will then decrease, and it will move slowest when it passes the aphelion point B. The earth is at the point A, on the 31st of December, and at the point B, six months after, or July 1st. If the inequality between the time indicated by the dial and that by the clock was caused wholly by this change in the velocity of the sun, then the dial and clock should agree exactly when the earth was in these two positions, for the earth occupies just 6 months in moving from A to B, and 6 months in returning from B to A, just what it would if its orbit was a circle, and in which case the dial and clock would agree. But by actual observation, the dial and clock are not together twice in the year, but four times, and then not when the earth is at A and B, December 31, and July 1st, but on December 24th, April 15th, June 16th, and August 31st, as we have already intimated. We must look, therefore, to another source, which, united with the one we have just considered, will fully explain all the observed phenomena, and we find it in the inclination of the sun's apparent path to the equator. As the earth turns on its axis, we may suppose a rod which extends from the centre of the earth, and through its equator to the sky, tracing out a line, or circle, in the heavens, which is called the celestial equator. This circle is, as we have already shown, divided into 24 parts, called hours, each hour comprehending 15°, and all these spaces are exactly equal. If the sun's yearly path in the heavens had corresponded with the equator, or had been in the same plane, then all the difference between the dial and clock would have been simply what was due to his moving sometimes apparently faster than at others, in consequence of the earth's elliptical orbit, but this is not the case, the plane of the ecliptic, or sun's path, is inclined to the plane of the equator. Now, on the supposition that the orbit is circular, let us see what effect this would have upon the sun-dial. In the next diagram, the circle 0, 1, 2, 3, 4, 5, &c., which are hour divisions, represents the equator, and I, II, III, IV, V, VI, &c., which are also hour divisions, the ecliptic. Clock time is measured on the former, for this is the circle, or others parallel to it, in which the stars, and other heavenly bodies, seem to move on account of the diurnal rotation of the earth. Dial time is measured on the ecliptic, and

we have just shown that the dial was graduated, or marked, with

at II, IV, VI, &c., indicate the position of the sun each month from the vernal equinox, P is the north pole of the heavens, and P1, P2, P3, &c. are meridians cutting the ecliptic I, II, &c. above the equator; 0 is the place of vernal equinox, VI the position of the summer solstice, XII the place of the autumnal equinox, and XVIII of the winter solstice. On the 2d day of May, which is about midway between the vernal equinox and the summer solstice, the sun would be at the point III, but if it had moved over three equal divisions of the equator, it would be at 3, and now if a meridian be passed through 3, as at P 3, it will intersect the ecliptic beyond III, i. e. on the side towards IV. Now III being the place of the sun, if we suppose a meridian passing through P and III, it will intersect the equator on that side of 3 towards 2, i. e. the sun would come to the meridian by the dial before it would by the clock, for the dial will show 12 o'clock, when the meridian, which passes through III, is in the mid-heavens, at any place, but the clock will show 12, when the meridian, which passes through 3, is in the mid-heavens, and this would be after the dial. On the supposition that the earth's orbit is circular, the dial and clock would now, when the sun is at III (May 2d), be farthest apart, after this they would come together and correspond at VI, and 6, the time of the summer solstice, after this the clock would

LONGITUDE.

81 be faster than the dial till the time of the autumnal equinox, then slower till the winter solstice, and again faster till the vernal equinox. The earth's orbit is not a circle, but if the line of apsides A B, see figure on page 78 corresponded with the line VI-XVIII, in direction, then the clock and dial would agree at the time of winter and summer solstice, i. e. December 23, and June 21st, but it does not, for we have seen that the earth is in perigee December 31st, and in apogee July 1st, hence, in forming a table to show the equation of time, i. e. the correction that must be applied to the dial, or apparent solar time, in order to obtain true solar, or what is called mean time, which is the time in ordinary use, we must compound the two inequalities, for sometimes when the dial would be fastest, on account of the unequal motion of the sun in his apparent orbit, it would be slowest from the effect of the inclination of the plane of the ecliptic, to the plane of the equator, thus, April 15th, the dial will be slower than the clock, from the inequality of the sun's motion, about 7m, 23s, and at the same time it will be faster, from the obliquity of the ecliptic, about the same amount, hence they are really together on that day. The tables of the equation of time, are thus constructed. We have now explained, somewhat at length, the method of obtaining true time, from the time indicated by the sun, for it is of the utmost importance to the astronomer, and the navigator, to be able, on all occasions, to determine the local time.

It must be evident, that inasmuch as the earth is round, the sun will appear, as the earth turns on its axis, to rise and come to the meridian successively at every point upon its surface. If, therefore, some particular spot, Greenwich for example, is chosen, whose meridian shall be the one from which the time, or longitude, is reckoned, then if we know what time it is at that meridian, when the sun happens to be on the meridian at another place, we can, at once, by taking the difference between the times, viz: noon at that place, and, perhaps 4 o'clock P. M., at Greenwich, determine that it is 4h, west of the meridian of Greenwich, or, allowing 15° to the hour, 60° west. The meridian of Greenwich, where the Royal Observatory is located, is generally acknowledged as the first meridian, and longitude is reckoned east or west from it. In

the United States, the meridian of Washington is very often used.

Navigators are accustomed to carry with them Chronometers, or very accurate time-keepers, which are set to Greenwich time, and give, at any moment, by simple inspection, the precise time which is then indicated by the clock at Greenwich. On a clear day, the true time on ship-board, or the exact instant of apparent noon, is ascertained by means of the quadrant, figured below. This is an arc of a circle, embracing something more than oneeighth of the whole circle, but it is graduated into 90°, for the degrees are only half the length they would be, if the angles were measured without being twice reflected.

A is called the index glass; it is a plane quicksilvered glass reflector, placed, by means of adjusting screws, truly perpendicular to the plane of the quadrant, and attached to the brass index arm A B, this index turns on a pin directly under A. C is called the

horizon glass, and is also adjusted to be perpendicular to the plane of the quadrant, the upper part of this glass is unsilvered, so that the eye, applied at the eye-hole D, may look through it. The index A B, carries, what is called a vernier, which subdivides the graduations on the limb of the instrument E F, into smaller portions, usually into minutes. When the index is set to 0, and the eye applied at D, the observer will perceive, if he looks through the horizon glass at the horizon, that the portion of the horizon glass which, being silvered, would prevent his looking through, will, nevertheless, show the horizon in it almost as plain as if it was transparent, it being reflected on to it by the index glass A, and then again reflected to the eye, thus, Fig. 1, A is the index

D

A

(Fig. 1).

(Fig. 2).

glass, its back being towards the eye, and C the horizon glass, and DE the horizon, seen almost as plain in the silvered portion of C, as through the transparent part. If the glasses are all rightly adjusted, then, even if the position of the quadrant be altered, as in Fig. 2, the line of the horizon will still be unbroken, but move the index ever so little towards 10, or 2o, and immediately the reflected image of the horizon will sink down, as shown in this diagram,

a space equal to that moved over by the index, and if a star should happen to be just so many degrees, or parts of a degree, above