PREFACE. Xlll 



must be acknowledged, that the whole of these trials hardly served in any 

 case to settle any thing with certainty, if, perhaps, the comet of the year 

 1770 is excepted. 



As soon as it was ascertained that the motion of the new planet, discov 

 ered in 1781, could not be reconciled with the parabolic hypothesis, astrono 

 mers undertook to adapt a circular orbit to it, which is a matter of simple 

 and very easy calculation. By a happy accident the orbit of this planet had 

 but a small eccentricity, in consequence of which the elements resulting from 

 the circular hypothesis sufficed at least for an approximation on which could 

 be based the determination of the elliptic elements. There was a concur 

 rence of several other very favorable circumstances. For, the slow motion of 

 the planet, and the very small inclination of the orbit to the plane of the 

 ecliptic, not only rendered the calculations much more simple, and allowed 

 the use of special methods not suited to other cases; but they removed the 

 apprehension, lest the planet, lost in the rays of the sun, should subsequently 

 elude the search of observers, (an apprehension which some astronomers might 

 have felt, especially if its light had been less brilliant) ; so that the more 

 accurate determination of the orbit might be safely deferred, until a selection 

 could be made from observations more frequent and more remote, such as 

 seemed best fitted for the end in view. 



Thus, in every case in which it was necessary to deduce the orbits of 

 heavenly bodies from observations, there existed advantages not to be de 

 spised, suggesting, or at any rate permitting, the application of special 

 methods ; of which advantages the chief one was, that by means of hypo 

 thetical assumptions an approximate knowledge of some elements could be 



