In getting your longitude by a time sight of a star, you proceed somewhat differently from the method used when observing the sun. What you wish to get first is G.S.T., i.e., the distance in time Greenwich is from the First Point of Aries. If you can then get the distance the ship is from the First Point of Aries, the difference between the two will be the longitude in, marked East or West according as to which is greater. By looking at the diagram furnished you when we were talking of Sidereal Time, all this becomes perfectly clear. The full rule for finding longitude by a star is as follows, which put in your Note-Book:

Correct your CT to get your G.M.T. From the G.M.T. get the G.S.T. From the observed altitude of the star, obtain the star's H.A. at the ship in the same way L.A.T. is secured in case of the sun. To or from the R.A. of the star add, if West of your meridian, subtract if East of your meridian, the star's H.A. at the ship, just obtained. The result is the R.A. of the ship's meridian or L.S.T.

Find the difference between G.S.T. and L.S.T. and the result is the longitude, marked East or West according as to whether G.S.T. is less or greater than L.S.T. Note: Always take the star's H.A. from the top of the page of Table 45.

Dec. 2, 1919. A.M. Observed altitude Star Sirius 2O° 05' 20", West of meridian. CT 11h 45m 29s P.M. CC 1m 28s slow. IE - 1' 20". HE 21 ft. Latitude by D. R. 38°57' N. Required longitude in.

Assign for Night Work or work in the class room examples similar to the following:

1. April 16, 1919, in Latitude 11° 47' S. Observed altitude of the Star Aldebaran, West of the meridian 23° 13' 20". CT 6h 58m 29s. CC 2m 27s fast. IE - 2' 00". HE 26 ft. Required longitude in.

2. Dec. 10th, 1919. Observed altitude of Star Sirius 20° 05' 40" West of meridian. CT 11h 45m 29s. CC 1m 28s slow. IE - 1' 20". HE 21 ft. D.R. latitude 38° 57' N. Required longitude in.

Note to Instructor: If any time in the period is left or for Night Work assign examples to be worked by Marc St. Hilaire Method, changing slightly the D.R. Lat. and Longitude just obtained by the Time Sight Method.

WEDNESDAY LECTURE

Examples on Longitude by Chronometer Sight of a Star

1. Dec. 9th, 1919. In latitude 36° 48' N. Observed altitude Star Capella, East of meridian 46° 18' 30". IE 2' 50" off arc. HE 33 ft. CT 10d 3h 05m 05s A.M. CC 1m 18s slow. Declination of star is 45" 55' N. Required longitude in.

2. October 26th, 1919. In latitude 39° 54' S. Observed altitude Star Rigel, West of meridian 42° 18' 40". CT 27d 10h 32m 55s A.M. CC 2m 18s fast. IE 4' 20" off arc. HE 42 ft. Required longitude in.

3. April 11th, 1919. P.M. at ship. In latitude 43° 16' 48" S. Observed altitude Star Spica 33° 18' 20", East of meridian. CT 11h 08m 44s P.M. IE 3' 20" on arc. CC 4m 18s slow. HE 39 ft. Required longitude in.

4. September 15th, 1919. P.M. at ship. In latitude 49° 38'N. Observed altitude Star Deneb, East of meridian, 36° 16' 50". IE 3' 40" off arc. HE 40 ft. CC 6m 18s slow. CT 10h 00m 13s P.M. Declination of star is 44° 59' 36" N. Required longitude in.

If any time is left, work same examples by Marc St. Hilaire Method assuming a position near the one found by Time Sight.

Assign for Night Work any of the above examples, to be worked either as Time Sights or by the Marc St. Hilaire Method, and also the following Arts. in Bowditch: 326-327-328-329.

THURSDAY LECTURE

Latitude by ex-meridian Altitude of the Sun

You have learned that when you calculate your latitude from a meridian altitude of the sun, one of the necessary requisites is to have the sun exactly on your meridian. In fact, that is just another way of expressing meridian altitude, i.e., an altitude taken when the sun is on your meridian. Now suppose that 10 or 15 minutes before noon you fear that the sun will be clouded over at noon so that a meridian altitude cannot be secured. There is a way to calculate your latitude, even though the altitude you secure is taken by sextant some minutes before or after noon. This is called latitude by an ex-meridian altitude. It must be kept in mind that this method can be used accurately only within 26 minutes of noon, either before or after, and only then when you know your longitude accurately. Put in your Note-Book:

1. Get your L.A.T. (S.H.A.).

2. Subtract it from 24h 00m 00s, or vice versa, according as to whether L.A.T. is just before or just after local apparent noon. Call the result "Time Interval from Meridian Passage."

