Besides the variation or declination of the magnetic needle from the direction of the earth's axis, it is subject to another irregularity, by which in the northern hemisphere that end pointing to the north is drawn a little downwards from the horizontal line, and the reverse in the southern : this is called the dip of the needle. At the equator the needle being equally acted upon by both poles of the earth, maintains a horizontal position; but if it be moved towards either pole, the end next to the pole towards which it is removed will gradually dip more and more below the horizontal line; and would probably, if it could be carried quite to the pole, there stand perpendicular to the surface of the earth. At London in the year 1786, the north end of the magnetic needle dipped 17° 52′ below the horizon, and in 1805, the dip was found to be 19° 39'.

The instruments usually employed to ascertain the distance run in a given time by a ship at sea, are the log, and the half-minute glass. The log is commonly a thin piece of timber, shaped like the quadrant of a circle of 5 or 6 inches radius, having a plate of lead attached to the circular part, so as to make the log swim perpendicularly in the To this piece of timber is fastened a small cord or line from 100 to 150 fathoms in length, divided into equal

water.

parts

parts by pieces of twine, with as many knots on them as there are spaces between each and the first mark from the log: from this the distances themselves are called knots, and they ought to bear the same proportion to the nautical mile that half a minute bears to an hour, or the knots ought to be of a nautical mile, which being equal to a minute of a degree of a great circle on the earth, or to 6,100 English feet, each knot should contain nearly 51 feet: as a precaution however against mistakes and accidents, it is customary to make the distance between any two knots only from 48 to 50 feet. The glass employed at sea is a small sand-glass of the ordinary construction, but containing only so much sand as will run from the one end to the other in half a minute. When the log is thrown from the ship into the water, the number of spaces or knots on the line run out while the glass runs half a minute is observed; and on the supposition that the ship's motion for a certain time, as an hour, is tolerably equable, it is ascertained by the following proportion: as the half minute run by the glass to the number of knots shown by the log, so is one hour to the number of miles sailed in that time.

In king's ships and East Indiamen it is usual to heave the log every hour, but in other vessels once in every two hours is considered to be sufficient: but with every precaution and allowance that can be applied, this mode of measuring a ship's rate of motion, notwithstanding the many improvements suggested by ingenuity and experience, must be subject to great uncertainty, from the unequal force of the winds during even the short space of an hour, from the motion of the water by currents and waves, and from other contingencies which do not admit of any accurate computation.

Were it possible at sea to determine a ship's position by celestial observation with sufficient accuracy, much of the uncertainty of the ordinary method of measuring her course

and

and distance would be removed; but certain nice astrono mical operations requisite for that purpose are found to be impracticable on board, from the motion of the vessel, and for which no sufficient remedy has yet been discovered. .

In the Introduction to Ceography, (vol. ii. pp. 9 and 10.) the nature and manner of computing the latitude and Jongitude of any place on the earth's surface were explained. The elevation of the north pole star above the horizon of any place on the northern hemisphere, being constantly equal to the latitude of that place, a correct measurement of this angular elevation would at all times indicate the Jatitude of the place of observation. A similar operation respecting the altitude of the south pole would in the southern hemisphere answer the same purpose. The usual way, however, of determining the latitude at sea, is by an observation of the sun's altitude above the horizon when on the meridian, or by two or more altitudes at determined intervals, when he is out of the meridian: the first method, when from clear weather or other favourable circumstances it is practicable, is always to be preferred.

Various instruments have been employed to measure the sun's altitude: but that which is now justly preferred to all others is Hadley's quadrant, by which through the adoption of certain optical principles, observations of the altitudes and relative distances of the heavenly bodies may be performed on ship-board with the greatest accuracy. The name quadrant expresses the fourth part of a circle or 90 degrees; this instrument however is only half of a quadrant, the circular part containing 45 degrees; but by means of the double reflection of the ray of light from the body observed, the same effect is produced as if the instrument comprehended double its arc. The index moving round the central point of the instrument, points out on the graduated limb or arch the quantity of the angle of elevation of the body observed.

Although

Although in fact the sun be fixed in the center of our system, and the earth be moveable round him, yet in common language, the reverse is usually admitted; when therefore the carth is, for example, in the tropic of Capricorn, we say the sun is in that of Cancer, and vice versa. Hence it is that we speak of the sun's place, of his motion, of his declination or distance from the celestial equator, and other particulars relatively applied to him, but in fact' belonging to the earth alone.

As the visible hemisphere at any place on the globe may be cor idered to comprehend an arch from the horizon on the north, to an opposite point on the south of 180 degrees, and that the arch intercepted between the north pole and equator is always a quadrant or 90°, it follows that the elevation of the pole above the horizon, and that of the equator above the opposite horizon, must together be equal to another quadrant or 90°. If then we can determine the elevation of the equator or of any body in it above the horizon, by subtracting this quantity from 90°, we obtain the elevation of the pole, which is always equal to the latitude of the place.

:

The sun being in the equator in all parts of the world on the days of the vernal and autumnal equinoxes, or about the 21st of March, and the 22d of September, let his meridian altitude be correctly observed at London to be 38° 29': this quantity taken from 180°, will leave the arch between the sun's body and the northern extremity of the meridian, or 141° 29' but the arch between the equator and the pole being always 90°, we may at once rubtract the altitude 38° 29', from another quadrant or 90°, and the remainder 51° 31', will be the elevation of the pole above the northern horizon, which as was before said is always equal to the latitude of the place of observation. By this simple opera tion therefore we find London situated in 51° 31′ of N. latitude.

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Again,

Again,if upon the 21st of June, when the sun is at the sum mer solstice in the tropic of Cancer, his meridian altitude at London be observed 61° 57', we first bring him back to the equator by deducting from his altitude the arch of the meridian, intercepted between the equator and the tropic, or in other words by deducting the sun's declination for that day, equal to the angle of inclination formed by the ecliptic with the equator, which is 23° 28'. This sum taken from 61° 57', the observed altitude will leave 38° 29', for the arch of the meridian between the southern horizon and the equator; which again subtracted from a quadrant or 90°, will give 51° 31', for the elevation of the pole and the latitude of London, the place of observation, as in the former example.

In the same way the latitude may be discovered by means of the sun's meridian altitude on any intermediate day, between the vernal and autumnal equinoxes, or while he is on the north side of the equator, as for example on the 12th of August, 1808, when his meridian altitude at London was observed to be 53' 28'; the sun's declination being on that day 14° 59′ N. If from the observed altitude 53° 28′, we subtract this declination, we bring down the sun to the equator, which therefore is elevated 38° 29', above the horizon at London, and the complement of this quantity to 90°, or 51° 31', is the latitude of London, as required.

On the other hand, from the autumnal to the vernal equinox, or while the sun is on the south side of the equator, his declination is to be added to the observed meridian altitude, and the sum, equal to the elevation of the equator above the southern horizon, subtracted from 90°, will give the latitude of the place of observation. Thus at London on the 22d of November, 1808, the sun's altitude at noon was observed to be 18° 18', when his declination was 20° 11', S.: these two quantities added together give 38° 29', for the elevation of the equator, and its complement to 90°,

or