46 General Method for determining 



As we have in this particular case I7 l^t we must employ 

 the equations (i), (3), and (4). These three equations give 

 X = 0,3t)107, 

 7/ = 2,258335, 

 r = 0,9733798. 



These values satisfy the equation (3) as much as we can 

 expect of aw equation which cannot be very exact on ac- 

 count of the little movement of the comet in longitude. 

 By substituting them in the expression of P, we find 

 P = — 0,183628. 



The necjalive siirn of P makes known that the comet has 

 not yet attained its perihelion. We aftewards find the 

 perihelion distance D = 0,9583309, and the anomaly v of 

 the comet, equal to 13° 16' 2-l", which answers to 10 days 

 40334 : from which it follows that the perihelion passage 

 took place on the 29th of November at 18'' 10' 34", 

 mean time at Paris. Having thus obtained nearly the pe- 

 rihelion distance and the instant of the passage of the comet 

 by this point, we may correct ihem by the following me- 

 thod, which has the advantage of being independent of an 

 intimate knowledge of the other elements of the orbit. 



Exact Determination of the Elements of the Orbit , ivhen 

 ice know pretty nearly the Perihelion Distance and the 

 Instant of the Passage of the Comet by this Point. 

 3. We shall select three observations removed from the 

 comet: by afterwards setting out from the perihelion distance, 

 and from the instant of the passage by this point, deter- 

 mined by what precedes, -we. shall easily calculate the three 

 anomalies of the comet, and the three vector radii corre- 

 sponding to the instants of the three observations ; let v, v' 

 and v" be these anomalies, those which precede the passage 

 of the comet bv the perihelion being necessarily supposed 

 to be negative : further let r, r', r" be the corresponding 

 vector radii of the comet, if —v and v" —v will be the angles 

 comprehended between r and / and between r and r'' ; let 

 U be the first of these angles and U' the second. 



Let us also call a, a', a", the three geocentric longitudes 

 observed of the comet ; 9, 9', i5'',its three geocentric latitudes, 

 the southern latitudes being supposed to be negative: 

 C, C, C, the tliree correspond in o- longitudes of the sun j 

 R, R', R", its three distances from the earth ; (3, jS', /3'', the 

 three heliocentric longitudes of the comet ; ra-, zn', •zzr", its 

 three heliocentric latitudes. This being done. 



We \\ ill imagine the letter S at the centre of the sun, the 

 letter Tat the centre of the earth, the letter C at the centre 



of 



