iy means of Two known Stars. gi 
{ ycotD dhicosit; 
+ dw = + dh\ WwW Ww tang h cot Ww) —_— Shikeal Dein Wk 
for we shall suppose D to be constant: thus — dW = 
dh, &c...,.(1). 
This equation may be put in another form: for, 
Let (90 — h) be the first side of the triangle, D the se- 
cond, W the angle comprised; we shall have — dW = 
sa oh a Ist side cos 2d side — cos Ist side sine 2d side cos contained ) 
sin ist side sin vd side sine contained angle 
dh sin 3d side 
+ sin ist side sine 2d side sin contained Z 
sin $d side-cos angle opposite 2d side dd 
(= Ist side sin 2d side sin operye 
Pata 7? 
sin Ist side sin 4 opposite 2d side 
cos £ opposite 2d side di 
oh pia tees aac? an Ist side sin 4 oppas. 2d side 
cos (A— 1 ; 
= ~ cos hsin (A—A’) + cosh sin (A—A’) aoe 
ing the azimuths in the two. observations, —dW = 
dhi—dhcos(A~A’) _. dh —dh + 2dhsin*® 3 (A—A’),. 1 
‘cos sin(A—A) -_ SH win | Absa Tete. 
IWe= dh cos (A—A')—dhi dicot (A—A’) PR: Se 
™ cos k sin(A—A‘) ~ ~ Gosh ™ cosfsin(A—A’) 
Fs Kew He 
 W-V =u, then dW = du when the two stars have 
been observed of the same side of the meridian; d= 
V — W, if they have been observed on different sides, then 
du = — dW. 
_In this second formula, it is supposed we are acquainted 
with A and A’, or at least (A—A’). 
sin W sin D 
cosh”? 
it must, besides, be known whether (A — A’) be more or 
less than y0°, so that no great advantage is obtained by 
preferring the second formula to the first. 
We have found above, sin g¢ = sin A sin } + cos h cos 3 
; : dh cos h sin 3—dh sin h cos} cos du sin u cosh cos 3 
eosu—dg= ——— a 
But as cos k:sinW:: sin D:sin(A=A’)= 
——————$ 
cos @ cos ¢ 
sin Ist side cos 2dside—cos !stsidesin 2d side cos 4 comp. 
NY. EN (A ageaesn-) 
sin 3d side 
\cos g sin Sd side 
ducoshsin A = dhcos A — du gos h sin A (3*) = dhcos A— 
Braer( AA dk sh sig Amdt cosh ee Ain 
— adu sin u cosh cosd dh sin 3d side cos angle Opposite 2d side 
ne —$—$—$—$_—2 =. —$— 
cosh sin(A—A’ sin (A—A‘) 
dh cos Asin (A — A’) — dh sin A cos (A—A‘) + dh’ sin A + 
we . Re ne 
dh sin 
