290 



NEW FORMULA RELATIVE TO COMETS. 



multiplied by h (t" — /'), the terms which depend on D will disappear 

 and we shall obtain a new set of values : 



I 



z,=h {t"My — i'M"y" — {t'—t")Mr]',j 



which are perfectly symmetrical, and preferable to (5), both as to form 

 and facility of computation. 



We presume that the advantage of our mode of solution is suffi- 

 ciently tested by the different results we have obtained. We shall 

 therefore proceed to the numerical application of formulae (A). In 

 the example chosen, the intervals f, t" are considerably different, and 

 f — t" is of no small magnitude. We have taken it as before men- 

 tioned from the Theorie Analytique du Systeme du Monde, vol. II., 

 p. 68. 



Data of Comet of 1805. 



Times of Observation. 



Nov. 23'' -3 2241 



" 30-51095 



Dec. 5-29581 



Longitudes Observed. 



/' =24°41'04" 

 / = 15 39 40 



Latitudes Observed. 



•^ =:27°25'35" 

 ^ = 19 25 28 



/ ' = 2 7 11 -K" = 3 20 45 



Intervals. 



/' = 7'-18854 

 t" = 4 -78486 



These have been corrected for aberration and parallax, and with re- 

 ference to mean time at Paris. 



From the tables of Delambre have been taken 



(Long, of O H- 180°) or L = 68° 25' 41 " ; log R = 9-9936673. 



To these I add from values before noticed ; 



«= 99° 34' 13"; L — tar = 31° 8' 32"; sin e = -01685151. 



