148 PHILOSOPHICAL TRANSACTIONS. [aNNO 1786. 



helium in 1532 and 1661, is 128 years, 89 days, 1 hour, 29 minutes (32 of the 

 years being bissextile), which added to the time of the perihelium in 1661, to- 

 gether with 11 days to reduce it from the Julian to the Gregorian stile, which we 

 now use, brings out the expected time of the next perihelium to be April 27th, 

 1^ 10"" in the year 1789. 



The periodic times of the comet, which appeared in 1531, 1607, and l682, 

 having been of 76 and 75 years alternately. Dr. Halley supposed, that the sub- 

 sequent period would be of 76 years, and that it would return in the year 1758 ; 

 but, on considering its near approach to Jupiter, in its descent towards the sun in 

 the summer of 168 1 , he found, that the action of Jupiter on the comet was, for 

 several months together, equal to a 50th part of the sun upon it, tending to in- 

 crease the inclination of the orbit to the plane of the ecliptic, and lengthen the 

 periodic time. Accordingly, the inclination of the orbit was found by the ob- 

 servations made in the following year 1 682, to be 22' greater than in the year 

 1607. The effect of the augmentation of the periodic time could not be seen till 

 the next return, which he supposed would be protracted by Jupiter's action to the 

 latter end of the year 1758, or the beginning of 1759- M. Clairaut, previous to 

 its return, took the pains to calculate the actions both of Jupiter and Saturn on it 

 during the whole periods from 1607 to l682, and from l682 to 1759, and 

 thence predicted its return to its perihelium by the middle of April. It came 

 about the middle of March, only a month sooner, which was a sufficient ap- 

 proximation to the truth in so delicate a matter, and did honour to this great 

 mathematician, and his laborious calculations. 



The comet in question is also, from the position of its orbit, liable to be much 

 disturbed both by Jupiter and Saturn, particularly in its ascent from the sun after 

 passing its perihelium, if they should happen to be near it, when it approaches to 

 or crosses their orbits ; because it is very near the plane of them at that time. 

 When it passed the orbit of Jupiter in the beginning of February l682, O. S. it 

 was 50° in consequentia of that planet ; and when it passed the orbit of Saturn in 

 the beginning of October l663, it was 17° in consequentia of it. Hence its 

 motion would be accelerated while it was approaching towards the orbit of either 

 planet by its separate action, and retarded when it had passed its orbit ; but, as 

 it would be subjected to the effect of retardation through a greater part of its or- 

 bit than to that of acceleration, the former would exceed the latter, and con- 

 sequently the periodic time would be shortened ; but probably not much, on ac- 

 count of the considerable distance of the comet from the planets when it passed 

 by them ; and therefore we may still expect it to return to its perihelium in the 

 beginning of the year 1789, or the latter end of the year 1788, and certainly 

 some time before the 27th of April 1789. But of this we shall be better in- 

 formed after the end of this year, from the answers to the prize question pro- 



