Dr. Maskelyne’s Advert Ifement, &c. 42^ 
The interval between the paffages of the comet by the peri- 
helium In 1532 and 1661 is 128 years, 89 days, 1 hour, 29 
minutes (32 of the years being biflextile), which added to the 
time of the perihelium in 1661, together with 1 1 days to reduce 
it from thq Julian to the Gregorian ftile, which we now ufe, 
brings out the expected time of the next perihelium to be April 
27th, 1 h. io / in the year 1789. 
The periodic times of the comet, which appeared in 15311 
1 607, and 1682, having been of 76 and 75 years alternately, Dr. 
Halley fuppofed, that the fubfequent period would be of 76 
years, and that it would return in the year 1758; but, upon con- 
lidering its near approach to Jupiter, in its defeent towards the 
fun in the fummer of 1681, he found, that the action of Jupiter 
upon the comet was, for feveral months together, equal to one- 
fiftieth part of the fun upon it, tending to inereafe 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 obfervations made in the following year 1682 to be 22 / 
greater than in the year 1607. The effect of the augmentation 
of the periodic time could not be feen till the next return, 
which he fuppofed would be protracted by Jupiter’s a&ion to 
the latter end of the year 1758, or the beginning of 1759. 
M ClaiPuAUT, previous to its return, took the pains to cal- 
culate the aCtions both of Jupiter and Saturn on it during the 
whole periods from 1607 to 1682, and from 1682 to 1759* 
and thence predicted ics return to its perihelium by the middle 
of April; it came about the middle of March, only a month 
fooner, which was a fufficient approximation to the truth in fo 
delicate a matter, and did honour to this great mathematician, 
and his laborious calculations. 
Vol. LXXVI. 
Kkk 
The 
