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:
 | |
| 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 |