Astronomical and Nautical Collections. 109 



The following directions will distinguish all the cases. 



1. When the observations are both on the same side of the me- 

 ridian, and the azimuth at the greater altitude is less than the other 

 azimuth, the fourth arc is equal to the sum of the second and 

 third arcs. 



2. When the first observation is taken on the E side of the me- 

 ridian, and the second on the W side, and the sum of the azimuths 

 is at the same time /ess than 180°, then also the fourth arc is equal 

 to the sum of the second and third arcs. 



3. In all other cases, the fourth arc is the difference of the second 



and third arcs. 



Example V. 



December 6, 1824, in N. latitude, let the altitude and azimuth of 



Regulus be respectively 12° 30', and 83°; four hours afterwards 



when on the same side of the meridian, let his altitude and azimuth 



be 56° and 132°. Required the latitude. 



To find arc I. To find arc V. 



I. cos. D = 9.989051 1. cos. A = 9.747562 



1. sin. X E =: 9.698970 1, cos. D ~ 9.989051 



29° 10' 47" 9.688021 1. s. 2 . 1. sin. IV = 8.946824 



I = 58 21 34 const.log. = 0.301030 



To find arc II. N = 96487 '8.984467 



1. sin. E = 9.937531 n. cos. A-D = 729108 



1. COS. D = 9.989051 — N = 96487 



1. cosec. I = 0.069890 Lat. = 39 14' 38" 632621 n.s. 



82° 42' 25" 9.996472 1. s. 

 11=41 21 12 — 



To find arc III. o , „ 



1. cosec. I =: 0.069890 I = 58 21 34 



1. sec. A = 0.252438 A = 56 



1. cos. I S + a = 9.650594 

 1. sin. h S-a = 9.890070 



2) 19.862992 



III = 58° 39' 28" 9.931496 1. s. 

 II = 41 21 12 5 . S + a = 63 25 47 



IV = 17 18 16 i.'S^srSO 55 47 



