On finding the Latitude. 85 
Then, if A be the latitude, and S the horary angle of the mid- 
die time, which are the things sought, we shall obtain the fol- 
lowing formule, by means of the premised lemma and the rules 
for solving right-angled spherical triangles. 
1. Sin b = cos D sin #, 
sin D 
‘cos 5? 
2. Cos p = 
3y Sin Y= 
sin 6 ? 
4. Cos a= cos y cos 6? 
5. Sin A = cos y cos (p F 2), 
6. Sin S = 
For the sake of illustration, I shall now subjoin some exam- 
ples; and I have purposely taken them from Dr. Brinkley’s Ad- 
dition to the Nautical Almanac 1822, in order that the two modes 
of calculation may be more easily compared. 
Example I. 
Alt. 21° 26’ A.M. | interval, 34 , 
Alt. 60° 56’ A.M. f ¢ = 22°30’ { recdcel. ti. 
Sink = 87406 (1) 
Sin A’ = 36542 (2) 
2A, 123948 
cosa’ 
2B, 50864 
A, 61974 
B, 25432 
Cos D, 9:99993 (3) Cos 4, 9:96563 (6) 
Sint, 958284 (4) ‘A.C 10°03437 
Sin J, 958277 (5) Sin D, 8:24186 (7) 
b = 22° 29/8 Cos p, 827623 (8) 
P= 88° 55° 
A.C Sin J, 10°41723 Cos b, 9-96563 
Log B, 940538 (9) Cosy, 9:87340 (11) 
Sin y, 982261 (10) -9°83903 
y = 41° 394 A.C. 10-16097 
Log A, 9°79221 (12) 
Cos x, 9:95318 (13) 
Cos y, 9°87340 
Cos (p—x), 9°66021 (14) x = 26° 78 
Sin a, 953361 (15) pax = 62 47 +2 
A = 19° 58’-7, latitude, 
Sin 
