104 Astronomical and Nautical Collections, 



from the nat. cosine A — D ; the remainder will be the nat. sine 

 of the true latitude. 



(a) 1. When the observations are both on the same side of the 

 meridian, and the azimuth at the greater altitude is less than the 

 other azimuth, then the fourth arc is equal to the smn of the second 

 and third arcs. 



2. Also, when the first observation is taken in the forenoon, and 

 the second in the afternoon, and the sum of the azimuths is less 

 than 180°, the fourth arc is equal to the sum of the second and 

 third arcs. 



3. In all other cases the fourth arc is equal to the difference of 

 the second and third arcs. 



The Rules when used as here directed, will in every case give the 

 latitude without ambiguity, and with sufficient accuracy, for the 

 purposes of navigation. In fact, when the common tables are used, 

 the difference between the true arc Ss or I, and that determined by 

 using the mean declination, will not, in general, be detected. In 

 practice, therefore, the latitude as determined by this method will 

 seldom differ from that which would have been obtained, if the 

 first arc had been computed by the most exact method. The de- 

 monstration of the rules is not given, as they are merely an attempt 

 to simplify the common method, and to facilitate the distinction of 

 the cases. In taking the altitudes, whether on the same or on dif- 

 ferent sides of the meridian, the observer should make X\\q difer- 

 ence between them as great as may be, without approaching very 

 near either to the horizon or to the meridian. The elapsed time, 

 therefore, should not at any time exceed eight hours. 



