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

74

TRIGONOMETRY

[Art. 52

rate when the distance sailed is more than 500 miles, especially
when the course is less than 45~ or the ship reaches a high latitude. In these cases Mercator's Sailing should be used.
In Mercator's Sailing we use two plane right triangles each
having an angle equal to the ship's course C. One triangle (Fig.
38) is drawn on a Mercator chart and has as legs the difference of
difft long.
C
FIG. 39
FIG. 38
longitude, and the meridional difference of latitude m corresponding to the actual latitudes of the point sailed from and the
point reached. The hypotenuse is not used. The other triangle
(Fig. 39) has as hypotenuse the distance D sailed and as vertical
leg the difference of actual latitudes; its horizontal leg is not used.
This plane triangle is the one which we saw (Art. 49) can be substituted for the spherical triangle on the earth's surface.
For computation by logarithms, we use the formulas
diff. long. = m tan C, diff. lat. = D cos C,
which follow from Fig. 38 and Fig. 39 respectively. To use
Table VI, we have only to note that, in Fig. 38, m is the leg adjacent to C and diff. long. is the leg opposite.
EXAMPLE 1. A ship in lat. 42~30'N and long. 58~51'W sails 300 miles
S 34~ E. Find the latitude and longitude arrived at, using Mercator's Sailing.
Solution. By Table VI, diff. lat. = 248.7 miles = 4~8.7' S.
lat. out = 42030' N, whose merid. parts = 2806.4
diff. lat.= 4~ 8.7' S
lat. in = 38021.3' N, whose merid. parts = 2480.8
merid. diff. lat. m = 325.6.