You have already been given instructions for finding a Line of Position by the Marc St. Hilaire Method, using a sight of the sun. Today we will work out the same method by using a sight of a star. Put this in your Note-Book here and also under I(b) of the formula given you in Week IV - Friday's Lecture:
Get G.M.T. from corrected chronometer time. With your G.M.T. find the corresponding G.S.T. according to the formula already given you. With your G.S.T. apply the D.R. longitude
to get the L.S.T. With the L.S.T. and the star's R.A. subtract the less from the greater and the resultis the star's H.A. at the ship or "t." In using Sun Azimuth tables always take "t" from the P.M. column. Mark Azimuth N or S according to the lat. in and E or W, according as to whether the Star is East or West of your meridian. Then proceed as in the case of a sun sight. Formula:
(or vice versa if Star's R.A. is greater) = Star's H.A. at ship (t). Then proceed as in case of sun sight.
Example:
On May 31st, 1919, in D.R. Lat. 50° N, Lo. 45° W, G.M.T. 31d 14h 33m 30s. What was Star's H.A. at ship?
Now let us work out some examples by this method:
1. Nov. 29th, 1919. CT 30d 2h 14m 39s A.M. CC 3m 14s fast. D.R. position Lat. 41° 14' N, Lo. 68° 46' W. Observed altitude Star Aldebaran East of meridian 50° 29' 40". HE 29 ft. Required Line of Position by Marc St. Hilaire Method and most probable position of ship.
2. Jan. 23rd, 1919. P.M. at ship. CT 3h 45m 40s. Lat. by D.R. 38° 44' 19" N. Lo. 121° 16' 14" E. Observed altitude Star Rigel 28° 59' 20" West of meridian. IE + 4' 30". HE 42 ft. Required Line of Position by Marc St. Hilaire Method and most probable position of ship.
Assign for Night Work one or two examples similar to the above.
1. At sea, Dec. 5th, 1919. Observed meridian altitude Star Aldebaran 69° 28' 40" S. No IE. HE 26 ft. Required latitude in.
2. At sea, Jan. 20th, 1919. CT 21d 2h 16m 48s A.M. In longitude 56° 29' 46" W. Observed altitude of Star Polaris 48° 44' 30" N. IE + 10' 20". HE 37 ft. Required latitude in.
3. At sea, June 4th, 1919. A.M. at ship. CT 10h 16m 32s. CC 5m 45s fast. Lat. by D.R. 42° 44' N, Longitude 53° 13' 44" E. Observed altitude of StarAltair East of meridian, 52° 19' 30". IE - 14' 00". HE 56 ft. Required line of position by Marc St. Hilaire Method and most probable position of ship.
Etc.
Assign for Night Work the following Articles in Bowditch: 336 through 341, disregarding the formulas.
You have now learned, first, how to get your latitude by a meridian altitude of the sun or a star and second, how to get your Line of Position and most probable fix, including both latitude and longitude, by the Marc St. Hilaire Method, using for your calculations either the sun or a star. We are now going to take up a method of getting your longitude only. This method requires as much, if not more, calculation than the Marc St. Hilaire Method. Its results, on the other hand, are far less complete, for while the Marc St. Hilaire Method will give you a fairly accurate idea of both your latitude and longitude, this method will, at best, only give you your longitude. Moreover, you can use it for accurate results only when the sun bears almost due East or West of you, for that is the best time, as you have already learned, to get a line of position running due North and South, which is nothing more than a meridian of longitude. The only reason we explain this method at all is because it is in common practice among merchantmen and may, therefore, be of assistance to you, if you go on a merchant ship. Remember, however, that it belongs to Old Navigation as distinguished from New Navigation, exemplified by the Marc St. Hilaire Method. It is undoubtedly being used less and less among progressive, up-to-date navigators, and will continue to be used less as time goes on. The fact remains, however, that at present many merchantmen practice it, and so it will do you no harm to become familiar with the method, too.
This method is based on securing your longitude by a time sight or longitude by chronometer sight, meaning that at the time the sun bears as near due East or West as possible, you take a sight of it by sextant and at the same instant note the time by chronometer. With this information you proceed to work out your problem and secure your longitude according to the following formula. Put in your Note-Book:
To find your longitude by chronometer (or time) sight.
1. Take sight by sextant only when the sun bears as near as possible due East or West. At exact time of taking sight, note chronometer time.
2. Get G.M.T. from corrected chronometer time. Apply Equation of Time to get the corresponding G.A.T.
3. Correct observed altitude to get T.C.A. Also have at hand Lat. by D. R. and Polar Distance. (Note: Secure P. D. by subtracting Dec. from 90°, if Lat. and Dec. are of same name. If Lat. and Dec. are of opposite name, secure P. D. by adding Dec. to 90°.)
4. Add together the T.C.A. the Lat. by D.R. and the P.D. Divide the sum by 2 and call the quotient Half Sum. From the Half Sum subtract the T.C.A. and call the answer the Difference.
