Science & Technology Studies
University College London
Newton's 1702 Lunar Theory
Return of the Epicycles
Epicycles were reintroduced into astronomy in the 1713 edition
of Newton's Principia, a century after Kepler had banished them.
He had three epicycles, as part of a recipe for finding lunar longitude,
two of which he had invented. The one invented by Jeremiah Horrox in 1638
(Figure 1), whereby lunar eccentricity and its apse equation co-varied,
revolved every six and a half months; Newton added a smaller one was added
onto that in 1713 causing its radius to expand and contract with the seasons,
so Newton's Horrox-wheel was larger in the winter than in the summer by
several percent, an adjustment Halley had suggested to him in 1694. This
second epicycle was (I found) no improvement to his theory, and was not
widely adopted. Halley incorporated a small table for it in his 1749 (posthumous)
opus. A third epicycle was required by TMM for its second node equation.
Let's quote from Whiteside's myth-busting tercentenary
address to the Royal Greenwich Observatory, about this aspect of Newtonian
'It is, unfortunately, one
of the most tenacious myths of Newtonian hagiography that this demi-god
of our scientific past made his dynamical explanation of the moon's motion
in all its irregularity the supreme proof of his monolithic principle of
the universal inverse-square law of gravitation which governs all celestial
and terrestrial movement, and this in a surpassingly rigorous geometrical
manner which he made inimitably his own. "Who", to quote Whewell's eulogistic
phrase of a century and a half ago, "has presented in his beautiful geometry,
or deduced from his simple principles, any of the [lunar] inequalities
which he left untouched?" The truth, as I have tried to sketch it here,
is rather that his loosely approximate and but shadowily justified way
of deriving those inequalities which he did deduce was a retrogressive
step back to an earlier kinematic tradition which he had once hoped to
transcend, and to a limited Horrocksian model which was not even his own
invention' (Whiteside, 1976, Vistas in Astronomy, 19, p.324).
More recently, Curtis Wilson concluded a fine study of the
matter by saying, that the Newtonian lunar endeavour had come unstuck because:
'Newton's effective adoption
of Horrock's lunar theory, by interfering with ongoing insight into perturbations
not actually embraced by that theory, proved ultimately an insurmountable
obstacle to him' (General History of Astronomy, p.267).
The French took a sceptical view of the British penchant
for epicycles, especially their claim that it had been derived from gravity
theory. Of the British trend, one author commented:
'Ce qu'il y a de plus remarquable
dans ce trait ... adopt' aujourd'hui de presque tous les Astronomes, et
sur-tout par Newton, c'est que M. Machin y fait revivre les Epicycles,
pour expliquer tous les mouvements et toutes les irregularities lunaires'
('De l'Orbite de la Lune dans le syste'me Newtonian', Histoire de l'Academie
Royale des Sciences, Paris 1746, p.128).
John Machin had composed an exposition on lunar theory for
a 1729 English translation of the Principia. When in the mid-eighteenth
century French astronomers such as Clairaut developed a lunar theory that
really was based upon Newtonian gravity theory, they saw themselves as
throwing out the Horroxian mechanism.
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the copyrighted, intellectual property of Nicholas Kollerstrom. Details.
rev: May 1998