PLA3TE SAILING.] 



NAVIGATION. 



1053 



The course being 3 points is 33 45' ; hence 

 1. To find the diff. lat. 

 By logarithms. 



Asrad -10 



: cos. course, 33 43' . . 9-9199 

 :: distance = 98 . . . 1'9912 



i diff. lat. = 81-49. 



1-9111 



. Without logarithms, 

 diff. lat. = cos. course X distance, 

 cos. course, 33 45' . . . '8315 



distance . . . 



66.520 

 74835 



Diff. lat = 81-487 



Huice the difference of latitude is 81 '49 miles, S. 



2. To find the departure. 



By logarithms. 

 As rad. . . . . . 10 



: sin. course, 33 45' . . 97447 

 : : distance = 98 . . 1-9912 



s departure = 54-44 . . 1'7359 



Without logarithms. 



dep. = sin. course X distance. 



sin. course, 33 45' . . . "5556 



distance . . . . . 98 



44448 

 60004 



544488 



47 .SO 7 N. 

 1 21' S. 



Hence the depanire is 54-45 miles, W. 

 The latitude from . 

 The difference of lat. 



Latitude in . 



40 9' N. 



degrees . 1 21', 



Departure 54 miles W. 



The example is here worked by computation : there is 

 another way of obtaining the results namely, In 

 tiim. This latter method requires reference to a table 

 called the Traverse Table, ana which is to be found in 

 every collection of navigation tables. The table is 

 arranged much like a table of sines and cosines ; the 

 angles of the courses are inserted at the top of the page, 

 when they do not exceed 45", and at the bottom when 

 they do, and the distances are placed down the margin. 

 By entering the table with any given course and distance, 

 the corresponding difference of latitude and departure 

 can be taken out from the body of the table.* 



This table is a very useful one for seamen, as it com- 

 putes for him the two formula worked by in the right- 

 hand column of operations above ; that is, entering his 

 table with the proper course and distance, he finds, 

 under the respective heads "Lat." and "Dep.," the 

 values of 



cos. course X distance, and sin. course X distance 

 already worked out for him, usually as far as two places 

 of decimals, which is an extent amply sufficient. A table 

 of natural sines and cosines is thus all that is wanted to 

 construct a traverse table. In such a table each sine and 

 cosine is multiplied by all distances from 1 up to 120, 

 which is the ordinary limit to which the columns of dis- 

 tances are carried. Distances which exceed 120 miles 

 may be cut up into smaller distances, and the portions 

 brought within the compass of the table. 



2. A ship from latitude 47 3tf N. , sailing N. W. b W., 

 finds that she has made 82 miles of departure : What is 

 her distance run, and her latitude in I 



The course being 5 points is 5C 16'; hence 



Set Table* ul IMgce 1063 and 1069. 



1. To find the distance. 



By logarithms. 



As sin. course, 56 15' . .- 9 '9198 

 : radius . . . .10 

 : : departure = 82 . . 1-9138 



: distance = 98-62 . . 1-9940 



Without logarithms, 

 dist. = dep. -;- sin. course. 



sin. course, 56 15' . 8.3.1.5)82 P ' (98 "6 



7484 



716 

 605 



51 



.'.distance = 98 -6 miles. . 60 



2. To find the diff. lat 



By logarithms. 



As tan. course, 56 15' . - 10-1751 



: radius . . . .10 



: : departure = 82 . 1-9138 



: diff. lat = 54-79 . . 1-7387 



Without logarithms, 

 diff. lat. = dep. -=- tan. course, 

 tan. course, 50 15' . 1-4.9,6.6)82 (54-8 



7483 



717 

 699 



.*. Diff. lat. = 54-8 miles 

 Latitude from . 



118 

 119 



- 55' X. 

 47 30' N. 



48 25' N. 



Latitude in . . 

 3. A ship has sailed S.E. 6 S., from lat. 47 30' N. to 

 lat. 46 8' Is. llequired the distance run and the departure 

 made. 



The course being 3 points is 33 45': 

 , ( lat. from 47 30 7 N. 

 !0 ( lat. in 46 8' N. 



diff. lat. 1 22' N. = 82 miles. 

 1. To find the distance. 



By logarithms. 



As cos. course, 33 45' . . - 9 -9198 

 : radius . . . .10 

 : : diff. lat. = 82 . . 1-9138 



: distance = 98-62 . . 1-9940 



Without logarithms. 



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



cos. course, 33 45' . -8,3,1,5)82 (98-62 



74835 



.'. dist. 98-62 miles 



7165 

 6652 



613 



499 



14 

 17 



2. To find the departure. 



By logarithms. 



As radius .... 10 

 : tan. course, 33 45' . . 9 -8249 

 : : diff. lat. =82 . . 1-9138 



: departure = 54-79 



1-7387 



