fast on mean time at Greenwich on January 23rd, and losing 4.5s. daily. Required the true longitude.

Ship date April 14d. 20h. 35m.

106° long. W.

7h. 4m.

Approx. Gr. date Apr. 15 3 39

Hence chron. corrected gives Gr. date April 15d. 3h. 47m. 48.

Cor. Dec. 9° 53' 10" N. Cor. Eq. T.-3s. T. alt. 19° 20′ 2′′.

Ex. 1882, August 21st, at about 8h. A.M. at ship, in estimated long. 12° W.; the observed altitude of sun's lower 24° 29′, with index error 1′ 49′′ to add; eye 14 feet; time by chron. 8h. 49m. 54s., which had been found 1m. 12s. slow on M. T. at Greenwich on

At noon the lat. by meridian altitude of sun was found to be 60° 57′ N.; the course and distance from about 8h. A.M. until noon, having been S.E. by E. E. (true) 17 miles. Required the longitude brought up to noon.

Course S. 5 pts. E. and dist. 17'=8′ S. and 15′ E. Į sce pp. 26
Dep. 15' E. in lat. 61° 31′ diff. long.

Gr. date M. T. by chron.

Cor. Dec. 12° 7' 19" N.;

Aug. 20d. 20h. 47m. 40s.

}

and 27.

cor. Eq. T. + 3m.; T. alt. 24° 41′;

Lat. carried back to 8h. A.M. 61° 5' N.;

Log. of H.-angle 9.402675 giving 4h. 1m. 27s.;

Long. at time of morning sight 11° 31′ 45′′ W., and carried forward to noon 11° 0′ 45′′ W.

Work out the example and get the same results.

Note.-Being in N. lat. if you make northing in the interval between the A.M. sights and noon, your lat. for A.M. sights must be less than that at noon; for southing, greater.

Note.-Being in W. long., and having found the longitude for A.M. sights, easting in the interval decreases the long. at noon; westing increases it.

Ex. 1882, September 1st, in Long. by D. E. 7" 20' E.; the obs. mer. alt. of sun's lower limb was 33° 0' 30" South of observer; eye 13 feet. At about 5h. P.m. of the same day the mean of five obs. alts. was 12° 2', and the mean of times by Chron. Sept. Id. 4h. 40m. 12s.; chron. had been found lm. lis. fast on M. T. at Greenwich on May 20th, and losing 5s. daily. Required the Latitude at noon, and brought down to the time of taking the sights; also the Longitude; the true course and distance run from noon was S. 40" W. 30 miles.

Ans. Lat. at noon 65° 3' 3" N.; Lat. brought down for run 64° 40' 3" N.; Long. 6° 47' 45" E.

LATITUDE BY AN EX-MERIDIAN ALTITUDE OF THE SUN.

Should the weather be cloudy and uncertain, a tolerably fair latitude may generally be obtained by taking an altitude of the sun when near the meridian; and for this purpose the error of the watch for the ship's position should be known as accurately as possible. For this problem you will naturally use Towson's "Tables for the Reduction of Ex-Meridian Altitudes." They give two corrections—one to be applied to the declination, and the other to the altitude —and then, by a process similar to the ordinary latitude problem, p. 70, you get your ship's latitude. There are limits to the time of taking the altitude, but these need not be stated here, as, if you keep within the range of Towson's Tables, you will be correct. A problem worked in full will give you an idea of the process.

The altitude may be observed at A.m. or P.m., and the time from noon is one of the elements. Note.—It is apparent time.

Ex. 1882, April 28th, A.M. at ship; Lat. by D. R. 47° 40′ N.; Long. 17° W.; the observed altitude off the meridian of sun's lower limb was 56° 10′ South of the observer; eye 16 feet;

time by watch 11h. 56m. 20s. A.M., which had been found 14m. 30s. fast on apparent time at ship, but the ship had made 19' diff. long. to westward since the error for time had been found. Required the true Latitude?

AMPLITUDE AND AZIMUTH, AND THENCE THE ERROR AND DEVIATION OF THE COMPASS.

Your chart and sailing directions will generally indicate the variation of the compass; but if you are in an iron boat, or a steamer, your compass will be affected by deviation, and this you can only find out, when at sea, by an Amplitude or an Azimuth. I will first give you a few definitions of terms; these you must carefully read, and reflect on and then you will see the drift of the subsequent remarks.

1. Amplitude.--The arc of the horizon between an object at rising and the E. point, and the object at setting and the W. point. Note.—The Amplitude is only observed at sunrise and sunset.

2. Azimuth.—The arc of the horizon between the N. or S. point and the circle of altitude passing through a celestial body. Note.—The true Azimuth or bearing must be calculated, or otherwise taken from a Table by Inspection: the observed Azimuth is the object's bearing by compass.

3. The Variation of the Compass is the angle between the magnetic and true meridians.

4. The Deviation of the Compass is the angle through which the compass needle is deflected from the magnetic meridian. Note. Or, The deviation of the compass is the angle between the magnetic meridian and the direction of the magnetic needle influenced by the magnetism of a ship.

5. The Error of the Compass is the angle through which the compass needle is deflected from the true meridian. Note.—The Error of the Compass includes variation and deviation, and is the angle between the geographical meridian and the direction of the magnetic needle of the compass on board.

6. The True Course of a Ship is the angle that a ship's track makes with the true meridian.

7. The Magnetic Course is the angle that a ship's track makes with the magnetic meridian. Note.— The magnetic, or (as it is now generally called) the correct magnetic course, being the angle between the magnetic meridian at the place and the ship's track as shown by a compass unaffected by deviation, such a course is affected only by the variation of the compass.

8. The Compass Course is the angle that a ship's track makes with the compass needle. Note.The com

pass course being the angle between the ship's track and the direction of the magnetic needle of the compass on board, such a course may be affected with variation and deviation.

If you are in an iron ship, Tables by which you can instantaneously take out the sun's true bearing (Azimuth is only another word for bearing) are indispensable.

For Latitudes from 60° to 30° Burdwood's "Sun's True Bearings" are sufficient.

But if you go into the tropics these must be supplemented by Davis' "Sun's True Bearings."

There is also Labrosse's "Azimuth Tables," which range from 61° N. to 61° S.

These give the Sun's true bearings at any time that the object is above the horizon; with explicit directions as to their use, so it is unnecessary to repeat them here. One or other of these works you must have if you wish to be well posted as to what your compass is doing, and where you are going. All I purpose now to do is, to show you how to obtain the Error of the Compass and the Deviation, when you have sought out the true bearing of the object, and looked at your chart for the variation.

1. The True Amplitude must be named from East at A.m. or rising, but from West at P.m. or setting; towards North for Declination N., but towards South for Dec. S.

Thus, in February, when the Dec. is 15° S., we should say the sun rose E. 23° 40' S.; and, in May, when tho Deo. is 20° N., we should say the sun set W. 32° 10' N., in the Channel.

2. For the Error of the Compass.—Under the true write the observed (or compass) Amplitude, reckoned from the same point as the true, E. or W. as the case may be.

If both are N., or both S. take their difference; if