Much was done, between 1682 and 1759, in the way of advancing the principles and methods of celestial mechanics. It was now possible, as it was not seventy-five years earlier, to determine the effect of the planetary perturbations and thus reduce to narrow limits the uncertainty as to the time of appearance. The matter does not seem to have been taken up seriously, however, until 1757, when Clairaut, who had already proved himself a brilliant mathematician, attacked the problem. Elaborate discussions of the problem of three bodies had already been developed, but they were not adapted to this case, on account of the great eccentricity of the orbit. This made it necessary to attack the problem in a very different manner from that employed in the case of the moon and the planets. Clairaut, however, proved himself equal to the task, though the practical application involved an immense amount of numerical work, and the time remaining was short. He was ably assisted, however, by Lalande, then a youth of seventeen, and a lady, Madame Lepaute.
The final result indicates a retardation of 618 days, 518 being due to the action of Jupiter, 100 to Saturn. The time of perihelion passage was fixed at April 13, 1769, but, as it had been necessary for want of time to abridge the work, by omitting some small terms, Clairaut stated that the true time might differ from this by as much as a month. He states further that a body passing into regions so remote, and which is hidden from our view during such long periods, might be exposed to the action of forces, totally unknown, such as the