Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch. VI]

NAVIGATION: DEAD RECKONING

79

(lat. 37048' N, long. 122024' W), the variation being 14020' E, and deviation 5040' E.
57. Dead reckoning. Given several successive short sailings
each with a constant course, we find the true courses, then compute the net difference of latitude and net departure as in Traverse
Sailing, and finally find the course and distance made good and
the position at sea usually by Middle Latitude Sailing (not by
Plane Sailing as in the final step in Traverse Sailing), but by
Mercator's Sailing if still greater accuracy is needed.
EXAMPLE. A ship sails from a point near Cape Henry lighthouse (lat. 36~
55.6' N, long. 76~ 0.5'W) on the following series of courses, with variations and
deviations of compass and leeway shown. Find the course and distance made
good and the position by dead reckoning.
Compass Varia- Devia- Total True Dis- W
I N S E w
course tion tion eewy error course tance
28~ 6~W 30E 0 30 25~ 1.4 1.3 0.6
530 50 W 30 E 3 W - 5~ 48~ 27.6 18.5 20.5
191~ 6~ W 0 3~ E -3~ 188~ 31.5 31.2 4.4
67~ 6~W 3 E 5 W — 8~ 59~ 14.2 7.3 12.2
1770 6~ W 0 6~ E 0 177~ 11.0 11.0 0.6
42~ 8~W 3 E 3 W — 8~ 340 87.0 72.1 48.7
99.2 42.2 82.6 4.4
Made good 53054' 96.82 82.6 4.4
57.0 78.2
Diff. lat. 57.0' N Dep. 78.2 = D cos L,
Lat. out = 36055.6' N D = diff. long. = 98 for L = 37~
Lat. in = 37052.6' N 99.2 for L = 38~
Mid. lat. L = 37024.1' 98.5 for L = 37~24,
Long. in = 7600.5' - 138.5' = 74022' W.
EXERCISES ON DEAD RECKONING
1. From lat. 48~20.5'N, long. 10~10' W, a ship sailed 22.2 miles on
compass course 257~, variation - 20~, deviation - 3~; thence 216.5
miles on compass course 232~, variation - 20~, deviation - 1~. Find
lat. in and long. in.
2. From lat. 49040.51 N, long. 15~ W, a ship sailed the courses