3. With your D.R. latitude, declination and Time Interval from Meridian Passage, enter Table 26 to get the proper amount of Variation of Altitude in one minute from meridian passage.

4. With the Time Interval from Meridian Passage and the Variation, enter Table 27 to get the total amount of Variation of Altitude.

5. Add this total amount of Variation to the true observed altitude taken before or after noon, and the result is the corrected altitude.

6. Then proceed to get your latitude according to the rules already given you for latitude by meridian altitude.

Example: At sea, Jan. 23rd, 1919. CT 4h 22m 14s. CC 1m 10s fast. Longitude 66° 04' W. Latitude by D.R. 19° 16' 00" N. Circle with line under 50° 51' 00" S. HE 49 ft. IE - 1' 30". Required latitude in.

24h - 00m - 00s
- 23 - 44 - 58
——————————
15m - 02s = Time Interval from Meridian Passage.

Dec. 19° 34' 48" S Table 26 = 2.8 Variation
Lat. 19° 16' 00" N For 1 min. 0 altitude.

Time Interval from Meridian Passage 15m 02s - 2.8" Variation for 1 minute

Assign for work in class room and Night Work, examples similar to the following:

1. At sea, July 11th, 1919. Latitude by D.R. 50° 01' 00" N. Longitude 40° 05' 16" W. Observed ex-meridian altitude Circle with line under 61° 45' 30" S. HE 15 ft. IE - 4' 10". CT (corrected) 2h 38m 00s. Required latitude in.

2. At sea, June 6th, 1919. Latitude by D. R. 49° 21' N, Longitude 18° 18' W. Observed ex-meridian altitude Circle with line under 61° 30' 22" S. HE 42 ft. CT 1h 06m 18s. CC - 1m 14s. IE 0' 30" off the arc. Required latitude in of ship.

If any time is left, work similar examples by Marc St. Hilaire Method.

FRIDAY LECTURE

Examples: Latitude by ex-meridian Altitude of the Sun

1. Jan. 1st, 1919. WT 11h 53m 18s A.M. C-W 5h 56m 16s. Latitude by D. R. 58° 05' S. Longitude 89° 00' 48" W. Circle with line under ex-meridian 55° 16' 30" N. IE 2' 00" off the arc. CC 1m 28s fast. HE 36 ft. Required latitude in.

2. March 11th, 1919. CT 11d 9h 14m 39s A.M. Latitude by D. R. 39° 20' N, Longitude 39° 48' 16" E. Circle with line under ex-meridian 46° 17' 30" S. IE 2' 00" on the arc. CC 1m 16s slow. HE 29 ft. Required latitude in.

3. April 26th, 1919. CT 26d 4h 46m 38s A.M. Latitude by D. R. 24° 25' S, Longitude 107° 16' 56" E. Circle with line under ex-meridian 52° 18' 50" N. IE - 2' 40". CC 3m 56s slow. HE 33 ft. Required latitude in.

4. May 10, 1919. CT 2h 18m 46s A.M. Latitude by D. R. 23° 54' S, Longitude 143° 20' 18" E. Circle with line under ex-meridian 48° 26' 20" N. IE 3' 20" on the arc. CC 4m 18s fast. HE 41 ft. Required latitude in.

5. June 21st, 1919. CT 4h. 56m 18s. Latitude by D. R. 42° 01' N, Longitude 75° 00' 18" W. Circle with line under ex-meridian 71° 29' 40" S, IE - 2' 30". CC 3m 04s slow. HE 28 ft. Required latitude in.

6. Dec. 18th, 1919. WT 11h 50m 18s A.M. C-W 3h 14m 18s. Latitude by D. R. 11° 55' S. Longitude 48° 02' 29" W. Circle with line under ex-meridian 78° 32' 30" S. IE 3' 30" on the arc. CC 2m 44s slow. HE 35 ft. Required latitude in.

If there is any time left, give examples of latitude by meridian altitude, Marc St. Hilaire Method by sun or star sight, etc.

