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222. Thus it is plain, that an absolute turn of An abso. the Earth on its axis (which is always completed lute turn when any particular meridian comes to be parallel to
its situation at any time of the day before) never Earth on
brings the same meridian round from the Sun to the never fi- Sun again; but that the Earth requires as much solar day. more than one turn on its axis to finish a natural day,
as it has gone forward in that time; which, at a mean state, is a 365th part of a circle. Hence, in 365 days, the Earth turns 366 times round its axis ; and therefore, as a turn of the Earth on its axis completes a sidereal day, there must be one sidereal day more in a year than the number of solar days, be the number what it will, on the Earth, or any other planet, one turn being lost with respect to the number of solar days in a year, by the planet's going round the Sun; just as it would be lost to a traveller, who, in going round the Earth, would lose one day by following the apparent diurnal motion of the Sun; and consequently would reckon one day less at his return (let him take what time he would to go round the Earth) than those who remained all the while at the place from which he set out.
So, if there were two Earths revolving equally on their axes, and if one remained at A until the other had gone round the Sun from A to A again, that Earth which kept its place at A would have its solar and sidereal days always of the same length; and so would have one solar day more than the other at its return. Hence, if the Earth turned but once round its axis in a year, and if that turn were made the same way as the Earth goes round the Sun, there would be continual day on one side of the Earth, and continual night on the other.
223. The first part of the preceding table shews how much of the celestial equator passes over the meridian in any given part of a mean solar day, and is to be understood the same way as the table in the 220th article. The latter part, intituled,
Accelerations of the fixed Stars, affords us an easy to know method of knowing whether or not our clocks and by the watches go true: For if, through a small hole in a window-shutter, or in a thin plate of metal fixed to curl: 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.
Of the Equation of Time.
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
equal only tion in an elliptic orbit, cause the Sun's apparent mo-on four. tion in the heavens to be unequal: for sometimes he days of the 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 ,
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. Use of the
225. The tables of the equation of natural days, equation at the end of the following chapter, shew the time
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 with. out 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 draw a
drawing a meridian-line is this: Make four or fiveconmeridianline. centric circles, about a quarter of an inch from one an.
other, on a fat 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 rouinc biunt 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, ; 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
explain the effects of these causes separately, and then the united effects resulting from their combi. nation.
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 part of the is oblique to the equator, the equable motion of the equation
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 equa. tor; as the paper contained within any circle may be justly termed the plane of that circle,