II ALLEY'S COMET 



17 



Much was done, between 1682 and 1759, in the way of advanc- 

 ing 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 him- 

 self equal to the task, though the practical application involved an im- 

 mense 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 



Orbits of the Planets and the Comet (the smallest Circle is the Earth's Orbit). 

 vol. lxxvi.— 2. 



