MERCATOK'S SAILING.] 



NAVIGATION. 



IOCS 



and thence determine the whole difference of latitude 

 and departure, as also the corresponding direct course 

 and distance, exactly as in plane sailing. (See page 

 1052). 



The traverse now being reduced to a single course, 

 find the corresponding difference of longitude, either by 

 mid-latitude or Mercator's sailing. 



This method is less accurate than that which follows ; 

 because, as already observed (page 1056), the aggregate 

 of the several departures is not, in general, the same as 

 the single departure due to the correct course and dis- 

 tance. It is better, therefore, to take the several differ- 

 ences of latitude and departures separately, and thus to 

 determine the difference of longitude due to each distinct 

 course, and thence the whole difference of longitude 

 made. The second method is, therefore, this : 



2. Fill up the columns of the traverse table, as directed 

 above ; but fiud the aggregate of the diff. latitude 

 columns only. By means of the successive latitudes 

 reached at the end of each course, find the corresponding 

 mid-latitude ; and with this, and the departure, deduce 

 the difference of longitude made at the end of each course 

 by mid-latitude sailing, and thence the whole diff. long, 

 made good. 



But if Mercator's, instead of the mid-latitude method 

 be employed, then the several departures need not be 

 inserted in the traverse table at all. An example will 

 sufficiently show the mode of proceeding by each 

 method. 



Examples. 



1. A ship from latitude 38 14' N., longitude 25 5C' W., 

 has sailed the following courses and distances, namely 



1st. N.E. 6N. JE., 66 miles. 2nd. N.N.W., 38 miles. 

 3rd. N.W. 6 W., 46 miles. 4th. S. S E. , 30 miles. 5th. 

 S. // \V., 20 miles. 6th. N.E. b N., 60 miles. Required 

 the latitude and longitude in, and the direct course and 

 distance to it 



BY THE FIRST METHOD. 



The direct coursj and distance, due to diff. lat. 108-4, 

 and dep. 21-6, are found by reference to the traverse 

 table, or by computation, as at page 1055, to be as 

 above. 



To find the diff long, by Mid-Latitude Sailing. 



Latitude left 

 Diff. lat. 108 m. . 



Latitude in 

 Sum of lats. 



. 38 14' N. 

 . 1 48' N. 



. 40 2' N. 

 . 78 16' 



Half sum = mid. lat . . 39 8' 



Diff. long. = dep. -r- cos. mid. lat. 



= 21 6 H- -7757 . 

 Longitude left .... 



Longitude in . . . . 



= 28' E. 

 25 56' W. 



25 28' W. 



BT THE SECOND METHOD (MID-LATITUDE). 



Diff. latitude 108-4 N. 



To find the tame by Mercator's SaUiny. 



Latitude left, 38 14' mer. pta. . 2486 

 Latitude in, !< li . . 2625 



Meridional diff. lat. . . . 139 



Diff. long. = mer diff, lat. x tan. course. 



= 139 X "199 - . 28' E. 



Longitude left .... 26 56' W. 



Longitude in 25 28 W. 



The diff. long, columns may bo filled up from the tra- 

 verse tible, by taking the complement of each mid. lat. 

 a a course, and, with the corresponding departure, 

 finding the proper number of miles or minutes in the 

 distance column of the table ; or, which is somewhat 

 simpler, take the middle latitude itself as a course, and 

 seek the corresponding departure in the diff. lat. column 

 of the table, against which, in the dist. column will be 

 found the number of miles of diff. long. In this way 

 the two diff. long, columns, as exhibited above, have 

 been formed. 



Difference of longitude 27' E. 



BY THE SECOND METHOD (MEECATOR). 



Conn 



N.E.4N.JE. 

 N N.W. 

 N.W. \V. 

 S.S.E. 

 S. 6 W. 

 N.E. li N. 



Difference of latitude 10S 4 N. Difference of longitude 27-1 E. 



The diff. long, columns are here also supplied from the 

 traverse table by entering it with the given course and 

 mer. diff. lat. taken as the proper ditf. lat. : the corre- 

 sponding departure, furnished by the table, is the ditf. 

 long. 



The longitude in, by the second method, whether the 



The 40 corresponding to this In the " Lat." column is more nearly 

 39J. io that 50 5 u written instead of 50'7, given in the table 



60 