5. Add together the secant of the Latitude, the cosecant of the P.D., the cosine of the Half Sum and the sine of the Difference (Table 44). The result will be the log haversine of the S.H.A. or L.A.T. It must always be less than 10. If greater than 10, subtract 10 or 20 to bring it less than 10.
6. From Table 45, take out the corresponding S.H.A. (L.A.T.), reading from the top of the page if P.M. at ship, or from bottom of page if A.M. at the ship.
7. Find the difference between L.A.T. and G.A.T. This difference is Lo. in Time which turns into degrees, minutes and seconds by Table 7. If G.A.T. is greater than L.A.T. longitude is West; if G.A.T. is less than L.A.T. longitude is East. Example:
August 26th, 1919, A.M. CT 26d 2h 29m 03s A.M. CC 16m 08s slow.Circle with line under44° 57' 00". IE - 1' 30". HE 32 ft. D.R. Lat. 4° 55' 32" N. Required longitude in at time of observation.
I wish to caution you about confusing this method with the one Bowditch uses, and still another which Henderson uses in his book "Elements of Navigation." It is not exactly like either one. It requires one operation less than either, however, and it also requires the use of fewer parts of the various tables involved. For that reason it is given you.
Assign for work in class room and also for work at night examples similar to the following:
1. Oct. 1st, 1919. A.M.Circle with line under17° 15' 00". G.M.T. 1d 11h 30m 00s A.M. D.R. Lat. 40° 30' N. IE - 2' 20". HE 25 ft. Required longitude in.
2. Oct. 10th, 1919. P.M.Circle with line under25° 14' 30". CT 1h 15m 20s. CC 4m 39s slow. IE - 3' 10". HE 26 ft. D.R. Lat. 41° 29' 00" S. Required longitude in.
3. May 27, 1919. P.M. Lat. by D.R. 40° 55' N.Circle with line under34° 4' 00". IE + 1' 10". HE 10 ft. CT 8h 55m 42s. CC 2m 02s fast. Required longitude in.
4. May 18th, 1919. A.M.Circle with line under29° 41' 15". WT 7h 20m 45s. C-W 2h 17m 06s. CC 4m 59s slow. Latitude by D.R. 41° 33' N. IE - 1' 30". HE 23 ft. Required longitude in.
5. August 24th, 1919. A.M.Circle with line under23° 32' 10". IE - 2'00". HE 16 ft. In latitude 39° 04' N. CT 24d 2h 47m 28s A.M. CC + 4m 28s. Required longitude in.
6. June 26th, 1919. P.M.Circle with line under44° 08' 20". IE - 2' 20". HE 37 ft. CT 8h 18m 45s. CC 3m 20s fast. Latitude by D.R. 6° 43' S. Required longitude in.
7. July 29th, 1919. A.M. CT 29d 11h 14m 39s A.M. CC 2m 18s slow.Circle with line under28° 08' 30". IE + 0' 30". HE 38 ft. Latitude by D.R. 39° 48' N. Required longitude in.
8. May 22nd, 1919. P.M. CT 9h 14m 38s. CC 5m 28s slow.Circle with line under21° 07' 40". In latitude 41° 26' N. IE + 3' 10". HE 40 ft. Required longitude in.
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.
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.
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 minutesbeforenoon 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 under50° 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 VariationLat. 19° 16' 00" N For 1 min. 0 altitude.
Time Interval from Meridian Passage 15m 02s - 2.8" Variation for 1minute
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 altitudeCircle with line under61° 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 altitudeCircle with line under61° 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.
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 underex-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 underex-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 underex-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 underex-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 underex-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 underex-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.
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 toget 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. andat 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'snoon 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?
The easiest and most accurate way to find the error of your compass is, first, to find the bearing of the sun by your pelorus. If you set your pelorus, so that it will exactly coincide with the course you are steaming as shown by the compass in your chart house and then get a bearing of the sun by noting where the shadow from the pelorus vane cuts the circumference, this bearing will be the bearing of the sun by compass. At the same time, get your true bearing of the sun from the Azimuth Tables. The difference between the two will be the compass error, marked East or West according to the following rule which put in your Note-Book:
1. Express your Compass Bearing and your True Bearing by NEW compass reading.
2. If TZ is to the right of CZ, C.E. is East. Formula: True - Right - East.
3. If TZ is to the left of CZ, C.E. is West. Formula: True - Left - West.
You must now remember that what you have is a Compass Error, consisting of both Variation and Deviation. To find the Deviation, the Variation and C.E. being given, is merely to apply the rules already given you under Dead Reckoning. For instance, if you had a C.E. of 10° W and a Variation of 4° E, the Deviation would be 14° W.
Put this example in your Note-Book:
LAT 20h 59m 57s Lat. 4° 55' N Dec. 10° 39' 30" N
Ship heading N 11° W. CB of (.) S 88° E. Variation 10° W. What was the ship's true course and Deviation of Compass on direction ship was heading?
Course being sailed
Let us now work out some of the following examples:
1. L.A.T. 22h 14m 18sLat. 30° 29' SDec. 17° 28' 44" NShip heading S 84° WCompass Bearing 44°Variation 10° W.
Required T.C. and Deviation on ship's loading.
