ons of the orbits depended. In this way, he
found the limiting values of the eccentricity and inclination for the
orbit of each of the principal planets of the system. The results
obtained by that great geometer have been mainly confirmed by the recent
researches of Le Verrier on the same subject. (_Connaissance des Temps_,
1843.)--_Translator_.

[32] Laplace was originally led to consider the subject of the
perturbations of the mean motions of the planets by his researches on
the theory of Jupiter and Saturn. Having computed the numerical value of
the secular inequality affecting the mean motion of each of those
planets, neglecting the terms of the fourth and higher orders relative
to the eccentricities and inclinations, he found it to be so small that
it might be regarded as totally insensible. Justly suspecting that this
circumstance was not attributable to the particular values of the
elements of Jupiter and Saturn, he investigated the expression for the
secular perturbation of the mean motion by a general analysis,
neglecting, as before, the fourth and higher powers of the
eccentricities and inclinations, and he found in this case, that the
terms which were retained in the investigation absolutely destroyed each
other, so that the expression was reduced to zero. In a memoir which he
communicated to the Berlin Academy of Sciences, in 1776, Lagrange first
showed that the mean distance (and consequently the mean motion) was not
affected by any secular inequalities, no matter what were the
eccentricities or inclinations of the disturbing and disturbed
planets.--_Translator_.

[33] Mr. Adams has recently detected a remarkable oversight committed by
Laplace and his successors in the analytical investigation of the
expression for this inequality. The effect of the rectification rendered
necessary by the researches of Mr. Adams will be to diminish by about
one sixth the coefficient of the principal term of the secular
inequality. This coefficient has for its multiplier the square of the
number of centuries which have elapsed from a given epoch; its value was
found by Laplace to be 10".18. Mr. Adams has ascertained that it must be
diminished by 1".66. This result has recently been verified by the
researches of M. Plana. Its effect will be to alter in some degree the
calculations of ancient eclipses. The Astronomer Royal has stated in his
last Annual Report, to the Board of Visitors of the Royal Observatory,
(June 7, 1856,