579] GOLD MEDAL OF THE SOCIETY TO PROFESSOR SIMON NEWCOMB.
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he observed, however, that this failure is accounted for by an accidental mistake in
the computation of the perturbations of the radius vector by Jupiter.
Professor Newcomb’s theory of Neptune is published in the Smithsonian Contributions
under the title “ An Investigation of the Orbit of Neptune, with General Tables of its
Motion,” (accepted for publication, May 1865). The errors of the published ephemerides
were increasing rapidly; in 1863 Walker’s was in error by 33", and Kowalski’s by
22"; both might be in error by 5' before the end of the century. The time was come
when (the planet having moved through nearly 40°) the orbit could be determined
with some degree of accuracy. The general objects of the work are stated to be:
(1) To determine the elements of the orbit of Neptune with as much exactness
as a series of observations extending through an arc of 40° would admit of.
(2) To inquire whether the mass of Uranus can be concluded from the motion
of Neptune.
(3) To inquire whether these motions indicate the action of an extra-Neptunian
planet, or throw any light on the question of the existence of such planet.
(4) To construct general tables and formulae, by which the theoretical place of
Neptune may be found at any time, and more particularly between the years 1600 and
2000.
The formation of the tables of a planet may, I think, be considered as the
culminating achievement of Astronomy: the need and possibility of the improvement
and approximate perfection of the tables advance simultaneously with the progress of
practical astronomy, and the accumulation of accurate observations; and the difficulty
and labour increase with the degree of perfection aimed at. The leading steps of the
process are in each case the same, and it is well-known what these are; but it will
be convenient to speak of them in order, with reference to the present tables: they
are first to decide on the form of the formulae, whether the perturbations shall be
applied to the elements or the coordinates—or partly to the elements and partly to
the coordinates; and as to other collateral matters. These are questions to be decided
in each case, in part by reference to the numerical values (in particular, the ratios
and approach to commensurability of the mean motions), in part by the degree of
accuracy aimed at, or which is attainable—the tables may be intended to hold good
for a few centuries, or for a much longer period. The general theory as regards these
several forms ought, I think, to be developed to such an extent, that it should be
possible to select, according to the circumstances, between two or three ready-made
theories; and that the substitution therein of the adopted numerical values should be
a mere mechanical operation ; but in the planetary theory in its present state, this is
very far from being the case, and there is always a large amount of delicate theoretical
investigation to be gone through in the selection of the form and development of the
algebraical formulae which serve as the basis of the tables. In Prof. Newcomb’s theory
the perturbations are applied to the elements; in particular, it was determined that
the long inequality arising from the near approach of the mean motion of Uranus to
twice that of Neptune (period about 4,300 years), should be developed as a perturbation,
not of the coordinates, but of the elements. And it was best, (as for a theory designed