by means of Two known Stars. _ . 193 
Mr. Gauss’s formule are simpler, but they suppose that 
the two azimuths are determined, in order to which it is 
sometimes necessary to make use of the longest formule, 
to avoid all uncertainty on the description of the angle. 
For the greater uniformity and generality, I chose the 
following formula : 
tang d cos @ — sin @ cosa 
ea: REE ES Rie SS 
sin aA 
Tang? 9:1683 —sin ¢@ —9°8937 
Cos g  9°7939 - cosa 9°9905 
+0°09166 §°9622 —0'76594 —9'8842 
—0°76594 
—0'67428 —9'8288 negative denominator. 
C sin A +0°6849 positive denominator. 
Cot A = (162° 57’ 50”) 0°3137. A must be in the se- 
cond quadrant. 
We shall obtain the other azimuth A’ by a similar for- 
mula. 
Tang 3 ......-.+. 9°7263 —sing...... —9°8937 
COS Gi. eee = 9°7939 cos (A—9) . 9°8023 
+0°33115 95202 —0°49660 —9°6960 
—0°49660 . 
—0°16545 —9°2187 denominator negative. 
C sin (A—8) —0°1118 numerator negative. 
Cot A’=257° 55’ 10” +.9°3305 A’ will be in the 3d qua- 
162 57 10 {drant. 
A’—A 94 57 20...0°0016 Csin (A’—A) 0°0016 
0:2601 Ccos¢g...... 0°2601 
+cos A’—9°3208 —cos A + 9:9805 
—0°3824dh 9°5825 +1°7467dh’ 0°24299 
bA = — 0°3824dh + 1°7467dh’ = +4 13°643, in sup- 
posing dh = dh’ = 10”, 
0°0016 C sin (A’—A).... 0°0016 
_ + sin A’ —9'9903 =a SITTIA A Pate iets —9'4668 
“—0-9815dh —9-9919 — 0'29402h’ 9°4684 
dg = 0'9815dh — 0°2940dh’ = —12”,7555, supposing 
dh = dh’ =10". 
The azimuths are computed from the inferior meridian, 
which [ suppose to be § to 360, eastward. The a are po- 
Sitive on the east side, and negative onthe west. They are 
of 180° at the lower meridian, 360° or O at the upper. 
The differential expressions dh=dg cos A—da cos gsinA 
dh’ =d¢co3.A'—dacos¢ sin A’ 
' Vol. 37. No. 155. March 1811. N 
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