This is a method mentioned in David Burch’s book, Emergency Navigation. It is a means of ascertaining longitude from the time of sunrise or sunset. The accuracy is based on any number of things including watch error and DR position. It is an instructive procedure to follow as it reinforces basic principles of the movements of the sun.
The premise is as follows: if we can time the moment at sunrise, when the upper limb of the sun becomes visible on the horizon, and compare that to the tabulated time listed in the daily pages of the Nautical Almanac, we can reasonably calculate our longitude based on the time difference between the observed and the tabulated times. If we choose to use this method at sunset we would time the sight at the moment that the lower limb of the sun touches the horizon.
Let’s see how it works:
On the morning of Feb. 10, 2010, we are at a latitude of 25 degrees north. We want to calculate the longitude based on the sunrise.
We note that the time of the upper limb appearing on the horizon is at 10 hours 42 minutes 15 seconds GMT.
On that day the tabulated time of sunrise at latitude 20 degrees is at 6 hours 32 minutes LMT. The time for sunrise at 30 degrees is 6 hours 44 minutes. My latitude is halfway between so I take one half the difference of 12 minutes of time and get 6 minutes. I add this on to the time of sunrise at 20 degrees and get a calculated time of sunrise at 6 hours 38 minutes at 25 degrees north latitude.
Now I take the observed time and subtract from that the tabulated time:
10: 42: 15 Observed time
-6: 38 Tabulated time
4 hrs 4 min 15 sec
This time is then converted to degrees by using the Arc to Time conversion table and the increments and corrections tables at the rear of the Nautical Almanac. To wit:
4 hours equals 60°
4 min. equals 1°
15 sec. equals 3.8′
Therefore our longitude equals 61° 03.8′