COMETS. 



turbing action of Jupiter in 1779, and taking the observations of 

 1770 within their possible limits of error. 



He further demonstrates, that the orbit in which the comet 

 moved antecedently to the disturbing action of Jupiter upon it in 

 1767, not only could not have been a parabola or hyperbola, but 

 must have been an ettipse, whose major axis was considerably 

 less than that which Laplace deduced from the insufficient 

 observations of Messier. He shows that, before that epoch, 

 the perihelion distance of the comet could not, under any 

 possible supposition, have exceeded three times the earth's 

 mean distance, and most probably was included between 1^ and 

 2 times that distance; and that the semi-axis major of the 

 orbit could not have exceeded 4^ times the earth's mean distance, 

 a magnitude 3 times less than that assigned to it by the calcula- 

 tions of Laplace. 



41. It must not, however, be supposed that it is sufficient to 

 compare the actual elements of each periodic comet thus dis- 

 covered, with the elements given in the table of M. Le Yerrier, 

 and to infer the absence of identity from their discordance. Such 

 an inference would only be rendered valid by showing, that in 

 past ages, the comet in question had suffered no serious disturbing 

 action by which the elements of its orbit could be considerably 

 changed. To decide the question a much more laborious and 

 difficult process must be encountered: a process from which the 

 untiring spirit of M. Le Yerrier has not shrunk. It is necessary, 

 in fine, to the satisfactory and conclusive solution of such a 

 problem, that the periodic comet in question should be traced 

 %ack through all its previous revolutions up to 1779, that all 

 the disturbances which it suffered from the planets which it 

 encountered in that interval be calculated and .ascertained, and 

 that by such means the orbit which it must have had previous to 

 such disturbances, in 1779, be determined. Such orbit would 

 then be compared with the table of possible orbits of Lexell's 

 comet, as given by M. Le Yerrier ; and if it were found to be 

 identical with any of them, the identity of the comet in ques- 

 tion with that of Lexell, would be inferred with the highest 

 degree of probability; but if, on the other hand, such discre- 

 pancies were found to prevail as must exceed all supposable 

 errors of observation or calculation, the diversity of the comets 

 would follow. 



42. M. Le Yerrier has applied these principles to the comets of 

 Faye, De Yico, and Brorsen ; tracing back their histories during 

 their unseen motions for three-quarters of a century, and ascer- 

 taining the effects of the disturbing actions which they must 

 severally have sustained from revolution to revolution, until he 



170 



