388 PARABOLIC ELEMENTS. [SECT, xxxvi. 



sive corrections, from a number of observations, distant from 

 one another. When the motion of a comet is retrograde, the 

 place of the ascending node is exactly opposite to what it is 

 when the motion is direct. Hence the place of the ascend- 

 ing 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 recognise a comet on its return, be- 

 cause its orbit would be very much changed if it passed 

 near any of the large planets of this or of any other system, 

 in consequence 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 orbit, determined 

 by Messier, did not agree with those of any comet that had 

 hitherto been computed, yet Lexel ascertained that it de- 

 scribed an ellipse about the sun, whose major axis was only 

 equal to three times the length of the diameter of the terres- 

 trial orbit, and consequently 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 



