CHAPTER XV.

COMPASS ERROR BY AMPLITUDES.

ART. 72.-Variation is the angle between the terrestrial and magnetic meridians. It shows how much the magnetic needle is disturbed from a true north and south direction by the action of the earth. It changes with the geographical position of the observer, and also with a lapse of time; the annual change is about 6' annually. The amount of the variation for a particular year is entered on Admiralty charts.

Deviation is the angle the compass needle on a ship makes with the magnetic meridian. It shows how much the compass north is deflected from magnetic north by the action of iron in the ship or cargo. The amount varies with the direction of the ship's head, with the heel of the ship, and with her geographical position.

Compass Error is the angle the compass needle on a ship makes with the true meridian. It includes variation and deviation; and is the difference between the true and compass. bearing of any object. The compass bearing of an object may be observed at any time, and one method of determining true bearings is by " Amplitude," which is the bearing of an object reckoned from east when rising, or from west when setting. Thus it is possible for the sun to be used for this purpose twice each day; and suitable stars can be selected continually at night. ART. 73. Proof of Amplitude.-In the figure NESW is the horizon, X the position of an object on the horizon; the arc WX is its amplitude. In the right-angled triangle PNX, N=90°; PN latitude; PX = pol. dist. or co. dec.; NX = co. amp.

=

Sin (co. PX) = cos PN.cos NX
cos PX cos PN.sin WX

N

P

X

The equinoctial cuts the horizon in the east and west points, hence when an object is on the equinoctial, that is, has declination = 0°, it rises due east and sets due west. Again, when an

=

=

observer is on the equator the formula becomes sin amp. sin dec., since sec 0° Î; hence in this case amp. = dec. It is also observed that when an object has north dec., it rises to the north of east, and sets to the north of west; if south dec., it rises south of east, and sets south of west; the name of the amplitude is therefore the same as the declination.

ART. 74. To find the Time of rising or setting of a Celestial Object. In the figure the hour angle is ZPX, which is the supplement of NPX. Then from triangle NPX

sin (co. P) tan PN. tan (co. PX)

cos Ptan PN.cot PX

ART. 75.-The process for finding compass error by amplitude is as follows:

(1) Find Greenwich time, and correct declination.

(2) To L. sin declination add L. sec latitude, reject 10 from index, and take back sin true amp., which reckon from E. if A.M. at ship, and W. if P.M. at ship; and same name as declination. Under true amp. place comp., bearing reckoned from E. or W. like the true amp.

(3) When the true and comp. amps. are of the same name N. or S., their difference is the comp.err.; when of contrary names, their sum is the comp. err. It is named E. or W. according as the true amp. reads to the right or left of the comp. amp.

(4) Under the comp. err. place the variation; if of same names subtract; if of contrary names add; this gives the deviation, which is to be named like the error, unless the error is subtracted from the variation, when it is of contrary name to error.

Examples.-

(1) September 28th, at 5" 53" A.M., mean time at ship in lat. 23° 25' S., long. 12° 40′ W., the sun's compass bearing was E. N. Find the comp. err. and deviation for the position of the ship's head, if the variation from chart was 28° 30′ W.

M.T.S. Sept. 27d 17h 53m 0°
Long. W.
+ 50 40

12° 40'
4

(2) August 1st, at 8h 35m P. M. apparent time at ship, in lat. 61° 45′ S., long. 176° 30' E., the sun's compass bearing was N. 66° 30′ W. If the variation from chart is 22° 15' E., find compass error and deviation.

The bearing in the question N. 66° 30′ W. is subtracted from 90° to reckon it from W., the same point as the true amp. Since true and comp. bearings are of same name N., they are subtracted for error, which is named E., because the true amp. reads to the right of the comp.; the difference of error and variation, because of same name E., is the dev., which is of contrary name to error, because error is subtracted from variation.

1. August 2nd, at 7" 10" P.M. mean time at ship, in lat. 42° 20′ S., long. 65° E., the sun's comp. bearing was N.N.W. ₫ W., the variation being 28° 30′ W. Find comp. err. and dev.