2. August 29th, 1919. CT 2h 29m 18s A.M. Longitude 120° 19' 46" E. Latitude 44° 14' N. Ship heading 98°.Compass Bearing S 42° E.Variation 4° E.
Required T.C. and Deviation on ship's heading.
3. June 17th, 1919. CT 4h 18m 44s A.M. Longitude 60° 14' 59" E. Latitude 38° 48' 00" S. Ship heading SW x S.Compass Bearing 40°Variation 12° W.
Required T.C. and Deviation on ship's heading.
Etc.
We are now almost ready to begin the discussion of a day's work at sea. The only method we have not taken up is the one which is the subject of today's lecture. It is a method to correct your longitude to correspond with the difference between your latitude by Dead Reckoning and your latitude by observation.
Suppose you take a sight in the morning for longitude. The only latitude you can use is a D. R. latitude, advanced from your last known position. Now suppose you run until noon and at that time take a sight for latitude. In comparing your D. R. latitude, advanced the true course and distance steamed to noon, and your latitude by observation taken at noon, suppose there is a difference of several minutes. The question is—How can we correct our longitude to correspond with this error discovered in the latitude? This is the method which put in your Note-Book:
Find the difference between the latitude by D. R. and the corresponding latitude by observation (in most cases secured from a sight at noon or from the Star Polaris). Call this the Error in Latitude. With the D. R. Latitude of the preceding sight and the azimuth or bearing of the preceding sight (always expressed as a bearing of less than 90°, old compass reading) enter Table 47 for the correct Longitude Factor. Multiply this Factor by the Error in Latitude. The result is the correction to apply to the Longitude. It is applied East orWest according as to whether the Latitude by Observation is to the East or West of the D. R. Latitude on the Line of Position (the line at right angles to the Azimuth) of the preceding sight.
Example:
Position about 7:30 A.M. Latitude by D. R. 25° 40' S, Longitude (just secured by observation) 104° 05' 38" E. L.A.T. 7h 32m 30s A.M., Declination 4° 59' N. Thence ship ran to noon 109°, true course, 46 miles, when the latitude by meridian altitude of the sun was found to be 25° 52' S. Required corrected longitude at noon.
Enter Table 47 with azimuth (S 105° E) N 75° E as bearing and Latitude 25° 40' or 26°, Factor is found to be .3.
3' (Error in Latitude) times .3 (Factor) = .9' or 54", Correction in Longitude. Is it East or West? Since azimuth is N 74° E, Line of Position is N 16° W. The D. R. Latitude and Latitude by Observation are plotted on this line as follows:
Latitude by observation is West of Latitude by D.R. Hence correction in longitude of 54" is applied West. Position by observation, therefore, is as follows:
Lat. by obs. 25° 52' S
Note to Instructor:
Assign the following examples for work in the class room:
1. April 20th, 1919 A.M. at the ship. G.M.T. 20d 10h 28m 24s A.M.Circle with line under31° 55' 40". HE 30 ft. No IE, CC. Latitude by D. R. 26° 30' N. Longitude 36° 55' West.
Ship then sailed a true course of S 36° E—40 knots until noon when observed altitudeCircle with line under75° 40' 50" S. What was the position at noon corrected for Longitude? (Note: Work the A.M. sight by both Time Sight and Marc St. Hilaire Method.)
2. June 25th, 1919, A.M. Latitude by D. R. 36° 20' S. Longitude 96° 30' E. CT 1h 37m 16s A.M. CC 1m 30s fast. IE 2' 30" off arc. HE 36 ft.Circle with line under7° 34' 20". Log registered 114.
True course to noon S 76° E. Log registered 174. Same IE, HE, CC. Observed altitudeCircle with line under29° 44' 40" N. Required position at noon by Longitude factor. (Note: Work A.M. Sight by Marc St. Hilaire Method.)
3. At sea, May 30th, 1919. In D. R. Latitude 38° 14' 29" N. Longitude 15° 38' 49" W. Observed altitudeCircle with line under39° 05' 40" and bearing by compass 259°. IE 1' 00" on arc. HE 27 ft. WT 3h 04m 49s. C-W 1h 39m 55s. CC 1m 52s fast.
Changed course to 94° p.s.c. and steamed 75 knots to about 8 o'clock. WT 8h 06m 18s. C-W 1h 39m 58s. At this time observed altitude of Star Arcturus 68° 30' 40", East of meridian. Same IE, HE, CC.
Changed course to 95° (true). Steamed 60 knots until midnight when ran into heavy fog. Slowed down to 7 knots per hour until 8 A.M. when observed altitudeCircle with line under48° 45' 10". CT 9h 45m 18s A.M. Same HE, IE, CC.
Required fix at 8 A.M. by Marc St. Hilaire Method, laid down on chart.
Note to Instructor:
Spend rest of period in familiarizing pupils with laying down runs and intersecting lines of position on Mercator plotting charts.