86 On finding the Latitude. 
Sin y, 9°$2261 
Secta, 10:02696 (16) 
SinS  9°84957 (17) 
S.= 45° 0"7 
S+ 7, 67° 30:7 | Horary angles at the two 
S—. 22 307 observations. 
Here there is no ambiguity, since p + 2 is greater than 90°. 
The exact latitude is 19° 58’ 45”, although the example may 
have been originally framed by taking it equal to 20°. This is 
Dr. Brinkley’s 2d example (p. 10), who brings out 19° 59’ by 
one operation of Douwes’s rules and the correction by his own 
method. By the process here followed, to find the latitude re- 
quires taking out fifteen numbers from the Tables. Now one 
operation of Douwes’s rules requires taking out twelve numbers, 
and the correction must double this labour: perhaps it does 
more, if we consider the length of the calculation, and the embar- 
rassment of having to use different formule. Delambre’s me- 
thod requires nineteen different logarithms, ‘besides employing 
additions and subtractions of the arcs not wanted here, 
Example Il. 
Alt. 76° 6’ A.M. ) interval 6° 20’ [ ©’s decl. 20° N. 
Alt. 8°3’ P.M. f ¢=47° 30’ | Lat. by account 9° N,. 
Sin kh = 97072 
Sin A’ = 14004 
2A, 111076 
2B, $3068 j 
A, 55538 
B, 41534 
Cos D, 9:97299 Cos J, 9:85800 
Sin t, 9°86763 A.C.  10°14200- 
Sin J, 9°84062 Sin D, 9°53405 
b = 43° 5]’-2 Cos p, 967605 
p= 61° 41-2 
A.C, sin b, 10°15938 Cosy, 9°90330 
Log B, 961840 Cos 4, 9°85800 
Sin y, 9:77778 9°76130 
y = 36° 50’ A.C. 10-23870° 
Log A, 9°74459 
Cos y, 9°90330 Cos x, 9-98329 
Cos p4+ax, 9:33608 Poti pio aera 
Sina, -9°23938 heap 
4 = 9° 59%5 pt+e=77 28'7 sin 
