Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

Halley and the Saros

Halley was the first known astronomer to use the Saros for eclipse predicton, although this 18-year cycle was known to antiquity. His skill in eclipse prediction was based upon it, as Nicholas DeLisle observed in his letter on the subject (Journal des Scavans, Paris 1750), and this expertise became transferred to the problem of longitude. A section entitled 'Saros' in Charles Leadbetter's opus of 1742 seems to be its first mention in an astronomy textbook, in which its duration was specified. Its author apologised because earlier he had '...called [it] Mr Whiston's Period; but Dr Halley assured me, that that gentleman had it from himself & desired me to let the world know so much' (A Compleat System of Astronomy, Vol. 1.), indicating its novelty to astronomers of the period.

In Paris, Nicholas Delisle, who was in wide correspondence with other astronomers, affirmed that: 'M.Halley avoit 'tabli cette p'riode de 223 lunations [the Saros] ou r'volutions synodiques de la Lune, que s'achevoient, suivant lui, en 18 ans,10 ou 11 jours, 7 heures, 43 minutes, 45 seconds' (letter of 1750), adding that Halley had in 1714 'chosen' the Saros that began in 1700 to compute solar and lunar eclipses. Shortly after, D'Alembert referred to 'Le p'riode de M.Halley' as comprising 223 lunations (1754, Vol.3, p.xv). It is thus clear that his contemporaries on both sides of the Channel credited him with discovering this period.

However, astronomers ignored or rejected Halley's way of using of the Saros throughout his tenure as Astronmer Royal, as an error-correction procedure. The French doubted that errors in a theory would recur in such a manner, with Delambre damning the method as 'useless', and worse, 'ce n'etait pas selon le science' (D'Alembert 1754, p.xv; Delambre 1827, p.282). In Britain it was widely misunderstood. My thesis endorsed Halley's procedure, on the basis of a computer reconstruction of the synchrony which Halley sought, which confirmed that his method would in fact have worked (for a more recent discussion, see 'Halley and the Saros', by Sir Alan Cook, Q.J. of the Roy Astr. Soc., 1996).

In antiquity, Ptolemy's Almagest specified the Saros period in relation to three types of lunar months, viz. the synodic, anomalistic and draconic, showing the Saros as representing an extraordinarily exact interlinking of these monthly periods. There is however no basis for assuming that they 'used' it eg for lunar eclipse prediction. Otto Neugebauer argued against the view that the Chaldeans used the Saros cycle for such, or even that they assigned a definite meaning to the term 'Saros', describing these notions as 'generally accepted historical myth.' Neugebauer merely accepted that the ancients had used a 'crude 18-year cycle' for predicting lunar eclipses, noting that 'There exists no cycle for solar eclipses visible at a given place' (1957, pp.141, 142; 1975, 1, p.310). For a more recent discussion see North, 1994, pp.35-47, see the bibliography.

The Saros cycle was named unintentionally by Halley, during his historical researches. He named it in 1691, by mistake (Armitage, Edmond Halley 1966, p.126; Phil. Trans. 1691, Vol.16, Emendationes ac Notae p.537; Gingerich, The Saros Cycle in Babylonia, JHA,1992, 23, p.229). When in 1682 the 26-year old Halley turned his telescope towards the Moon from his Highbury residence, it was his ambition to follow a complete 18-year Saros cycle, but turbulent events took him to London instead, involving the funding of the Principia from his wedding-dowry, which was probably just as well for posterity; however, once established as the Astronomer Royal in 1720 at the age of 64 he recommenced this scheme, that he had first aspired to 38 years earlier. Between 1720 and 1738 he did  indeed follow a complete Saros Cycle, using the new Greenwich technique of meridian-transit timed observatons.

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998