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Accelerations of the fixed Stars, affords us an easy to know method of knowing whether or not our clocks and by ihe watches go true: For if, through a small hole in a window-shutter, or in a thin plate of metal fixed to clərk goes a window, we observe at what time any star disap- true or pears behind a chimney, or corner of a house, at a little distance; and if the same star disappear the next night 3 minutes 56 seconds sooner by the clock or watch; and on the second night, 7 minutes 52 seconds sooner; the third night 11 minutes 48 seconds sooner; and so on, every night as in the table, which shews this difference for 30 natural days, it is an infallible proof that the machine goes true; otherwise it does not go true, and must be regulated accordingly; and as the disappearing of a star is instantaneous, we may depend on this information to half a second.

CHAP. XIII.

Of the Equation of Time.

THE

HE Earth's motion on its axis being per224.

fectly uniform, and equal at all times of the year, the sidereal days are always precisely of an equal length; and so would the solar or natural days be, if the Earth's orbit were a perfect circle, and its axis perpendicular to its orbit. But the Earth's di. The Sun urnal motion on an inclined axis, and its annual mo- cqual only tion in an elliptic orbit, cause the Sun's apparent mo- on four

days of the tion in the heavens to be unequal: for sometimes he revolves from the meridian to the meridian again in somewhat less than 24 hours, shewn by a well-regulated clock; and at other times in somewhat more; so that the time shewn by an equal-going clock and a true Sun-dial is never the same but on the 14th of April, the 15th of June, the 31st of August, and the 23d of December. The clock, if it go equably and true all the year round, will be before the.

year.

Sun from the 23d of December till the 14th of April; from that time till the 16th of June the Sun will be before the clock; from the 15th of June till the 31st of August the clock will be again before the Sun; and from thence to the 23d of December the Sun will be faster than the clock.

225. The tables of the equation of natural days, Use of the equation at the end of the following chapter, shew the time table.

that ought to be pointed out by a well regulated clock or watch, every day of the year, at the precise moment of solar noon; that is, when the Sun's centre is on the meridian, or when a true sun-dial shews it to be precisely twelve. Thus, on the 5th of January in leap-year, when the Sun is on the meridian, it ought to be 5 minutes 52 seconds past twelve by the clock: and on the 15th of May, when the Sun is on the meridian, the time by the clock should be but 56 minutes 1 second past eleven: in the former case, the clock is 5 minutes 52 seconds before the Sun; and in the latter case, the Sun is 3 minutes 59 seconds faster than the clock. But without a meridian-line, or a transit-instrument fixed in the plane of the meridian, we cannot set a sun-dial true.

How to 226. The easiest and most expeditious way of meridian. drawing a meridian-line is this: Make four or five conline. centric circles, about a quarter of an inch from one an.

other, on a flat board about a foot in breadth; and let the outmost circle be but little less than the board will contain. Fix a pin perpendicularly in the centre, and of such a length that its whole shadow may fall within the innermost circle for at least four hours in the middle of the day. The pin ought to be about an eighth part of an inch thick, and to have a round blunt point. The board being set exactly level in a place where the Sun shines, suppose from eight in the morning till four in the afternoon, about which hours the end of the shadow should fall without

all the circles; watch the times in the forenoon, when the extremity of the shortening shadow just touches the several circles, and there make marks. Then, in the afternoon of the same day, watch the lengthening shadow, and where its end touches the several circles in going over them, make marks also. Lastly, with a pair of compasses, find exactly the middle point between the two marks on any circle, and draw a straight line from the centre to that point : this line will be covered at noon by the shadow of a sinall upright wire, which should be put in the place of the pin. The reason for draw. ing several circles is, that in case one part of the day should prove clear, and the other part somewhat cloudy, if you miss the time when the point of the shadow should touch one circle, you may perhaps catch it in touching another. The best time for drawing a meridian line in this manner is about the summer solstice ; because the Sun changes his declination slowest and his altitude fastest on the longest days.

If the casement of a window on which the Sun shines at noon be quite upright, you may draw a line along the edge of its shadow on the floor, when the shadow of the pin is exactly on the meridian line of the board : and as the motion of the shadow of the casement will be much more sensible on the floor than that of the shadow of the pin on the board, vou may know to a few seconds when it touches the meridian line on the floor; and so regu. late your clock for the day of observation by that line and the equation-tables above mentioned, i 225.

227. As the equation of time, or difference Equation between the time shewn by a well regulated clock of natural and that by a true sun-dial, depends upon two caus- plained. es, namely, the obliquity of the ecliptic, and the unequal motion of the Earth in it; we shall first

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explain the effects of these causes separately, and then the united effects resulting from their combination.

228. The Earth's motion on its axis being perfectly equable, or always at the same rate, and the* plane of the equator being perpendicular to its axis, it is evident that in equal times equal portions of the equator pass over the meridian; and so would

equal portions of the ecliptic, if it were parallel to The first or coincident with the equator. But, as the ecliptic partof the is oblique to the equator, the equable motion of the of time. Earth carries unequal portions of the ecliptic over

the meridian in equal times, the difference being proportionate to the obliquity; and as some parts of the ecliptic are much more oblique than others, those differences are unequal among themselves. Therefore if two Suns should start either from the beginning of Aries or of Libra, and continue to move through equal arcs in equal times, one in the equator, and the other in the ecliptic, the equatorial Sun would always return to the meridian in 24 hours time, as measured by a well-regulated clock; but the Sun in the ecliptic would return to the meridian sometimes sooner, and sometimes later than the equatorial Sun; and only at the same moments with him on four days of the year; namely, the 20th of March, when the Sun enters Aries; the 21st of June, when he enters Cancer; the 23d of September, when he enters Libra; and the 21st of December, when he enters Capricorn. But, as there is only one Sun, and his apparent motion is always in the ecliptic, let us henceforth call him the real Sun, and the other, which is supposed to move in the

* If the Earth were cut along the equator, quite through the centre, the flat surface of this section would be the plane of the equator; as the paper contained within any circle may be justly termed the plane of that circle,

equator, the fictitious: to which last, the motion of Plate VI. a well-regulated clock always answers.

Let 7 g z t be the Earth, ZFRz its axis, Fig. III. abcde, &c. the equator, ABCDE,&c.the northern half of the ecliptic from op to on the side of the globe next the eye, and MNOP, &c. the southern half on the opposite side from top. Let the points at A, B, C, D, E, F, &c. quite round from op to op again, bound equal portions of the ecliptic, gone through in equal times by the real Sun; and those at a, b, c, d, e, f, &c. equal portions of the equator described in equal times by the fictitious Sun; and let Z z be the meridian.

As the real Sun moves obliquely in the ecliptic, and the fictitious Sun directly in the equator, with respect to the meridian, a degree, or any number of degrees, between q and Fon the ecliptic, must be nearer the meridian 2 pz, than a degree, or any corresponding number of degrees, on the equator from r to f; and the more so, as they are the more oblique: and therefore the true Sun comes sooner to the meridian every day while he is in the quadrant op F, than the fictitious sun does in the quadrant go f; for which reason, the solar noon precedes noon by the clock, until the real Sun comes to F, and the fictitious to f, which two points, being equidistant from the meridian, both suns will come to it precisely at noon by the clock.

While the real Sun describes the second quadrant of the ecliptic FGHIKL from co to -, he

es later to the meridian every day than the fic. titious sun moving through the second quadrant of the equator from f to ; for the points at G, H, I, K, and L, being farther from the meridian than their corresponding points at g, h, i, k, and I, they must be later in coming to it: and as both suns come at the same moment to the point +, they come to the meridian at the moment of noon by the clock.

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