Saturday Lecture
Longitude by Chronometer Sight of the Sun (Time Sight)
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 under 44° 57' 00". IE - 1' 30". HE 32 ft. D.R. Lat. 4° 55' 32" N. Required longitude in at time of observation.
| 26d 2h 29m 03s A.M. | |||||
| - 12 | |||||
| ————————— | |||||
| CT | 25d 14h 29m 03s | - 90° 00' 00" | |||
| CC+ | +16 08 | Dec. | 10 49 48 | ||
| ————————— | ——————— | ||||
| G. M. T. | 25d 14h 45m 11s | P. D. | 79° 10' 12" | ||
| Eq. T. | -2 05 | ||||
| ————————— | |||||
| G. A. T. | 25d 14h 43m 06s | - 1' 30" | |||
| + 9 27 | |||||
| Circle with line under | 44° 57' 00" | ———— | |||
| Corr. | 7 57 | Corr. | + 7' 57" | ||
| ————— | |||||
| Circle with line through | 45° 04' 57" | ||||
| Lat. | 4 55 32 N | sec. | .00160 | ||
| P. D. | 79 10 12 | cosec. | .00781 | ||
| —————— | |||||
| 2) | 129° 10' 41" | ||||
| —————— | |||||
| ½ S | 64° 35' 20" | cos. | 9.63266 | -9 | |
| Circle with line through | 45 04 57 | ||||
| —————— | |||||
| Diff. | 19° 30' 23" | sin. | 9.52350 | -14 | |
| —————— | |||||
| 9.16557 | +5 | ||||
| —————— | |||||
| log. hav. S.H.A. (L.A.T.) | 9.16562 | ||||
| S.H.A. (L.A.T.) | 25d 21h 00m 01s |
| G.A.T. | 25 14 43 06 |
| ———————— | |
| Lo. in T. | 6h 16m 55s E |
| Lo. (Table 7) 94° 13' 45" E | |
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 under 17° 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 under 25° 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 under 34° 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 under 29° 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 under 23° 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 under 44° 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 under 28° 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 under 21° 07' 40". In latitude 41° 26' N. IE + 3' 10". HE 40 ft. Required longitude in.