Oibers's Essaj/ on Comets. 141 



observations of a comet. It is true that the proportion, in 

 which the chords are supposed to be divided, is not mathema- 

 tically correct; but this source of error is by no means very 

 material: Euler and Lambert have supposed the same for 

 the orbit of the comet ; I have only extended the supposition to 

 that of the earth, and by this extension the inaccuracy will 

 never be considerably increased, and frequently even diminished. 

 None of the direct methods vhich have been proposed is so 

 accurate ; for they all take for granted, either tacitly or ex- 

 pressly, that the portion of the comet's orbit is a right line de- 

 scribed uniformly ; or if the arcs be assumed, with Laplace, 

 so small that the supposition creates no error, these arcs must 

 be determined by means of an awkward interpolation. I shall 

 also show, in the next section, how easily the error arising from 

 the imperfection of the supposition may be corrected. 



§. 46. 

 This method of calculation may, however, be more com- 

 pletely illustrated by an example; and I shall take for this 

 purpose that of the comet of 1769, partly because the ele- 

 ments of its orbit are so well established, and partly because 

 it has been the most frequently employed for an example of 

 other methods. The observations are from Pingre"s Cometo- 

 graphie. 



For these three observations we have 



Consequently <'=i"=:4 days, -;- =1, and T=8 days. 



