MERCATOK'S SAILING.] 



NAVIGATION. 



10G3 



As diff. lat. 690 Arith. Comp. 7'1612 



: departure 440 . . . 2 -6435 



t : mer. diff. lat. 967 . . 2 '9854 



i diff. long. 616-7 , 27901 



Hence diff. long. = 10 17' W. 

 Long, left 5" 11' W. 



Long, in 15" 28'. 



3. A ship from latitude 51 18' N., longitude 9 50 7 W., 

 anils S. 33 19 7 W., till her departure is 564 miles. Re- 

 quired her longitude in. 



We must first find the difference of latitude made ; 

 this, by Example 3, page 1059, is 858 miles, or 14" 18' S. : 

 the latitude left and latitude in will then become known; 

 and thence the meridional difference of latitude may be 

 found by the table of meridional parts, by aid of which 

 the difference of longitude is determined as below. 



the difference of longitude in Example 2, and the course 

 in this last example, without logarithms. 



For the diff. long. Ex. 2. 



mer. diff. lat. 'X dep. 



Dlff - lon - = -- 



mer. diff. lat. 



lat. left 51 18' mer. parts 

 ditf. lat. 14 18 



lat. in 37 ff 



mer. parts for diff. lat. ., 



As diff. lat. 854 Arith. Comp. 

 : departure 564 

 : : mer. diff. lat. 1205 



: diff. long. 7921 



Difference of longitude 

 Longitude left ... ... 



3598 



2393 

 1205 



7-0065 

 27513 

 3-0810 



2 -8988 



13 12 1 W. 



9 &y w. 



Longitude in ... 23 2' W. 

 Hence the longitude reached is 23 2 W. 



4. Required the course and distance from the east 

 point of St. Michael's to the Start Point. 



To find the course we must know the meridional dif- 

 ference of latitude and the difference of longitude ; the 

 course being determined, the distance will be found by 

 combining it with the proper difference of latitude, aa 

 below. 



Start Point lat. 50 13' N. Mer. pts. 3495 Lon. 3 38' W. 

 St .Michael's lat. 3748' N. Mer. pts. 2453 Lon. 2513' W. 



Diff. lat. 

 Proper diff. lat 745 miles. 



1042 



To find the course. 



As mer. diff. lat. 1042 



: diff. long. 121)5 



: radius 



: tan. course, 51 11' 



To find the distance. 



dist. = diff. lat. -=- cos. course 

 cos. 61 11' = -6208)745 (1189 

 6208 



21 35' W. 

 60 



1295m. 



3-0178 

 31123 

 10 



10-0945 



1182 

 627 



655 

 601 



64 



Hence the course is N. 51 11' E., and the distance 

 1189 miles. 

 It my be as well to exhibit here the work of finding 



967 

 4t 



3863 

 3868 



6.9)42548(616 -6 miles 

 414 



, diff. long. = 10 If' W. 



For the course Ex. 4. 

 diff. long. 



tan. course 



mer. ditt. lat. 



1.0,4,2)1295(1-243 = tau. 51 11' 

 1042 



253 

 208 



45 

 42 



3 

 Hence the course is N. 51 11' E. 



The examples already given, under the head of Middle 

 Latitude Sailing, may serve for exerciser in Mereator's 

 Sailing. A comparison of the results of the two methods 

 will also show the value of Workman's table for correct- 

 ing the middle latitude. It is necessary, however, that 

 the learner should notice, that the two reasons given at 

 page 1061, both conspire to render it uuadvisable to use 

 the ordinary table of meridional parts when the course 

 much exceeds 45 ; from 50 and upwards the middle 

 latitude method is to be preferred ; and, for the first of 

 the reasons mentioned, a small error in the course had 

 better be in defect than in excess. We shall now explain 

 the principles on which that table is constructed. 



CONSTRUCTION OF THE TABLE FOR CORRECTING TUB 

 MIDDLE LATITUDE. Let I represent the proper difference 

 of latitude, I' the meridional difference of latitude, L the 

 difference of longitude, and in the latitude in which the 

 distance measured on the parallel between the two meri- 

 dians is exactly equal to the departure. Then, first by 

 middle latitude and then by Mereator's sailing, we have 

 for the tangent of the course 



tan. course ' 



L Xcos. in 



L I 



.', cos. m = , 



Consequently, by dividing the difference of latitude 'I 

 taken in miles, by the meridional parts corresponding to 

 that latitude, we shall get cos. m, and thence m, the de- 

 grees of latitude in which the parallel between the two 

 meridians is exactly equal to the- departure. It is the 

 difference between m and the latitude of the middle 

 parallel that is given in the table at page 1060. 



By means of the corrected middle latitude, the dif- 

 ference of longitude, and the course, the nautical distance 

 is found thus : 



The expressions for the departure by plane sailin" 

 and by middle latitude sailing, are 



