We will conclude this treatise of the practical part of Nautical Astronomy with a series of examination papers given at the Royal Naval College, to candidates passing for lieutenants' and masters' commissions in the Royal Navy. They are also required to have some knowledge of arithmetic, algebra, and trigonometry: the papers now set on these subjects contain examples in arithmetic as far as vulgar and decimal fractions; in algebra, as far as simple equations, inclusive; and in trigonometry, the examples and problems are similar to those contained in Part I. of the author's Trigonometry.

257

ROYAL NAVAL COLLEGE EXAMINATION PAPERS.

Questions.-No. I.

1. Required the course and distance from A to B.

2. Required the course and distance from A to B.

W. 4

3. A ship bore from me S. E., and a current ran in the intermediate space S. W. miles an hour; how must I steer a boat to fetch the ship, supposing I can pull 6 miles an hour in still water ?*

4. On May 8, 1835, at noon, a point of land in lat. 48° 10' N., and long. 2° 2′ W., bore by compass E. by S. & S. distant 20 miles, (variation 3 E.); afterwards sailed as by the following log account; required the latitude and longitude in at noon, on May 9, 1835.

* The current sailing question is now omitted in the Navigation Paper at the Royal Naval College. It sometimes appears among the questions in trigonometry.

5. What bright star will pass the meridian of Canton in China the first after mean midnight on June 15, 1835, and how far N. or S. of the zenith?

6. June 15, 1835, in long. 100° 32′ E., the observed meridian altitude of the sun's lower limb was 20° 15′ 40′′ (zenith S. of the sun), the index correction was + 2′ 50′′, and the height of the eye above the sea was 14 feet; required the latitude.

7. April 23, 1835, at 9h P.M., mean time nearly, in long. 5° 10′ W., the observed meridian altitude of the moon's lower limb was 38° 40′ 45′′, (zenith N. of the moon), the index correction was 2' 50", and the height of the sea was 20 feet; required the latitude.

eye

above

8. June 18, 1835, the observed meridian altitude of the star a Scorpii (Antares) was 20° 10′ 50′′ (zenith north of the star), the index correction was + 4′ 50′′, and the height of the eye above the sea was 18 feet; required the latitude.

9. June 12, 1835, the observed meridian altitude under the S. Pole of a2 Crucis was 6° 40′ 10′′, the index correction was + 3′ 40′′, and the height of the eye above the sea was 18 feet; required the latitude.

10. December 10, 1835, at 2h 10m A.M., mean time nearly, in long. 76° 12' E., the observed altitude of a Ursa Minoris (Polaris), was 47° 50′ 25′′ the index correction was - 4' 10", and the height of the eye above the sea was 13 feet; required the latitude.

11. September 16, 1835, observed the following double altitude of the sun.

The run of the ship in the interval was E. b. N. 12 miles, the index correction was + 3′ 50′′, and the height of the eye above the sea was 18 feet; required the true latitude, the latitude by account being 51° N., and the longitude 50° 10' W.

12. March 2, 1835, at 7h 44m A.M., mean time nearly, in lat. 44° 25′ N., and long. by account 58° E., a chronometer showed 5h 10m 42s.5, and the observed altitude of a Arietis was 30° 10′ 40′′ W., of meridian, the index correction was + 4′ 20′′, and the height of eye above the sea was 18 feet; required the true longitude.

February 24, at Greenwich mean noon, the chronometer was fast on Greenwich mean time 1h 11m 22s, and its daily rate was 2.2 losing.

13. Sept. 3, 1835, at 9h 10m P.M., mean time nearly, in lat. 30° 10′ N., and long. by account 91° 5' E., the following lunar observation was taken.

The height of the eye above the sea was 12 feet; required

the true longitude.

14. July 5, 1835, at 7h 0m P.M., mean time, in lat. 50° 53′ N., and long. 120° 10' E., the compass bearing of the sun was W. 10° 15' N., and the observed altitude of its lower limb was 9° 40′ O", the index correction was + 3′ 50′′, and the height of the eye above the sea was 18 feet; required the variation of the compass.

15. On Dec. 20, 1835, at 4h 30m P.M., mean time nearly, in lat. 41° 12′ N., and long. 110° 45′ E., the sun set by compass S. W.; required the variation.

16. Required the time of high water at A., on June 10, 1835, A.M. and P.M.

Change tide. 3h 40m A.M. app. time.

Long. A. 65° W.

NOTE. In this and the following examination papers the compass is supposed to have no deviation arising from local attraction. In the Mercantile Navy the correction for deviation is not generally attended to: but in Her Majesty's Service all ships are now swung previously to their going to sea, and a table of deviations constructed similar to the one in p. 244 for the correction of courses, &c.

Elements from Nautical Almanac and Answers.

1. N. 30° 29′ 15′′ W. 377.2 miles.

2. E. 188.1 miles.

3. S.E. S.

4. Corrected courses N.W. & N. 20' departure course, N.b.W. W. 12'3; S. 14'8; S.E. b. E. E. 12'-7; E. & N. 34′·1; W.S.W. 42'7. Lat. in 48° 6' N., long. 2° 18′ W.

5. Right ascension mean sun on June 14, at Greenwich mean noon, 5h 32m 11s.85. y Draconis, 28° 23' N. of zenith. 6. Sun's declination on June 14, at Greenwich mean noon, 23° 15′ 26′′ N.; on June 15, 23° 18′ 24′′ N., semidiameter

7. Moon's declination on April 22, at 21h Greenwich mean time, 11° 35′ 58′′ S., at 22h..11° 23′ 53′′ S.; moon's horizontal semidiameter April 22, at Greenwich mean midnight, 15′ 4′′-1, April 23, at Greenwich mean noon, 15′ 0′′; corresponding horizontal parallax 55′ 17′′-8 and 55′ 2′′-8. Lat. 38° 57′ 50′′ N.

8. Declination a Scorpii (Antares) 26° 3′ 34′′ S.

43° 47' 34" N.

Lat.

9. Declination a2 Crucis 62° 11′ 25′′ S. Lat. 34° 20' 28" S. 10. Right ascension mean sun on June 16, at Greenwich mean noon, 17h 10m 2s.21; lat. 47° 51′ N.

11. Sun's declination on September 15, at Greenwich mean noon, 2° 49′ 54′′ N., on September 16, 2° 26′ 42′′ N., semidiameter 15′ 56′′. Lat. 50° 20' N.

12. Right ascension mean sun March 2, at Greenwich mean noon, 22h 38m 13s.55. Right ascension a Arietis, 1h 57m 51.5; declination a Arietis 22° 40′ 42′′ N. Hour angle 4h 37m 238 W. Long. 59° 12′ 15′′ E.

13. Right ascension mean sun September 3, at Greenwich mean noon, 10h 47m 36-37. Right ascension a Arietis 1h 57m 55s.3; declination a Arietis 22° 40′ 56′′ N. Horizontal semidiameter moon September 3, at Greenwich mean noon