2. September 28th, at 5h 50m A.M. mean time at ship, in lat. 50° 25′ S., long. 81° W., the sun rose by compass N. 64° 30′ E. Find true amp. and comp. err.; also if var. is 24° 15′ E., find dev.

3. August 9th, at 5h 15TM A.M. mean time at ship, in 125° W., the sun's comp. bearing was E. by N. comp. err.; and if var. is 11° 20′ E., find dev.

N.

lat. 33° 51′ N., long. Find true amp. and

4. September 30th, at 6h 23m P.M. A.T.S., in lat. 48° 19′ S., long. 76° E., the sun set by compass W. S. Find true amp. and comp. err.; the var. being 29° 45′ W., find the dev.

5. August 4th, at 5h 6m A.M., M.T.S., in lat. 37° 15′ N., long. 20° 30′ E., the sun's comp. bearing was E. by N. N. Find true amp., comp. err., and deviation, the var. being 11° 30' W.

6. September 26th, at 6h 5m P.M. M.T.S., in lat. 50° 15′ N., long. 126° 45' W., the sun's comp. bearing was S. 69° 30′ W. Find true amp., comp. err., and dev., the var. being 22° 40′ E.

7. August 7th, about 6 A.M., in lat. 20° 24' S. long. 134° W., when a chron. correct for M.T.G. showed 3h 20m, the sun's comp. bearing was E. Find the true amp., comp. err., and dev., the var. being 7° 15′ E.

8. September 7th, about 7 P.M., in lat. 60° 14′ N., long. 166° W., when a chron. correct for M.T.G. showed 6h 4m, the sun's comp. bearing was W. Find the true amp., comp. err., and dev., the var. being 12° 20′ E.

9. August 3rd, about 3h 10m A.M., in lat. 65° 22′ N., long. 170° 15′ W., when a chron. correct for M.T.G. showed 2h 35m, the sun's comp. bearing was N. W. Find the true amp., comp. err., and dev., the var. being 22° 40' E.

10. September 23rd, at 6 A.M. A.T.S. at ship, in lat. 0°, long. 50° W., the sun's comp. bearing was E. 10° S. Find the true amp., comp. err., and dev., the var. being 0°.

11. September 25th, at 6h 5m P.M. A.T.S. at ship, in lat. 13° 15' S., long. 95° Ê., the sun's bearing by comp. was N. 76° 30′ W. Find the true amp., comp. crr., and dev., the var. being 2° W.

12. September 23rd, about 6 P.M. at ship, in lat. 39° N., long. 78° 45' W., when a chron. correct for M.T.G. showed 11" 15" 23", the sun's comp. bearing was S. 88° W. Find true amp., comp. err., and dev., the var. being 6° 30′ E.

13. August 30th, at 5h 59m A.M., in lat. 0°, long. 180° W., the sun's comp. bearing, was N.E. by E. E. Find the true amp., comp. err., and dev., the var. being 9° 30′ E.

14. September 24th, about 6 A.M., in lat. 2° 20′ N., long. 101° 11' E., the sun's comp. bearing was E., when the chron. showed 11h 15m 14' correct M.T.G. Find the true amp., comp. err., and dev., the var. being 1° 15' E.

15. Find the time of sunrise on August 16th, in lat. 53° 20′ N., 4° W.

long.

16. If a star in the equinoctial rises at 7h 12m 18" by chronometer, what should the chron. indicate when star is on meridian.

17. At a certain place the sun rose E. 25° S. by compass, and set W. 15° N. by same compass. Find deviation, having given variation 22° W.

18. At a certain place a star when on the prime vertical has its altitude equal to its amplitude when setting. Find lat.

19. Find the greatest amplitude the sun can have in lat. 53° 20′ N.

20. In lat. 50 S. when sun's declination is 18° 40′ S.: find his altitude when on the prime vertical, and the approx. interval between then and setting.