108 BULLETIN OF THE 



I give below an example* of computation in the forms which 

 American navigators chiefly use. The preparation of the data 

 and Cols. 1 and 2 belong to the ordinary "iiyyie sight," which 

 IS employed daily in finding the longitude by a chronometer. 

 The only additional work required for Sumner's method is Col. 3 

 if two latitudes are used, or Col. 4 if the azimuth is to be found, 

 together with their results at the bottom of Col. 1. As the sec- 

 ond latitude is 20' greater than the first, the coi'responding half 

 sum and remainder will be 10' greater than those in Col. 1 ; 

 but it is not necessary to write them down; and the correspond- 

 ing logarithms in the two columns can be taken from the table at 

 the same opening. 



The ship is supposed to be in north latitude, and the altitude 

 of the sun observed in the morning. 



Greeuwichap. time 1 2 3 4 



by chronometer 2" 54'" 5^ P. M 1st lat. 2d. la*.. 1st lat. 



Corrected alt. of O 290 6/25" 360 30' 360 50' 360 30' 



1st latitude . . 36 30 1. sec. 0.09482 .09670 1. sec. 0.09482 

 O's polar distance no 26 56 1. cosec. 0.02827 .02827 1. sec. 0.45671 



Sum 176 3 21 



Half sum . . ,88 140 1. cos. 8.53674 .49841 1. cos. 8.53674 

 Half sum— alt. . 58 55 15 1. sine 9.93271 .93346 1. cos. 9.71284 



2)8.59254 .55684 2)8.80111 



1st local ap. timet '^-^^ 28°> 43^ A. I. 1. sine ^ 9.29627 

 2rl " " 10 32 27 1. sine -* 9.27842 



1st longitude . . 4 25 22 = 66© 20'. 5 W. 

 2d " 4 21 38 = 65 24. 5 W. 



Half azimuth of © 75 26 1. cos. J 9.40056 



Azimuth of 0- • N. 150 52 E. 

 " of line . N. 60 52 E. 



The line may be projected by the two positions, 



1st lat. 36° 30' N. ; long. 60° 20' 5 W. ; 

 2d " 36 50 N. ; " 65 24 .5 W. ; 

 or, by the 1st position, and the direction N. 60" 52 E. 



* Navigation and Nautical Astronomy, prepared for the use of the U. S. 

 Eaval Academy, p. 226, New York, 1866. 



t In Bowditch's Table the entire hour angle is given corresponding to 

 the 1. sine of its half. 



