XIV 



INTRODUCTION. 



If the azimuth be reckoned from the south, it must be subtracted from 180 ; and when <p 

 exceeds ;r the negative sign is to be used. 



Usually the altitudes of the sun's upper and lower limbs were measured alternately with the 

 horizontal angles. 



In such cases, and without knowledge of the time of observation, the true azimuth may be 

 calculated with like facility. For if <p and x have the same signification as in the preceding 

 formulas, and the true zenith distance of the object be represented by Z, 



j and 



sin k. sin (k 4- TT) 



Cos 2 A A = . _ \ 



sin Z. sin <p 



Deducing the true azimuth (A,) in accordance with the formulae, from the first observation 

 of the preceding series, as the assumed longitude of Santiago is 4A. 42m. 33s. 8 west of Green- 

 wich, the apparent time or hour angle (P) corresponding to 117i. 49w. 19s.55 sid. time, is 

 Ih. 47m. 32s.55 = 26 53' 8".3, at which instant the sun's north declination was 12 4' 49". 7. 

 The latitude of the station is 33 26' 25". 9 south. 



Hence 



= 13 26'34".l 



=102 4'49".7 



4 49.7 

 56 33 34.1 



45 31 15.6 

 38 23.8 



= 13 26 34.1 log. cot = 10. 621560 log. cot =10.621560 



= 224537.8 log. cos = 9.964792 log. sin = 9.587576 

 = 79 19 11.9 log. cos= 9.267932 log. sin = 9.992410 



= 11.318420 (A Y)= 10.216726 



= 87 14 59.2 

 tang! (A V) = 58 44 14.2 



.'. A=:145 59 13.4 



Calculating the other observations in like manner, we obtain the results embodied in the 

 following table : 



