There are various ways to calculate this allowance for the ship's speed, among the best of which is given in Bowditch, Art. 403, p. 179. Another, and even easier way, is the following, which was explained to the writer by Lieutenant Commander R.P. Strough, formerly head of the Seamanship Department of this School:-
1. Take the morning sight for longitude when the sun is on or as near as possible to the prime vertical.
2. Subtract the L.A.T. of the morning sight from 24 hours. This will give the total time from the morning sight to noon if the ship were stationary.
3. From the course to noon and speed of the ship, figure the change in longitude per hour in terms of seconds of time. For instance, suppose a ship were steaming a course of 275° at the rate of 11 knots per hour in approximately 38° North latitude. The change of longitude per hour for this speed would be 14' of arc or 56s of time.
4. Now the sun travels at the rate of 60 minutes or 3600 seconds per hour. To this hourly speed of the sun must be added or subtracted the hourly speed of the ship according as to whether the ship is going in an easterly or westerly direction. If, as mentioned above, the ship is steaming a course of 275° (W ½ N) and hence changing its longitude at the rate of 56s per hour, then the net rate of approach of the sun per hour would be 3600s - 56s, or 3544s per hour.
5. Divide the total time to noon from the L.A.T. of the morning sight (expressed in seconds of time) by the net rate of approach of the sun per hour. The result will be the corrected time to noon - i.e. the time at which the sun will be on the ship's meridian when the ship is changing its longitude to the westward at the rate of 56s per hour.
6. One more step is necessary. To the watch time of the morning sight, add the corrected time to noon. The result will be the watch time of Local Apparent Noon. Thirty minutes before will be the watch time of 11:30 A.M. and at 11:30 A.M. all deck clocks should be set to the local apparent time of the place the ship will be at local apparent noon.
The following example illustrates the explanation just given and should be put in your Note Book:-
Example:- At sea, August 7th, 1919. About 7:30 A.M. by ship's time, position by observation just found to be Latitude 30° 05' N, Longitude 58° 08' W. WT of morning sight 6h-53m-13s A.M. C-W 4h-37m-21s. CC + 3m-38s. Course 275°. Speed 11 knots. TZ N 90° E. What will be the Watch Time of Local Apparent Noon?
| WT | 6h 53m 13s A.M. | |
| + | 12 | |
| ————————— | ||
| 18 53 13 | ||
| C-W | 4 37 21 | |
| ————————— | ||
| CT | 23 30 34 | |
| CC | + 3 38 | |
| ————————— | ||
| G.M.T. | 23 34 12 | |
| Eq. T. | - 5 42 | |
| ————————— | ||
| G.A.T. | 23 28 30 | |
| Lo. in T. | 3 52 32 | |
| ————————— | ||
| L.A.T. | 19 35 58 | |
| 24 00 00 | ||
| ————————— | ||
| Total time to Noon | 4h 24m 02s |