Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

The Forgetting of Newton's 'Theory of the Moon's Motion'

Newton's 1702 lunar 'theory' (the word is Gregory's, not Newton's) lacked any calculus or gravity theory, now was it expressed in any sine or cosine functions. It did however have an epicycle (as devised by the young Englishman Jeremiah Horrocks in the 1630s), a century after Kepler had banished them. French historians of science adopted a sceptical tone over this, and were never convinced that Newton's TMM was based upon his theory of gravity. Typical is French historian Jean Bailly verdict on Newton's use of the Horroxian theory: adding tersely, of that lunar theory: In the mid-eighteenth century, lunar theories were developed on the Continent using the Leibnizian calculus that really were based upon gravity theory. Once these theories started to gain acceptance, the earlier, 'kinematic', geometrical, picture-based models, such as Newton's, faded into oblivion.

If one turns to a nineteenth-century account of these things, say Stevenson's Newton's Lunar Theory Exhibited Analytically, (1834) then what there majestically unfolds as 'Newton's Lunar Theory' has no trace of that double motion of the apse line: it has merely a single rotation in nine years. The whole thing much resembles Clairaut's lunar theory, and that of Horrocks is nowhere to be seen. Clairaut's view, to quote from his letter to Bradley, was: 'les différentes espèces de termes qui sont dans mon equation pourront bien faire le mème effet que les variations dans l'excentricité et dans le mouvement de l'apogee.' Stevenson's 1834 version thus apears as a mythologised version of the 'Newtonian theory'. In a preface the author assures us he has merely translated the theory 'from the hieroglyphics of geometry' into the workaday language of algebra.

While the second edition of the Principia (1713) had an almost complete version of TMM (Scholium, Propn. 25, Bk.III), though without any procedural sequence, this was far from being the case for the 3rd edition of 1726. The 3rd Edition had an incomplete list of components ('equations') with no instructions about how to put them together, and omitted a crucial paragraph, concluding the sequence of equations, which stated that, thereby the Moon's longitude was to be found. This omitted paragraph had also contained the fifth and seventh equations. As this was the only version of the Principia translated into English, soon no-one remembered that an operational procedure had been present. Thereby Newton himself contributed to the process of forgetting.

Only two science historians (Whewell and Wilson) have appreciated that TMM functioned as a working mechanism for finding longitude. The first of these was William Whewell. Concerning the lunar observations supplied by Flamsteed to Newton in 1694, he wrote:

A year later, he returned to the theme, this time in the context of Flamsteed's supposed reluctance to part with his observations, his comment upon what was achieved being: Whewell acknowledged TMM as the outcome of this endeavour (p.209), i.e., he appreciated that it generated longitude positions from a given time. This apprehension does not reappear until a century and a half later, in the 1989 account by Curtis Wilson (General History of Astronomy, Vol. 2A, pp. 266-268).Search for a Theory of Longitude

A typical account of the way science historians omit the entire subject has appeared in the recent Harvard symposium 'The Quest for Longitude,' 1997. (See Quest) This jumps straight from the abstract three-body problems of the Principia, to the lunar theories of Euler and Mayer in the latter half of the eighteenth century, without any hint that Newton had composed a working lunar theory that was in use in the first half of the eighteenth century, and which spread right across Europe!

The modern rediscovery of what Newton really did in this context, began with Tom Whiteside's (1975) essay 'Newton's lunar theory: From High Hope to Disenchantment'  (See Epicycles). This described the failure to derive the lunar inequalities from gravity theory, and how Newton was in consequence driven back to the earlier, kinematic Horroxian model. However, even Whiteside never believed that TMM embodied a workable mechanism or procedure, and I went ahead with my thesis despite his advice.

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