Olbets* Essaif on Comets, 425 



§ 32. 

 It does riot appear that either Duse'jour or Hennert was 

 aware of the natural reason of the inutility of this method; 

 but the former appears to hdve been practically convinced of 

 it, since he has, in his later work, substituted another, which, 

 with all possible respect for this celebrated mathematician, may 

 be confidently pronounced very troublesome, and prolix, €uid 

 inaccurate. He applies a very ingenious mode of analysis to 

 the determination of the proportional distances, but the expres- 

 sions include a factor depending on the distance from the sun ; 

 which must therefore be supplied by a previous approximation. 

 He thus reduces the distances to a single unknown quantity, 

 whence he determines the length of the chords, and compares 

 these, by means of Newton's approximation, with the times. 

 This method requires very laborious preparatory calculations, 

 and can only be employed when we have a long series of accu- 

 rate observations; nor is the result, after all, correct. We 

 may therefore conclude, that neither the equations of the first 

 nor of the second degree, that have been hitherto proposed, 

 can be employed in practice with real advantage. 



Section HI. 



A short and easy Method of finding the approximate Elements 

 of the Orbit of a Comet. 



§33. 



From the preceding observations it may be inferred, that 

 unless, like La Caille, we attempt the determination of the 

 orbit of a comet by numberless trials almost entirely conjectural, 

 we mtist begin with some supposition, not mathematically true, 

 although approaching to the truth, respecting the properties of 

 its motion. Boscovicii's assumption of rectilinear and equable 

 motion is somewhat too bold, being at once doubly erroneous. 

 We may approach much nearer to the truth by adhering to the 

 supposition, that the chord of the comet's orbit is divided by 

 the middle radius in the proportion of the times ; and if we 

 assume at the same time that the chord of the earth's orbit is 

 divided in the same proportion, we shall obtain an approximate 



VoL.X. 2 F 



