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

unequal divisions on this very account. The little cross strokes 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 wintersolstice. 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 P3, 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



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 moon, 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

(Fig. 1). (Fig.2). glass, its back being towards the eye, and C the horizon glass, and D E 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 1°, or 22, 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 is a star should happen to be just so many degrees, or parts of a degree, above


the horizon, as the index had been moved, and as shown at a, it

would appear in the quadrant, as in the figure preceding,brought to the line of the horizon. Now just before noon, on ship-board, thé sailor sets the index of his quadrant to about the altitude of the sun, and defending the eye by a set of dark glasses, shown at G, page 82 ha looks through the eye-hole D, and the unsilvered

portion of the horizon glass, and sees a distinct image of the sun,

almost touching the horizon, thus:

It is true, he cannot see the horizon in the silvered portion of the horizon glass, but he can bring the image close to the line where the silvering is removed from the glass, and then by inclining his quadrant a little, as in figure 2, page 83, he can make the sun, apparently, describe the dotted arc c d, just touching the horizon. We will suppose he is looking just before noon, i.e. before the sun comes to the meridian, or reaches his highest altitude in the heavens, and that an assistant stands near, ready to note the time when this highest point is reached. As he looks through his quadrant, the image of the sun, which a moment before described the arc c d, and appeared to touch the horizon in its course, will seem to rise a little, he therefore moves the index, and brings it down again, all the time sweeping backward and forwards; if it rises a little more, he again brings it down, very soon he perceives

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