298 PROCEEDINGS OF THE AMERICAN ACADEIVIY 



those of the comets of 1843 and 1844, M. Leverrier first un- 

 dertook to follow the former into the neighbom-hood of Ju- 

 piter and the other regions which it would have traversed up 

 to the years 1843 and 1844, and to ascertain, in this way, if 

 the comet of 1770 might not place itself upon the orbits of 

 one or the other of those discovered by M. Faye or M. Vico. 



On approaching the subject more nearly, M. Leverrier found 

 that the calculations of Laplace, in the Mecanique Celeste, 

 as to the direction given by Jupiter to the comet of 1770, 

 could not be depended on. Slight changes in the elements 

 of the orbit give routes so different to the aphelion, that it 

 remains uncertain whether it passed within or beyond the or- 

 bit of Jupiter, through the system of the satellites or outside 

 of them. M. Leverrier was accordingly obliged to com- 

 mence by studying the movement of the comet of 1770, leav- 

 ing to it all the latitude which resulted from the observations 

 made at the time. In pursuing this course, 



" I established," says M. Leverrier, " the following points : — 



" 1. That it was impossible that the comet should have been arrested 

 within the system of Jupiter, without falling into the planet itself; an 

 event very improbable, it is true, without being absolutely inadmissible. 



" 2. I showed that Jupiter might have forced the comet to pass off 

 in an hyperbola round the sun. In this case, we could not expect to 

 see it again, as it would continually move on to a greater distance from 

 our system, to enter into other spheres of attraction. 



" 3. It is possible that the comet, after having escaped the action of 

 Jupiter, might have pursued its course in ellipses of very long pe- 

 riod. But it is much more probable that it continued to move in 

 ellipses whose moderate period must permit us often to witness its 

 return. I have formed a complete table of all the possible ellipses, 

 which will serve henceforth as the basis of our further inquiries." 



The first inquiry will, then, be, whether the elements of 

 the new comet (that of Faye), as calculated from the obser- 

 vations, present themselves among the systems of this table. 

 If so, the problem is solved. 



Should this not be the case, it will be necessary to inquire 



