the Orhils of Comets. 8 7 



The scries of the values of t, £", ?', visibly indicates a 

 retrograde motion. ^ 



We shall afterwards form a second hypothesis, in which, 

 by preserving the foregoing inslant of the perihelion pas- 

 sage, we shall increase the perihelion distance by 0,003. 

 We shall find in this hypothesis 



m' = — 33' 53', n' = — 12' 54". 



Lastly, we shall form a third hypothesis, in which, by 

 preserving the same perihehon distance as in the former, we 

 shall vary by o'' io 'he instavi- of the perihelion passage, 

 which will thus be fixed on the 29th of November at 12*^ 

 10' 31"; this hvpolhesis will give 



VI" = 18' 16", ^2' = 27' 13"; 

 we shall extract from these values the two following equa- 

 tions, 3102 . a — iseg ./ — 1069, 

 1760 .u— an .t =z 1016, 



which gives 



?/ = O,8S140C, /= 0,910400 t 

 hence we conclude 



the true perihelion distance = 0,9609951, 

 and the true instant of perihelion passage, the 29th of No- 

 vember at 12" 42' 40" mean time at Paris. 



In order to ascertain if these elements are very accurate, 

 we may calculate the corresponding values of w and 77, and 

 see if they are null or very small ; now we shall find that 

 in tire present case these values amount only to a small 

 number of secouds ; for the corrected elemcuts giv«, for in- 

 stance, for the first and last observation, 



V = —60" 56' 37'', v" = 29^ 19' 22", 

 S7 = 10' 33"-i, ■u:"= 27'^ 11' 56"-], 



e= 77° 2' 22", e"= 34 6" 38' 53"j 

 from which we extract 



U' = go*" 15' 59', V' = 00' 16 3"i, 

 and consequently ?« = — 4''i. These elements being very 

 accurate, we shall extract from them by n)eans of the for- 

 nnilaj (c) and {e') the position j of the ascending node, 

 and the inclination of the orbit, and we shall find 



Place of ihe afcendina node = 77° 22' 55". 

 Inclination of the orbit = 27^^12' 4". 

 In order to determine the place of the perihelion, u e shall 

 observe that ?"— 7= 269° 15' 58', froat) which wc extract 

 269"" 20' 50', for the distance from the comet to its node, 

 reckoned on the orbit, at the instant of the third observa- 

 tion : on addino- to this distance the anomaly v" which the 

 comet has traversed bv a retrograde motion since its peri- 

 helion passage, we shall have 298" 40' 12", for the distance 

 from the perihelion, reckoned on the orbit, to its ascending 



F 4 node : 



