NAVIGATION CHART, i>CV. 315 



But whenever the ship is driven out of her intended course, 

 or her latitude and longitude has been determined more cor- 

 rectly by astronomical observations, the course must be again 

 adjusted,, either by drawing a new distance-line on the Special 

 Chart, which will shew the new angle of position to the in- 

 tended port sufficiently correct, or calculated by case seven of 

 Spherical Trigonometry, where two sides (the co-latitudes or 

 polar distances of the two points) and the included angle (dif- 

 ference of longitude) are given; as in the following example, 

 which is also necessary to shew in what manner a Special Chart 

 is constructed, being considered as part of a great circle, con- 

 taining in length the distance of the two places, with a few 

 contiguous degrees in breadth on each side, straightened into a 

 plane superficies or parallelogram ; the meridians crossing the 

 great circle at every five degrees of longitude, and shewing the 

 different angles of position. 



EXAMPLE. 



Suppose it was intended to sail from the latitude of 40° N". 

 and longitude 65° W. by the arc of a great circle, to the latitude 

 of 49° iif>' N. and longitude of 5° W. making the nearest 

 course to the Lizard from the above place ; and to construct a 

 Special chart in order to lay down the ships track. Required 

 the angles of position, nearest distance, and the courses that will 

 meet the great circle, at every five degrees difference of longi- 

 tude? 



To find the Angles of Position. 



Co-lat. or Polar.dist. 50° 0' /„ „ ^.. *, t . . ■- r- . ~ , . 



Co-lat. or Polar-dist. 40 34 (N- B. These two P. dists. must be from the same Pole.) 



As J the sum of P. dists. (x) 45 17 log. sine 9.851622 log. cos. 9.847327 



* the difference of ditto. 4 43 log. sine 8.915022 log. cos. 9 998527 

 I the diff. of longitude 30 log. cot- 0.238561 log. cot. 0.238561 



,, „ m jv„„„ Ol 20 log. tang. 9301961 log. tan. 0.389761 



: the corresponding arcs £ 6r 49 (t | kfi th | supplcment of ^ if s exceeJg < 



Sum of corresponding arc9 79 9=Angle of Position at the greater latitude. 

 Difference of ditto 56 C9= Angle of Position at the less latitude. 



90°-^ 