SATURDAY LECTURE

Finding the Watch Time of Local Apparent Noon

Noon at the ship is the pivotal point of the day's work at sea. It is then that the navigator must report to the commanding officer the latitude and longitude by dead reckoning, the latitude and longitude by observation, the course and distance made good, the deviation of the compass and the course and distance to destination. Apparent noon, then, is a most important time to calculate accurately, and to do so when the ship is under way, is not so easy at it first appears.

If the ship is stationary, and you know the longitude you are in, the problem is simple. Then it is merely a question of starting with L.A.T. of 00h-00m-00s, adding or subtracting the longitude, according as to whether it is West or East, to get G.A.T.; applying the equation of time with sign reversed to get G.M.T.; applying the C. Cor. with sign reversed to get the C.T.; and applying the C-W to get the WT. If, for instance, this WT happens to be 11h-42m-31s, when the watch reads that number of hours, minutes and seconds, the sun will be on the meridian and it will be apparent noon.

When the ship is moving, the problem is more difficult. At first thought you might imagine that all you would have to do would be to take the difference between the L.A.T. of the morning sight and 24 hours, calculate the distance the ship would run in this time and from that determine the longitude you would be in at noon. Then proceed as in the case of the ship being stationary. But such a calculation does not take into consideration the easting or westing of the ship itself. Suppose that at the morning sight the L.A.T. is found to be 20h-10m-30s. If the ship does not move, it will be 3h-49m-30s to noon. But suppose the ship is moving eastward. Then, in addition to the speed at which the sun is approaching the ship, there must be added the speed at which the ship is moving toward the sun - i.e. the change in longitude per hour which the ship is making, expressed in minutes and seconds of time. Likewise, if the ship is moving westward, an allowance must be made for the westing of the ship. And this change of longitude in minutes and seconds of time must be subtracted from the speed of the sun's approach since the ship, in going west, is traveling away from the sun.

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?

When, therefore, the watch reads 10h 51m 25s, the deck clocks should be set to 11.30 A.M. and thirty minutes later it will be apparent noon at the ship.

In all these calculations it is taken for granted that the speed of the ship and hence the change in longitude can be gauged accurately. A check on this can be made by comparing the longitude of the A.M. sight with the D.R. longitude of the same time. Any appreciable difference between the two can be ascribed to current. Now, if a proportionate amount of current is allowed for in reckoning the speed of the ship from the time of the A.M. sight to noon, then a proper correction can be made in the net rate of approach of the sun and the corrected time to noon will be very close to the exact time of noon. Of course there will be an error in this calculation but it will be small and the result gained will be accurate enough for ordinary work.

So much for finding the watch time of Local Apparent Noon. Careful navigators carry the process further and get the watch times of 15, 10 and 5 minutes before noon, so that by the use of constants for each one of these times, an accurate check on the noon latitude can be quickly and easily secured. We have not time in this course to explain how these constants are worked out but it is well worth knowing. The information regarding it is in Bowditch Art. 325, p. 128, and Art. 405, p. 181.

A word about the watch used by the navigator should be included here. This watch should be a good one and receive as much care, in its way, as the chronometer. It should be wound at the same time every day, carefully handled and, in other respects, treated like the fine time-piece that it is.

While authorities differ on this point, the best practice seems to be not to change the navigator's watch to correspond with the apparent time of each day's noon position. The reason for this is two-fold. First, because constant moving of the hands will have an injurious effect on the works of the watch, and second, because, by not changing the watch, the C-W remains approximately the same, and thus a good check can be kept on both the watch and the chronometer as well as on the navigator's figures in reckoning the times of his various sights.

Assign for night reading the following Arts. in Bowditch: 323, 324, 333. Also problems similar to the following:

1. At sea, July 28, 1919. Position by observation just found to be Latitude 44° 58' N, Longitude 22° 06' W. WT of morning sight 6h-02m-20s. CC 3m 34s slow. Course S 24° W. TZ N 90° E. Speed 9 knots. What will be the watch time of Local Apparent Noon?

2. At sea, August 9th, 1919. Position by observation just found to be Latitude 38° 48' N, Longitude 70° 46' W. WT of morning sight 8h-15m-01s A.M. C-W 3h-56m-32s. CC 3m-43s slow. Course 272°. Speed 12 knots. TZ N 90° E. What will be the watch time of Local Apparent Noon?