ind the _average_ or middle
latitude in which you have been sailing. Do this by adding the latitude
left and the latitude in and dividing by 2.

40 deg. 30' 00"
39 43 36
-----------
2)80 13 36
-----------
40 deg. 06' 48" Mid. Lat.

Take the nearest degree, i.e., 40 deg., as your answer. With this 40 deg. enter
the same Table 2 and look for your departure, i.e., 18.7 in the
_difference of latitude_ column. 18.4 is the nearest to it. Now look to
the left in the distance column opposite 18.4 and you will find 24,
which means that in Lat. 40 deg. a departure of 18.7 miles is equivalent to
24' of difference of Longitude. We were in 70 deg. 25' West Longitude and we
sailed South and West, so this difference of Longitude should be added
to the Longitude left to get the Longitude in:

Lo. left 70 deg. 25' W
Diff. Lo. 24
-----------
Lo. in 70 deg. 49' W

The whole problem therefore would look like this:

Lat. left 40 deg. 30' N Lo. left 70 deg. 25' W
Diff. Lat. 46 24 Diff. Lo. 24
------------- ----------
Lat. in 39 deg. 43' 36" N Lo. in 70 deg. 49' W

There is one more fact to explain. When the course is 45 deg. or less (old
compass reading) you read from the top of the page of Table 2 down. When
the course is more than 45 deg. (old compass reading) you read from the
bottom of the page up. The distance is taken out in exactly the same way
in both cases, but the difference of Latitude and the Departure, you
will notice, are reversed. (Instructor: Read a few courses to thoroughly
explain this.) From all this explanation we get the following rules,
which put in your Note-Book:

To find the new or Lat. in: Enter Table 2 with the true course at the
top or bottom of the page according as to whether it is less or greater
than 45 deg. (old compass reading). Take out the difference of Latitude and
Departure and mark the difference of Latitude minutes ('). When the
Latitude left and the difference of Latitude are both North or both
South, add them. When one is North and the other South, subtract the
less from the greater and the remainder, named North or South after the
greater, will be the new Latitude, known as the Latitude in.

To find the new or Lo. in: Find the middle latitude by adding the
latitude left to the latitude in and dividing by 2. With this middle
latitude, enter Tab