Wrens (London, 1750) (hereafter cited as Wren , Parentalia), 252.

Wren , Parentalia, 247–53.

Ibid., 251.

Ibid.

Roemer's conjecture that the speed of light is very high but finite was based on his observations of the passage of the satellites of Jupiter across the visible disc of the planet, or behind it. He noted that the times predicted by tables for the disappearance or re-emergence of the satellites, or for transits of them across the planet, differed from the observed times by an amount depending on the position of Jupiter relative to the Earth. Roemer's explanation was that light travelled with a large, but finite velocity.

Peters C. A. F. , “Recherches sur la parallaxe des étoiles fixes” (ref. 4), 8–12.

Letter from Roemer to Flamsteed, 1701 (see ref. 30).

Flamsteed to Wallis in Wallis, Opera mathematica, iii, 706: “quod Angulus SIE (latitudo stellae Polaris ab Ecliptica in Mense Junio) minor est quam SDE (latitudo visa in Dec) & proinde ejusdam declinatio minor est, & distantia a Polo major, in Mense Junio, quam in alio quovis Anni Mense.”

Bradley's own account of the discovery of aberration may be found in his “Account of a new discovered motion of the fix'd stars” in Philosophical transactions, xxxv (1727–8), 637–61.

Ibid., 661.