Science & Technology Studies

Nicholas Kollerstrom's

Newton's 1702 Lunar Theory

- 'Il [Newton] l'a laisse'
subsister comme une vraisemblance que peut faire attendre la verite' et
tenir sa place.' ['He has left this [Horroxian theory] as a semblance,
to await the true theory and take its place.']

- 'ce n'est point une cause physique.' ['it
does not have any physical cause.']

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:

- 'And during this interval
[i.e., after publication of the

- 'The reformation of the
tables [by Newton] turned out more difficult than had been foreseen, and
did not lead to any very great improvement till a later period.' (Whewell
1837, p.180)

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.

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*rev: May 1998*