which they are circumscribed in their motion, the small obliquity and eccen- 

 tricity of their orbits, and consequently the very slight disturbance which they 

 sustain from the attraction of the planets, render them, for all physical purposes, 

 nothing more than new planets of inappreciable mass belonging to our system. 

 Unlike other known comets, they do not rush from the invisible and inacessible 

 depths of space, and, after sweeping our system, depart to distances under 

 the conception of which the imagination itself is confounded ; they possess 

 uone of that grandeur which is connected with whatever appears to break 

 through the fixed order of the universe. It is still reserved for the comet of 

 Halley alone to exhibit a phenomenon, so far as we know, unique ; to afford a 

 splendid result of those powers of calculation by which we are enabled to follow 

 it through the depths of space two thousand millions of miles beyond the ex- 

 treme verge of the solar system ; and, notwithstanding disturbances which 

 render each succeeding period of its return different from the last, to foretell 

 that return with precision. 



LEXELL'S COMET. 



In the month of June, 1770, Messier observed a comet, which was after- 

 ward sufficiently observed to render its course through the system calculable. 

 It was found not to correspond with that of any comet previously known. It 

 remained visible for an unusual length of time ; and continued observations on 

 it proved that it moved, not as comets were then generally found to move, in a 

 parabola, or very elongated ellipse, but in an oval of very small dimensions. 



Its orbit was calculated by the celebrated Lexell, and found to be an ellipse, 

 of which the greater axis was only equal to three times the diameter of the 

 earth's orbit, which showed that its periodical revolution round the sun would 

 be completed in jive years and a half, 



With so short a period, the comet ought frequently to be seen. But here 

 springs up a difficulty. This comet was never seen before, and has never 

 been seen since ! What, then, has become of it ? and where and how did it 

 exist before its discovery by Messier ? Its appearance was too conspicuous 

 and its light too vivid to allow of the supposition that it could have been pres- 

 ent, yet not observed. 



The law of gravitation discovered by Newton, and fully developed by his 

 illustrious successors, enables us fully to explain this difficulty. We shall 

 adopt the words of Arago : 



Why has not the comet been seen every Jive years and a half before 177P ? 

 Because the orbit was then totally different from that it has since pursued. 



Why has not the comet been seen since 1770 ? For the reason that its pas- 

 sage to the point of perihelion in 1776 took place by day ; and before the fol- 

 lowing return, the form of the orbit was so altered, that had the comet been 

 visible from the earth it would not have been recognised. 



Lexell had already remarked, according to his elements of 1770, that the 

 comet ought to pass in the vicinity of Jupiter in 1767, less than the fifty-eighth 

 part of his distance from the sun ; that in 1779, when it returned to us, it would 

 be, near the end of August, about five hundred times nearer that same planet 

 than to the sun ; so that then, notwithstanding the immense size of the solar 

 globe, its attractive power on the comet was not the two hundredth part that 

 of Jupiter. Thus it could not be doubted that the comet had experienced con- 

 siderable perturbations in 1767 and 1779 ; but it is yet necessary to establish 

 that these perturbations were numerically strong enough to explain the total 

 want of observations, as well before as after the year 1770. 



The formularies in the fourth volume of the Mecanique Celeste give the ana- 



