On the observations of Comets. 97 
and supposing da and db of the same sign, this equation 
becomes 
dasina - dbsinbcosc 
snbsincsinz * 
dasin a db cot c ; 
~sinbsincsinz = sinz 
which shews that the agi Sidiciee the least errors are 
when cab is a right an 
In the triangle cap, let. cp=n, cap=z,ca=b, pa=n. Then 
cos v=cosz sin b sinn-+cos b cos 
s v'=cos 2’ sin b’ sinn-+cos b’ c 
cosv —cosv selene sinb —cosz'sinb’) sinn se —cosb’) cosn 
z— cos z’)sin b sinn-+(cos b — cos 6’) cos n, 
nearly ; — 2 sin} were) sind (v’ —v')= 
—2s ng (e+2) ) sin (z—2’) sinb sinn—2 sin} 
> Po 
aGsi-— 
(4-0) sini (b—b) 
dv sin} (v-+-v') =dz sing y(e-E2) ain b sin yah sin} na Osee )cosn 
»y=dz sinz sin bsinn+db sinbec 
2 
=dzrsinz aubainntcad sinbcosn ; 
sinv (2) 
sinbsin 
Let cpa=w, and we have sin w= aie and taking the 
differentials, 
/AL piper ‘tor ne py Boe 2: 3 i ee 
(ev VN ‘ / ret Sho 
sin v? 
_ dacosbsinz+ dzcosz sinb = dvsinbsinz 
sin v cos w ‘ Shier ( 
As an Seine I shall apply the above to the comet of 
1819, of which I made the following bueivaioke with a 
sextant. 
3) 
1819. apm Sie to Arcturus. to @ Lyra 
July 10, = . 9h 39’ 48”) 82° 6’ 30” 90° 32’ 30” 
Hi, + - - 19 20 37 81 26 26 90 6 34 
12, - - 9 29 41 80 46 25 89 37 58 
13, > - Cae oo 80 17 00 89 18 00 
14, - - 9 23-29 79 45 30 88 57 30 
16, - = - 19 33 25 78 49 30 88 25 45 
24. - 9 35 34 76 2 00 87 28 30 
Vout. XV —<No. 1. 13 
