On Encke's Comet. 



279 



On the 17th and 19th of July 1786, this comet was observed 

 in the constellation Aquarius by Messrs. Messier and Me- 

 chain. These two observations are not sufficient to determine 

 the elements, three being the least number that can possibly 

 be used. No notice is therefore taken of it in Delambre's 

 table. It appears however from the above elements of Encke's 

 comet, that it must have been near the perihelion about the 

 31st of January 1786, and the calculations of Prolessor Encke 

 confirm those of Dr. Gibers, proving that the following ele- 

 ments w^ll satisfy these two observations. 



d. 

 Time of passing the perihelion 1786, Jan. 30.88 

 Longitude of the perihelion _ _ _ 156° 38' 



Longitude of the ascending node - - 334 08 



Inclination of the orbit - - - 13 36 



Eccentricity _ _ - . 0.848 



Mean distance - - - 2.208 



It may be observed that other elements may be found, which 

 will also satisfy these l-ivo observations ; but as these elements 

 vary but little from those found for Encke's comet in 1 795, 

 1805 and 1819, there can be no doubt that it was the same. 



To compare these residts together, we must allow for the 

 jirecession of the equinoxes during the intervals of the succes- 

 sive appearances. Reducing them all therefore to the w.ean 

 equinox of 1806, the elements deduced from the observations 

 of the four diffisrent appearances of the comet will be respec- 

 tivelv, 



I 1786 I 1795 I 1805 | 1819 

 Time of Pcrihel. 'jan. 30.88 Dec. 21.47 Nov. 21.53 Jan. 27.27 



Long, of Perihel. 

 Do. Ascend. Node 

 Inclination | 



Eccentricity 

 Mean distauce I 



156 55 156 50 



334 25 334 48 

 13 36 13 42 



0.848 0.849 



2.208 2.213 



These elements agree remarkably well with each other, es- 

 pecially when we take into consideration that the disturbing 

 ibrces of the planets have been wholly neglected in jnaking 

 the calculations. Three revolutions of the comet have been 

 completed in each of the intervals between 1786, 1795 and 

 1805; and four revolutions between 1805 and 1819. Hence 

 it follows tiiat the periodical revolution is about -one thousand 

 two hundred and five days, which is rather loss than that of the 

 newly discovered planets. In the perihelion it passes within 

 the orbit of Mercury, and at the aphelion is about mid-way 

 l)etween the orbits of these small planets and that of Jupiter. 



From 



