On the observations of Comets. 



9? 



and supposing da and db of the same sign, this equation 



becomes 



das'ina- db sin b cose 



dx= ■■ — j—- : . 



sm 6 sm c sm x 



da sin a db cot c 



sin6sincsina; sin a; * ^ ^ 

 which shews that the distances producing the least errors are 

 when cab is a right angle. 



In the triangle cap, let cp=v, cap=z, ca=b, pa=n. Then 

 cos i5=cos z sin 6 sin n + cos b cos 7i 

 cos u' = cos z' sin 6' sin «+cos b' cosn — 

 cost) — cosu' = (cosz s'mb — cosz'sinfe') sinn -f- (cos6 — cos6') cosw 

 =(cos2: — cos 2') sin b sin w+(cos b — cos 6') cos w, 

 nearly ; - 2 sin^ {v-\-v) sin| (v' — v') = 



= — 2 sini (z^z') sin (z — z') sin b sin n — 2 sin^ 

 (6+6') sini (6—6') cosw. 



dvsm^ {v-{-v')=dz sm^(z-\-z')smb smn-^db s'm^ (6+6')cosm 

 dv=dz sins sin 6 sin n-^db sin 6 cosw 



sm V 

 =dx sin z s'mb s'mn-^db sin6cosn 

 siny 



(2) 



sin6sin2: 

 Let cpa=w, and we have sm w= "^^7—; and taking the 



sm V 



differentials, 



(db cos 6 s'm z-\-dz cos z sin b)s\nv — dv cos v sin 6 sin z 

 dw cos w= 



dw- 



sm V- 

 da cos 6 sine -f-^a; cosz sin 6 



dv sin 6 sin z 



(3) 



smucosiAJ sm 15 tan D cosifj 



As an example, I shall apply the above to the comet of 

 1819, of which I made the following observations with a 

 sextant. 



Vol. XVI.— No. 1. 



13 



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