Flamsteed's Lunar Data,1692–95,Sent to Newton

‘Memoranda by David Gregory’, The correspondence of Isaac Newton , iv, ed. by Turnbull H. W. (Cambridge 1967; hereafter: Correspondence), 7; Flamsteed's diary for 1 September 1694, in Baily F. , An Account of the Revd. John Flamsteed (1835; London, 1966), 61.

Correspondence 8; Westfall R. S. , Never at rest (Cambridge 1980), 541.

Chapman Allan , Dividing the circle (Cambridge, 1990), 57.

Newton Flamsteed , 17 November 1694, Correspondence , 46–48, p. 48.

Flamsteed Newton , 7 February 1695, Correspondence , 83–85, p. 85; original in Cambridge University Library Add. 3979, f. 29.

Newton Flamsteed , 29 June 1695, Correspondence , 133–4.

Westfall , Never at rest (ref. 2), 546.

Memorandum written on back of Newton's letter of 29 June 1695, Correspondence , 135–6.

Flamsteed J. , Historia coelestis Britannica , ii (London, 1725), 152–280.

‘A copy of the observations made with the Mural Arc, from Sept. 11, 1689 to Dec. 19, 1693’, Royal Greenwich Observatory Archives, Cambridge University Library, RGO 1/15.

Flamsteed J. , [ Halley E. (ed.)], Historia coelestis libri duo (London, 1712), II, 51–71.

Royal Greenwich Observatory Archives, Cambridge University Library Add. 3966, 13–15.

Newton Flamsteed , 16 January 1699, Correspondence 296; Westfall , Never atrest (ref. 7), 547; Wilson Curtis , ‘Predictive astronomy in the century after Kepler’, The general history of astronomy , ii A, ed. by Taton R. Wilson C. (Cambridge, 1989), 161–206, p. 206; idem, ‘The Newtonian achievement in astronomy’, ibid. , 233–74, p. 267.

Baily , op. cit. (ref. 1), 708–9.

Whiteside D. T. , ‘Newton's lunar theory: From high hope to disenchantment’, Vistas in astronomy , xix (1976), 317–28, p. 322.

Gingerich O. Welther B. , Planetary, lunar and solar positions, A.D. 1650–1805 (Cambridge, Mass., 1983), p. xv.

Whiston William , Astronomical lectures (London, 1715), 335; Howse Derek , Greenwich time and the discovery of longitude (Oxford, 1980), 38.

Gingerich Welther , op. cit. (ref. 16), p. xxi.

Flamsteed John , ‘A letter from Mr Flamsteed’, Philosophical transactions , xii (1683), 404–12, p. 405 (quoted in Harris's J. Lexicon technicum of 1704 under ‘Moon’).

Flamsteed would have generated the North Polar Distance in Table 1 from:

NPD = zenith distance — parallax + refraction + 90° — latitude.

Flamsteed Newton , op. cit. (ref. 5), 83.

Whiston William , ‘A collection of astronomical tables’, in Astronomical lectures (ref. 17), new pagination, 2–3.

Hughes D. W. Yallop B. D. Hohenkerk C. Y. , ‘The equation of time’, Monthly notices of the Royal Astronomical Society , ccxxxviii (1989), 1529–35.

The column for uncorrected clock-time readings was called ‘Tempora per Horologium oscillatorium’ in Flamsteed's Historia, while his clock (or ‘apparent‘) time corrected by solar noon transit was entitled ’Tempora vera apparentia’.

Halley (ed.), op. cit. (ref. 11), preface.

Forbes Eric G. , Greenwich Observatory , i (London, 1975), 48.

Chapman , Dividing the circle (ref. 3), 58; Chapman's earlier estimate was 15 seconds, see Chapman Allan , The Preface to John Flamsteed's Historia Coelestis Britannica (Greenwich, 1982), 5.

For reconstructing the historical lunar AZDs (‘Dist a Vertice Correcte’) the formula (see below) is:

AZD = zenith distance + parallax — refraction — oblateness,.

where oblateness is a correction for the non-spherical shape of the Earth.

Newton Flamsteed , 17 November 1694, Correspondence 49; 15 March 1695, ibid. 95. The latter table was published in Halley E. , ‘Some remarks on the allowances to be made for the refraction of the air’, Philosophical transactions , xxxi (1721), 169–172, p. 172.

Forbes Eric G. , ‘A new theory of astronomical refraction’, The Gresham Lectures of John Flamsteed (London, 1975), 65–69, p. 68.

Computation kindly performed by Catherine Hohenkerk, at the RGO's Nautical Almanac Office, using a program based on ‘The computation of angular atmospheric refraction at large zenith angles’, by Hohenkerk C. Y. Sinclair A. T. , NAO Technical Note, no. 63 (Herstmonceux, 1985), and inserting the conjectural parameters of 1010 mb pressure and temperatures of −5°C, 10°C, 10°C and 15°C for winter, spring, autumn, and summer, respectively.

Wrote Flamsteed Newton in 1695, that his latitude came to 51° 29′ 00′ ‘allowing the refractions of ye table you sent me’ (9 January 1695, Correspondence , 77–78, p. 78). However on 16 July 1713 he informed Sharp that ‘in the year 1690, it was determined by the Mural Arc, 51° 28′ 30′’ (Baily, op. cit. (ref. 1), 302); the modern value for the latitude of his Mural Arc is 51° 28′ 38′.

Royal Greenwich Observatory Archives, Cambridge University Library, RGO 1/54, ff. 142–5.

Given observed values of α and δ (right ascension and declination) and λ and β (the ecliptic latitude and longitude) of the Moon, the obliquity ε that Flamsteed used is determined from the equation: Tan ε = (sin λ tan δ — sin α tan β) / (tan β tan δ + sin α sin λ).

Wilson , op. cit. (ref. 13), 191.

Newton Flamsteed , 26 January 1695, Correspondence , 73–76, p. 75.

Improved lunar ephemeris (Washington, D.C., 1954). Improvements to ILE (j = 2); ‘Explanation, Moon’, The astronomical ephemeris (Washington, D.C., and London, 1972), 539, were incorporated in the computer program.

McCrea W. H. , Royal Greenwich Observatory: An historical review issued on the occasion of its tercentenary (London, 1975), 10.

Baily Francis , ‘Account of the astronomical observations of Dr Halley’, Memoirs of the Royal Astronomical Society , viii (1835), 169–90, p. 189.

Howse Derek , Greenwich Observatory , iii (London, 1975), 21, 113.

Wilson , op. cit. (ref. 13), 201.

Kollerstrom N. , ‘The achievement of Newton's ‘Theory of the Moon's Motion’ of 1702’, Ph.D. thesis, University of London, 1995.