522 LECTUHK XLIll. 



their near approach to the parabolic form, and the great disturbance which 

 their motions occasionally suffer, when they happen to pass through the 

 neighbourhood of any of the larger planets. The velocity of a comet in its 

 perihelion is such, that its square is twice as great as the square of the velocity 

 of a body revolving in a circle at the same distance. It was determined by 

 Halley and Clairaut, that the attractions of Jupiter and Saturn would delay 

 the return of rhe comet of 1759 about 618 days; and the prediction was ac- 

 complished within the probable limits that they had assigned for the error of 

 the calculation. The labours of Clairaut have indeed in many respects im- 

 proved the science of mathematical astronomy ; he was the first that ob- 

 tained a complete determination of the effects of the mutual actions of three 

 gravitating bodies, disturbing each other's motions; and his investigations, 

 which were founded on those of Newton, led the way to still further improve- 

 ments and refinements, which have been since made in succession by Euler, 

 Lagrange, and Laplace. 



