340 PARABOLIC ELEMENTS. SECT. XXXVI. 



tho place of the ascending node is exactly opposite to 

 what it is when the motion is direct. Hence the place 

 of the ascending node, together with the direction of the 

 comet's motion, show whether the inclination of the 

 orbit is on the north or south side of the plane of the 

 ecliptic. If the motion be direct, the inclination is on 

 the north side ; if retrograde, it is on the south side. 



The identity of the elements is the only proof of the 

 return of a comet to our system. Should the elements 

 of a new comet be the same, or nearly the same, with 

 those of any one previously known, the probability of 

 the identity of the two bodies is very great, since the 

 similarity extends to no less than four elements, every 

 one of which is capable of an infinity of variations. But 

 even if the orbit be determined with all the accuracy the 

 case admits of, it may be difficult, or even impossible, 

 to recognize a comet on its return, because its orbit 

 would be very much changed if it passed near any of 

 the large planets of this or of any other system, in con- 

 sequence of their disturbing energy, which would be 

 very great on bodies of so rare a nature. 



By far the most curious and interesting instance of 

 the disturbing action of the great bodies of our system 

 is found in the comet of 1770. The elements of its or- 

 bit, determined by Messier, did not agree with those of 

 any comet that had hitherto been computed, yet Lexel 

 ascertained that it described an ellipse about the sun, 

 whose major axis was. only equal to three times the 

 length of the diameter of the terrestrial orbit, and con- 

 sequently that it must return to the sun at intervals of 

 five years and a half. This result was confirmed by 

 numerous observations, as the comet was visible through 

 an arc of 170 ; yet this comet had never been observed 

 before the year 1770, nor has it ever again been seen 

 till 1843, though very brilliant. The disturbing action 

 of the larger planets affords a solution of this anomaly, 

 as Lexel ascertained that in 1767 the comet must have 

 passed Jupiter at a distance less than the fifty-eighth 

 part of its distance from the sun, and that in 1779 it 

 would be 500 times nearer Jupiter than the sun ; conse- 

 quently the action of the sun on the comet would not be 

 the fiftieth part of what it would experience from Jupi- 



