COMETS. 



an attraction from the great mass of that planet, more than three 

 times more energetic than that of the sun ; that consequently it 

 was thrown out of the orbit in which it previously moved, into the 

 elliptic orbit in-which it actually moved in 1770 ; that its orbit 

 previously to 1767 was, according to all probability, a parabola ; 

 and, in fine, that consequently moving in an elliptic orbit from 

 1767 to 1770, and having the periodicity consequent on such 

 motion, it nevertheless moved only for the first time in its new 

 orbit, and had never come within the sphere of the sun's attraction 

 before this epoch. 



Lexell further stated, that since the comet passed through its 

 aphelion, which nearly intersected Jupiter's orbit, at intervals 

 of somewhat above 5| years, and it encountered the planet near 

 that point in 1767, the period of the planet being somewhat 

 above eleven years, the planet after a single revolution, and the 

 comet after two revolutions, must necessarily again encounter 

 each other in 1779 ; and, that since the orbit was such that the 

 comet must in 1779 pass at a distance from Jupiter 500 times less 

 than its distance from the sun, it must suffer from that planet 

 an action 250 times greater than the sun's attraction, and that 

 therefore it would in all probability be again thrown into a 

 parabolic or hyperbolic path; and if so, that it would depart for 

 ever from our system to visit other spheres of attraction. Lexell, 

 therefore, anticipated the final disappearance of the comet, which 

 actually took place. 



In .the interval between 1770 and 1779, the comet returned 

 once to perihelion ; but its position was such that it was above the 

 horizon only during the day, and could not in the actual state of 

 science be observed. 



38. At this epoch analytical science had not yet supplied a 

 definite solution of the problem of cometary disturbances. At a 

 later period the question was resumed by Laplace who, in his 

 celebrated work, the " Mecanique celeste," gave the general 

 solution of the following problem : 



u The actual orbit of a comet being given, what was its orbit 

 before, and what will be its orbit nfter being submitted to any 

 given disturbing action of a planet near which it passes ? " 



39. Applying this to the particular case of LexelPs comet, and 

 assuming as data the observations recorded in 1770, Laplace 

 showed that, before sustaining the disturbing action of Jupiter in 

 1767, the comet must have moved in an ellipse of which the semi- 

 axis major was 13-293, and consequently that its period, instead 

 of being 5^ years, must have been 48| years ; and that the 

 eccentricity of the orbit was such that its perihelion distance 

 would be but very little less than the mean distance of Jupiter, 



168 



