ve not changed your longitude at all.

In sailing East or West, however, your problem is more difficult. Only
on the equator is a minute of longitude and a nautical mile of the same
length. As the meridians of longitude converge toward the poles, the
lengths between each lessen. We now have to rely on tables to tell us
the number of miles in a degree of longitude at every distance North or
South of the equator, i.e., in every latitude. Longitude, then, is
reckoned in _miles_. The number of miles a ship makes East or West is
called Departure, and it must be converted into degrees, minutes and
seconds to find the difference of longitude.

A ship, however, seldom goes due North or South or due East or West. She
usually steams a diagonal course. Suppose, for instance, a vessel in
Latitude 40 deg. 30' N, Longitude 70 deg. 25' W, sails SSW 50 miles. What is the
new latitude and longitude she arrives in? She sails a course like this:

[Illustration]

Now suppose we draw a perpendicular line to represent a meridian of
longitude and a horizontal one to represent a parallel of latitude. Then
we have a right-angled triangle in which the line AC represents the
course and distance sailed, and the angle at A is the angle of the
course with a meridian of longitude. If we can ascertain the length of
AB, or the distance South the ship has sailed, we shall have the
difference of latitude, and if we can get the length of the line BC, we
shall have the Departure and from it the difference of longitude. This
is a simple problem in trigonometry, i.e., knowing the angle and the
length of one side of a right triangle, what is the length of the other
two sides? But you do not have to use trigonometry. The whole problem is
worked out for you in Table 2 of Bowditch. Find the angle of the course
SSW, i.e., S 22 deg. W in the old or 202 deg. in the new compass reading. Look
down the distance column to the left for the distance sailed, i.e., 50
miles. Opposite this you find the difference of latitude 46-4/10 (46.4)
and the departure 18-7/10 (18.7). Now the position we were in at the
start was Lat. 40 deg. 30' N, Longitude 70 deg. 25' W. In sailing SSW 50 miles,
we made a difference of latitude of 46' 24" (46.4), and as we went
South--toward the equator--we should subtract this 46' 24" from our
latitude left to give us our latitude in.

Now we must find our difference of longitude and from it the new or
Longitude in. The first thing to do is to f