Wednesday Lecture
Correcting Longitude by a Factor
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 or West 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.
| 7:30 A.M. D.R. Lat. | 25° 40' S | Lo. | 104° 05' 38" E | |
| 109°—46 k. | 15 S | 48 18 E | ||
| ————— | —————— | |||
| Noon—Lat. by D.R. | 25° 55' S | Lo. | 104° 53' 56" E | |
| Noon—Lat. by obs. | 25° 52' S | |||
| ————— | ||||
| Error in Lat. | 3' |
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:
Difference in Latitude by DR and Observation
Lat. by obs. (25° 52' S)
Lat. by D.R. (25° 55' S)
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:
| Lo. | 104° 53' 56" E |
| Corr. in Lo. | 54 W |
| —————— | |
| Lo. by obs. | 104° 53' 02" E |
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 under 31° 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 altitude Circle with line under 75° 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 under 7° 34' 20". Log registered 114.
True course to noon S 76° E. Log registered 174. Same IE, HE, CC. Observed altitude Circle with line under 29° 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 altitude Circle with line under 39° 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 altitude Circle with line under 48° 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.