Ex. 5. 1872, July 13th, longitude 50' o' E., observed meridian altitude sun's L.L. 68° 2' 0", bearing north; index correction, 41"; height of eye 17 fect.

When the zenith distance and declination are numerically equal, and of contrary names, the ship is on the Equator.

Ex. 6. 1872, December 17th, longitude 175° 45′ W., observed meridian altitude sun's L.L. 89° 54' 20' bearing north, index correction + 4′ 4′′, height of eye 24 feet.

Ex. 7. 1872, September 22nd, long. 90° 15′ W., observed meridian altitude sun's L.L. 40° 9', bearing north, index correction + 20", height of eye 18 feet.

Green. date (A.T.) Sept. 22nd, 6h 1m. Decl. page I, N.A., Sept. 22nd, at noon 0°5′52′′ N., decreasing, Hourly diff. 58'47. H. diff. Sept. 22nd,noon 58" 47

Ex. 8.

Obs. alt. sun's L.L.
Index correction

40° 9' 0" N. +

20

By Raper: index corr. +20; dip, 4′ 10′′; refr.—1'9"; par.+7; semid. +15' 59"; true alt. 49° 39′ 54′′; latitude 49° 39′ 54′′ S.

1872, June 25th, longitude 59° 15' E., observed meridian altitude sun's

U.L. 60° 24' 10" (zenith South of observer); index correction 30 feet.

- 3′ 17"; height of eye

Decl. June 25th at noon 23°23′28′′ N. decr.
Correction + 18

Reduced declination 23 23 46 N.

The decl. is taken out for the nearest noon to Green. date, viz., June 25th at noon, and corrected for the interval between it and the Green. time, viz., 3h 57m (= 3'95 hrs.). We might have found the correction for 4, and taken from this result the change for 3m or one-twentieth of the hourly difference.

Latitude

• 37 S. 23 23 46 N.

6 36 51 S.

By Raper: Ind. corr. 3' 17; dip. 5 20; refr. 334; par. + 42; Semi-d. 15' 46'; true alt. 59° 59′ 18; latitude 6° 36′ 56′′ S.

In each of the following examples the latitude is required:

VARIATION BY AN AMPLITUDE.

THE VARIATION is found by comparing the bearing of the sun or other celestial body, as shown by the compass, with the true bearing, as found by calculation.

THE TRUE AMPLITUDE is the bearing of a celestial body at rising or setting (ie. when its centre is on the rational horizon), from the true East or West point, found by calculation, from the latitude of the place and declination of the body, or taken by inspection from a table, of which these quantities are the arguments (Table XLII, Norie, or LIX, Raper).

THE MAGNETIC AMPLITUDE is the bearing of a celestial body at rising or setting from the compass East or West points, found by direct observation with an instrument fitted with a magnetic needle, as the Azimuth Compass.

The magnetic amplitude is distinguished as observed, or apparent, and corrected. The observed or apparent magnetic amplitude of a celestial body is its bearing from the compass East or West point, when it appears in the sca-horizon of an observer standing on the deck of a ship. The corrected magnetic amplitude is the bearing of the body from the compass East or West point, when on the rational horizon, as it would appear to a spectator at the centre of the sphere through a uniform medium. The diurnal circles of the celestial bodies being, except at the equator, inclined to the horizon, and more and more the higher the latitude, any cause which affects the time of rising will affect the apparent amplitude, and in a greater degree as the latitude increases. The following are the causes:-(1) The elevation of the observer depresses the sea-horizon, while it does not affect the place of the celestial body-hence by reason of the dip, the body appears to rise before it is truly on the sensible horizon. (2) The great refraction at the horizon causes the body to appear to rise considerably before it comes to the sensible horizon. (3) When a body is in the sensible horizon, to an eye at the centre of the sphere it has already passed the rational horizon. This being the effect of parallax, is only of importance in the case of the moon. These corrections will be found in Table 59 A, Raper.

RULE LXII.

1° With the ship date and longitude in time, find the Greenwich date (see Rule LV, page 144).

The time of sunrise and sunset is generally given in apparent time.

2°. Take out of Nautical Almanac the sun's declination for this date (see Rule LVI, page 147).

3. Take from the Table the log. sine of declination, and log. secant of latitude (rejecting 10 from the index); the sum of these is log. sine of true amplitude, which take out of Tables. (Table XXV, Norie, or Table LXVIII, Raper).

4. If the body is rising, or A.M., mark true amplitude East; if it is setting, or P.M., mark it West: mark it also North, when declination is North; or South, when declination is South.

(a) When the declination is o, the true amplitude is o; that is, it is East if the object is rising-West if it is setting.

(b) When the latitude is 0, the declination is the true amplitude.

5°. Under the true amplitude write the magnetic amplitude; then if they are both marked North, or both marked South; take their difference; but when one is marked North and the other South, take their sum: the result in either case, is the variation.

The magnetic amplitude must be reckoned from East or West towards the North or South, before it is placed underneath the true. Thus: the magnetic amplitude S.E. by E. E. is E. 2 points S., or E. 28 7′ 30′′ S.

6. The variation is named East, when the true amplitude is to the right of magnetic amplitude; West when true is to the left of magnetic: the observer being supposed looking from the centre of the compass, in the direction of the magnetic amplitude.*

EXAMPLES.

Ex. 1. 1872, January 6th, at 4h 44m 27 apparent time at ship, lat. 37° 59' S., long. 36° 24′ W., the sun's magnetic amplitude was S.E. by E. E.: required the true amplitude and variation.

Ship's date (A.T.), Jan. 5d 16h 44m 27° Long. in time +225 36

Green, date (A.T.) Jan. 5 19 10 3

Decl. page I, N. A.

Jan. 5th, 22° 39′ 49′′ S.

H. diff. noon, 6th

17267

Time from noon, 4h 50m X 483

5301 14136 7068

6,0)85'3461

22 34 24 S.

6th, 22 32 59 S.

(A.M. and S. decl.) True amplitude E.

The decl. is here taken out for the nearest noon, viz., the 6th, and since the Green. time wants only 4h 50m of being noon of 6th (24h om

19h 10m 4h 50m), we multiply the hourly diff. by this quantity, and apply the resulting correction the opposite way, to throw it back, for since the declination is decreasing, the declination at 4h 50m before noon, will be more than it is at noon, hence we add the correction.

29° 8' S.

(S.E. by E.E.) Mag. amplitude E 28 7 S. E. 24 points.

The amplitude can be taken out by inspection in a table constructed for the purpose and given in most Nautical Tables, Table XLII, Norie, and Table LIX, Raper; the arguments being the declination and latitude.