ing been taken by means of a quadrant or sextant, the following corrections must be applied to it, and in the order given :—

1. That due to the instrument, and which is called. the Index Error, may be additive or subtractive, as already explained on p. 62.

2. Subtract the Dip due to the height of the eye above the sensible horizon; this correction comes from Table. VIII., which is entered with the height of the eye of the observer above the sea level, opposite to which is the dip; thus 15 feet gives 3' 49" to subtract.

3. Subtract the Refraction in Altitude, since the bending of the rays of light due to passing through an atmosphere of increasing density causes an object to appear at a greater altitude than it really has; this correction comes from Table XV., thus App. Alt. 43° 10' gives refraction 1' 2" to subtract.

4. From Naut. Alm., p. II., of the month, take out the sun's semi-diameter: add this to the alt. of the lower limb to get the alt. of the centre.

5. Add the Parallax in Alt. taken from Table XIV., under 9 at the top, since the sun's Hor. Par. is just less than 9"; enter Tab. with App. Alt.; thus App. Alt. 42° gives 7" to add.

Par. in Alt. is the correction that gives the object the Alt. it would have if it were seen from the earth's centre that for the sun is small and might be neglected, but that of the moon is very considerable.

LATITUDE BY MERIDIAN ALTITUDE OF SUN.

It may be as well now to collect together the substance of what has been said about finding the latitude by a meridian altitude of the sun.

1. Correct the Sun's Declination for the Longitude (see p. 68), always taking the Dec. from Naut. Alm., p. I. of the given month.

2. For the True Altitude.—Correct the observed Altitude for Index Error (if any), Dip, Refraction, Semidiameter, and Parallax (see p. 69). The result will be the True Alt.

3. For the Zenith Distance.—Subtract the True Altitude from 90°; and name the remainder N. when sun bears S., but S. when sun bears N.

4. For the Latitude.—Under the Zen. Dist. write the reduced Declination, each having its proper name N. or S.; if both are N., or both S., take their sum for the Latitude; if one is N. and the other S. take their difference for the Latitude, of the same name as the greater. If Zen. Dist. is 0, the Declination is the Latitude; if Declination is 0, the Zen. Dist. is the Latitude.

The following is an example in full, by which all future similar observations may be solved :—

Example. August 26, 1882. Long. 92° E. Observed meridian Altitude of sun's lower limb, 56° 42' 10" bearing N. Eye 18 feet. Index Error 1' 32" to be subtracted. What is the latitude in ?

Long. 92° 6h. Sm.=6·1h.

Then 52" 25 × 6·1=318" 725-5′ 18′′ 7 correction of Dec. to be added because Long. is E. and Dec. decreasing.

Here the zenith distance being S., and the declination N. (of different names), we take their difference, and the latitude in is S., of the same name as the greater; had both been S., or both N., we would have taken their sum for the latitude in. On the North side of the equator the sum or remainder must, of course, be always in north latitude.

Ex. 1882; January 20th; long. 35° 40′ W.; observed meridian altitude of sun's lower limb 26° 10' bearing south; height of eye 16 ft; index error 1′ 40′′ to add. Required the latitude in.

Ans. 43° 34' 33" N.

Ex. 1882; March 20th; longitude 91° W.; observed meridian altitude of sun's lower limb 66° 0′ 40′′ bearing south; eye 19 feet; index error 2′ 50′′ to subtract. Required the latitude in.

Ans. 23° 51′ 53′′ N.

Ex. 1882; June 14th; long. 21° W.; observed meridian altitude of sun's lower limb 51° 1′ 40′′ bearing south; eye 15 feet. Required the latitude in.

Ans. 62° 4' 7" N.

Ex. 1882; August 25th; long. 42° 1′ W.; observed meridian altitude of sun's lower limb 49° 51′ 30′′ south of observer; eye 17 feet. Required the latitude.

Ans. 50° 38′ 5′′ N.

Ex. 1882; October 20th; long. 30° 1' E.; observed meridian altitude of sun's lower limb 45° 50′ bearing south; eye 17 feet. quired the latitude in.

Ans. 33° 36′ 5′′ N.

Re

Ex. 1882; September 23rd; long. 60° 10′ E.; observed meridian altitude of sun's lower limb 55° 1′ bearing north; eye 20 feet. Required the latitude in.

Ans. 34° 52′ 9′′ S.

Note.-In order to take the sun's altitude when greatest, continue, by means of the tangent screw, to bring the lower limb of the sun down to the horizon, so long as the sun is on the ascendant. Persevere in doing this until the imaged sun ceases to rise above the horizon; persist in bringing it down to the horizon, but never up to it. The instrument should be vibrated so that the image may skim the horizon, for the altitude must be measured to the point vertically below the sun.

Should the learner be on land, and desirous of becoming conversant with the use of the quadrant, and perfect in the preceding operation, he should furnish himself with the Artificial Horizon, by which means he will, on going to sea, be better prepared than if he had never taken an observation. He must remember that the Artificial Horizon will, from its structure, give double the sun's observed altitude; and, therefore, after reading off the number of degrees indicated on the limb of the quadrant, he must first add or subtract the index error, and then halve the remainder for the observed altitude of the sun.

Assuming that the learner has attentively studied his subject, and mastered the contents of the preceding pages, he should be competent to find his latitude in any part of the globe. Should he, however, still further pursue his studies, with the view of becoming capable of finding his longitude by means of the quadrant and chronometer, he will thus acquire great

advantages while roaming the ocean, where he may chance to be several successive days without a sight of the land, and when, after such an interval, his longitude by Account or Dead Reckoning might prove to be seriously wide of the truth. In addition to this, his being enabled to ascertain the mean time either at sea or on land, which is included in the operation of finding the longitude, cannot be deemed superfluous.

Knowing the latitude and longitude there will be no occasion to get into the latitude of the port bound for, and then to sail along that parallel, as you must do if you know only the latitude.

ON FINDING THE LONGITUDE.

The appearances of sunrise, noon, and sunset, it is needless to observe, are occasioned by the rotation of the earth on its axis; and when the sun is just rising to the inhabitants of London, it will not do so to those of Pembroke until a number of minutes later—while it had risen to the people of Antwerp previouslyin each case in proportion to their longitude east or west of London. Knowing the rate at which the earth thus rotates (900 miles in an hour), if we also know when it is noon at London and when at Pembroke, we can ascertain the difference of longitude between the two places: thus of two clocks, one set to London time and the other to Pembroke time, when the London clock showed noon, or 12h., the Pembroke clock would show 19m. 48s. to 12, indicating that Pembroke was 4° 57' W. of London.

By means of our quadrant we are enabled to find the true time at Pembroke or at any other spot on which be but we are not able to know our meridian distance east or west from Greenwich, unless we also

we may

E