314 DESCRIPTION OF GARNETT/'s 



To find the Distance, 



As either angle of position 89 79' 9' log. sine. 9.99216G 



: its opposite polar distance SO log. sine- 9 884254 



; : the difference of longitude 60 log. sine. 9.937531 



: nearest distance 42° 29' =2549 miles log. sine. 9.829619 



To find the Latitude at the middle Longitude, 



Latitude 40° 0' nat. tang. 0839100 (N. B. Should no table of nat. tang. 



Latitude 49 26 nat. tang. 1 168095 be at hand, take the numbers tq 



the log. tangents.) 



Sum of natural tangents. 2.007195 



Half sum of ditto. 1.003597 log.0001558 



Half the dift. of longitude 30° subtr. log. cos. 9-937531 



Gives the lat. at the middle long, or central mcr. 49° 12'J tang. 0.064027 

 So that the angles of position T a b, I b a are 79 9 and 56° 29' 

 The distance ab . ■ • , .42 29=2549 miles 

 The latitude of d, at the middle longitude 49 12i 



From which data the Special Chart has been constructed accord- 

 ing lo the directions given in the Scholium, and the first course as 

 far as 5° difference of longitude is found by adding 96'= 1° 36', 

 (half the angle of the inclination of the meridians in the lati- 

 tude 4-0° by the Table in page 3 15) to the angle of position 56° 

 29'; making N. 58° 5' E. for the course from the longitude of 

 65° W. to 60° W. or if the course had been taken from the 

 angle of position in the special chart at the longitude of 621. 

 it would be the same, according to Prop. 2d. and perhaps this 

 last is as simple a rule as can be given, for it appears to be a 

 useless labour to calculate all the angles of position by Spheri- 

 cal Trigonometry, as different accidents may make the ship 

 occasionally deviate from the intended calculated track, and 

 a Special Chart will always shew the courses to sufficient exact- 

 ness, if the ship were even to deviate 5 degrees of latitude on 

 either side of the first intended track or great circle. 



In the same manner a SPECIAL CHART can be construct- 

 ed for any other track, by means of which it is easy to sail from 

 any part on the globe to any other, the shortest way possible, 

 supposing there are no intervening obstructions, or local reasons 

 for taking a different course; the Special Uiart being an exten- 

 sion of that part of the globe through which the track lies, all 

 the bearings and distances are truly represented. 



