OF ARTS AND SCIENCES. 299 



if the new comet may not have experienced perturbations 

 since 1779, which would account for the present want of co- 

 incidence in the elements with those of Lexell's comet in the 

 table. If no such considerable deviation from a regular course 

 can be admitted as probable, the hypothesis of identity with 

 the comet of 1770 must be given up. 



But if the new comet has experienced considerable pertur- 

 bations since 1779, these must be calculated before we can 

 pronounce against the suspected identity. As the observations 

 made at one appearance cannot be depended upon as a suffi- 

 cient foundation for fixing its position for a period of more 

 than sixty years, it became necessary to pursue the same 

 course, in reference to the new comet, which had been fol- 

 lowed in regard to Lexell's, and " to determine all the posi- 

 tions which it could have occupied in 1779, and the elements 

 of all the orbits in which it could have moved conformably 

 with the recent observations." 



The great complexity and difficulty of the problem under- 

 taken by M. Leverrier are now apparent. He proceeds to 

 solve it by examining the positions and elements of the comet 

 of Faye, in the reverse order of time, during several successive 

 periods, viz. : 1. from 1843 to 1839; 2. from 1839 to 1819; 

 3. from 1819 to 1814; 4. from 1814 to 1797; 5. from 1797 

 to 1792. 



The paper of M. Leverrier, as transmitted to the American 

 Academy, being itself an abstract of the memoir read to the 

 Academy of Sciences at Paris, hardly admits, in this portion 

 of it, a further condensation, which could not be made with- 

 out impairing the clearness of the discussion. At the close 

 of the examination of these successive periods, M. Leverrier 

 arrives at the definite conclusion, " that the periodical comets 

 of Faye and Lexell are two different bodies.''^ 



In concluding the memoir, M. Leverrier briefly considers 

 the question. At what time did the action of Jupiter give to 

 the comet its present orbit ? Or rather. What is the least re- 

 mote time at which this phenomenon may have taken place ? 



