Mercator Sailings Example 2
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L1: 1306'S
L2: 706'N

λ1: 17545'E

λ2: 17715'W

If you know both the starting and ending positions and are attempting to find the course and distance from one location to the next, as described above, begin by finding the meridional parts (M) between each of the positions and the equator.
Notice that M for P1 is written as M1, and M for P2 is written as M2.
Then find the difference between L1 and L2, l,  in degrees and tenths, and the difference between M1 and M2, m, in minutes of longitude at the equator. Notice that as we cross the equator in this example, the two M values are added to find m, as are the two L values added to find l.
The letters in the parenthesis after l and DLo indicate the direction of travel. If moving in a northerly direction, (N) follows l. If moving in a westerly direction, (W) follows the DLo.

L2: 706'N
M2: 424.2'

λ2: 17715'W

L1: 1306'S
M1: 787.7'

λ1: 17545'E

l: 2012'(N)
= 1212nm
m: 1211.9'

DLo: 7(E)
= 420'(E)

Next, enter the known m value and the known DLo value into the sine and cosine equations to find your course and distance. (See tables at right)

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tan C = DLo/m
tan C = 420 / 1211.9
C = N 19.1 E
Cn = 019.1 T

cos C = l/D
Cos 19.1 = 1212/D
D = 1282.6nm