the Orl'ds of Comets. 41 



of the comet equally as far as possible removed from eaeh 

 other: we should embrace within four observations an in- 

 terval of 30 degrees, and within five observations an inter- 

 val of 36 or 40 degrees, and so forth : but the interval 

 comprehended between the observations must always be the 

 larger the greater the number, in order to diminish the in-f 

 fluence of their errors. 



This being done, let /3, /3', /S", ^"' , Sec. be the successive 

 geocentric longitudes of the comet 3 y, 7', y", y"\ Sec. the 

 corresponding nortiiern latitudes, the southern latitudes 

 being supposed to be negative. Divide the difference p' — /3 

 by the number of days which separate the second from the 

 first observation : divide in the same way the difference 

 /3"— /3' by the number of days which separate the third 

 from the second ol)servation : divide also the difference 

 P'" — /3" by the number of days which separate the fourth. 

 from the third observation, and so forth. Let $(3, ^/3', ^,8", 

 0/3'", &c. be the consequence of these quotients. 



Divide the difference i'/S' — c/3 bv the number of days 

 which separate the third from the lirst observation : divide 

 in the sauie way the difference Sjj"—S(5' bv the number of 

 days which separate the fourth from the second observation : 

 divide also the difference Sj3'^' — Sj^''' by the number ol days 

 which separate the fifth from the third observation, See. 

 Let 0-/3, S'-p, 5^/3" be the consequence of these quotients. 



Divide the difference $'jS'~S-p by the number of days 

 which separate the fourth from the first observation : di- 

 vide in the samp way the difference S'-(5" — S'Id' by the num- 

 ber of days which separate the fifth from the second obser- 

 tion, &c. Let <J'/3, iJ^/3', &c. be the consequence of these 

 quotients. We may go on in this way until we succeed in 



forming 5"~ .ft, n being the number of the observations 

 employed. This being accomplished, 



s?. Take a mean or nearly mean epoch between the in- 

 stants of the two extreme observations, and by naming 

 ?', i', i", i'", &c. the number of days by which it precedes 

 every observation ; i, i' , &c. being supposed to be negative 

 for all the observations anterior to this epoch; the longi- 

 tude of the comet after a small number « of days counted 

 from the epoch, will be expressed by the formula 

 ft- i.lft + i.i'.o'^.ft- i.l'.i" $\ft + i.i'.i".i"'.S\ B - Sec. 

 iS.ft-{i + i').S\ft + {i.i' + i.i" + i'.i'').P.ft) 

 + a. < —{ii'i" + i i' i'" + i.i".i"' + i'.i".i"').i*. ft> . . {p) 

 I + 8cc. S 



■ S* ft -{i + i' + i") .S\ ft + {i . i' + i . 1" + i.r X 

 + i'.i" + /■', :'" + j". i'") .S'ft~8cc. S 

 The coefficients of —S.ft, -{- S^ft, &c. in the part indepen- 

 dent 



'■{' 



