96 On the observations of Comets. 
d D=d N' cos za’'c' +d N cos zea’ 
,¢cos N—cos Deos N’ cos N’—cosD cos N 
aN ( sin D sin N’ )+an (~S ~~ sinDsinN | ) 
i sN , 
=dN (=F, D an —cot D cot N ) 
os N’ 
+d N Zaae —cot D cot N) 
ites! vo eel ent laa _aN tenure earest 
nD 
and calling a the alates of the comet, r its airesiow. A the 
altitude of the star, and R its refraction, the preceding for- 
mula becomes 
Rsin asec A+rsin A sec a R tan ale tan a 
dD= 
sin 
Hanae corrected the distances, find in the “angle pab 
} ting P 
triangle cap, having the sides pa and ca, and the angle pac, 
the side cp and the angle cpa will be ascertained, and there- 
fore the declination, and the right ascension of the comet. 
_ In order to determine the effect produced in the positions 
of the comet by an error in the distances, let ch=a, ca=b, 
=c, and cab=z. agit we have 
cos a—cosb ¢ 
cos == — 
sin 6 sinc 
_ cos a’ —cos b’ cosc 
cos 2’ = - : 
b’ sin : 
and on account of the little difference between sin b and sin 6’, 
we may suppose 
cos @—cos a’ if se c 
sak Sah os a’+(cos b’ —cos b) cos 
sin 6 sine 
inz (¢+2"') sin} (zx—2z')= 
—2sin; sint (ates Bey wee a’)—2 sin} (b’+-5) sini (b’ —b) cose 
sin 6 sinc 
making x—ax'=dzx, a—ad =da, and bh’ — age and sup- 
posing these are equal to their sines, we hav 
ldzsini(r+2’)= $da sin} (a+a)+4 db sin} (b+) COs € a 
sin bsinc 
es da sin a+dbsin 6 cos c nese: 
~ gin bsin csin x 
