With this end in view he expounded to the Berlin academy in 1849 a mode of determining an elliptic orbit from three observations, and communicated to that body in 1851 a new method of calculating planetary perturbations by means of rectangular coordinates (republished in W.
In his Recherches sur differents points importants du systeme du monde (1754-1756) he perfected the solution of the problem of the perturbations of the planets, which he had presented to the academy some years before.
In any case the orbits of comets are exposed to such tremendous perturbations from the planets that it is unsafe from the present orbit of a comet to conjecture what that orbit may have been in remote antiquity.
It has not indeed proved practically available; but his system of calculating cometary perturbations by means of "mechanical quadratures" has formed the startingpoint of all subsequent researches on the subject.
The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton.