by means of Two known Stars. ° 18g 
Trigonometrical Method. 
Corp... O'B9B80484 tank oe we wees 0'2845877 ' 
Cee ROMS SU 2G'668 5677" sin! Wes PN 408 9°8158318 
Ta,v=40°52' 22",30=09°9372161 
d= 8 2243 ,10 C cos (d+.2).. .. 0°1852598 
é+”7=49 15 5,4 tan V 62°36 58”,79 0°2856793 
Both methods require seven logarithms, which are either 
the same as in the second operation, or arithmetic comple- 
ments of one another, as in.the first. F and 2, F — ¢ and 
é--ax are arcs complements of each other. 
On the contrary, the operations required in order to find 
out the third auxiliary angle are quite different. 
Calculation of the Angle W according to Mr. Gauss. 
Sim Pat sk 98786157 nS 12343 3, Wien 0 3270489 
Csin ® .... 0°3278629 BOseV, Le gis. Wiaksei s 1 &/ O30027075 
C cos (F—¢) 0°1205703 tang PSone 2». 00113399 
cot (F—0),.......... 0 0646895 
Sig@esis i. STite ek eee cos W = 52° 0 14’,259 7893035 
hema near... 6k Se V = 6236 58,79 
m= 2°123433 03270489 V—W=u= 10 36 44 ,54 
This operation requires nine logarithms im the case of 
h = h’; it would require eleven, if the altitudes were un- 
equal. 
In the case of both being equal, the trigonometrical me- 
thod would have much the advantage. I neglect it in order, 
to give calculation the disposition requisite for all cases. 
Trigonometrical Calculation. ; 
CosVis its. caves. 96627075 © n—1=1'123433.. 0'0505666 ~ 
Tang (O+A).....- 0'0646895 Tangh.......... 00113399 
Cot D=6:° 54'20",5 9:7273970 Cot D......, ++ ++ 97273970 
Ce 0. =. hae 03270490 ©9S W=52°0'14",25 9°7893035 
SURINOT ooo cate eels ee ves se | 
el Reg heb “edie 
n= 2°123433 = 0327090 
T must first find cot D = cos-V tang (+2). The lo- 
garithms of cos V and tang (9+) = vos (F—9) are comr 
mon to both methods. The arc D is the third side of the 
triangle which has given V. 
In the case of both being equal, the cosine of D-is the 
number x of the analytical method, Commonly 2 = 
cos D sin h : Eterna - 
ho oy ae m—1 1s common to both methods, they-assign 
a same value to the angle W. 
The trigonometrical method only requires eight lo- 
garithms 
