The Relationship between Time and Longitude
Ordinarily, we use mean solar time, which is measured by the motion of
the mean Sun around the Earth. Lets suppose your ship is on longitude
60°W. When the Sun is on your longitude or meridian, it is noon. As the
Sun continues to move west and crosses over longitude 61°W, it is noon
there and the time on your meridian is later. In fact it is the time
equivalent of 1° later. But you cant measure 1° on your watch; you must
convert this 1° of arc to units of time.
To have a standard reference point, every celestial observation is timed
according to the time at the Greenwich meridian. Usually this is
determined by means of the chronometer which is set to GMT. To clarify
the relationship between time and arc, lets consider a situation in which
you know your longitude exactly at noon, and you want to find out the
time in Greenwich.
Arc to Time
When the Sun is on a particular meridian, it is noon at that meridian. In
other words, when the Sun is on the Greenwich meridian (0°), it is noon
by Greenwich time. To make the problem easier, lets say youre in 90°W
longitude. Its noon where you are, so the Sun must also be in 90°W
longitude. So, since leaving Greenwich, the Sun has traveled through 90°
of arc. Because it was 1200 (noon) Greenwich time when the Sun was at
0°, the time at Greenwich now must be 1200 plus the time required for
the Sun to travel through 90° of arc.
The following information provides all the elements of a problem for
converting arc to time. If you know that it takes 24 hours for the Sun to
travel 360° or one complete revolution, it should be easy to find how long
it takes it to go 90°. If the Sun goes 360° in 24 hours, it must go 15° in
1 hour. If it goes 15° in 1 hour, it must go 1° in 4 minutes. Then, to go
90°, it takes 90 x 4 minutes, or 360 minutes, which is the same as 6
hours. Six hours ago it was 1200 Greenwich time; therefore, the time at
Greenwich now must be 1800. You actually have converted 90° of arc to
6 hours of time. In doing so, you discovered the basic relationship
between arc and time. This relationship is stated as 15° of longitude (arc)
equals 1 hour of time.
Your problem could be converting time to arc--the reverse of the one we
worked out. Tables for converting either way are in The Nautical
Almanac and in Bowditch, but if you acquire the following easy methods
of converting, you wont have to refer to publications. First, you must
memorize the values for arc and time.