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latitude. The only difference between longitude as reckoned on the earth, and right ascension as measured in the heavens, is, the former is reckoned east or west from any arbitrary point, Greenwich, or Washington, for example, but the latter is reckoned eastward, or in the order of the signs, completely around, and always from the first point of Aries, which is a determined point in the sky, being the position of the vernal equinox, and which turns around, apparently, with the whole celestial concave, in its diurnal revolution. When a new comet appears, and is announced as having a R. A. of 6h, and 10m, and N. D, of 2° 15', the astronomer places his transit telescope, or other similar instrument, so as to point 2° 15' north of the imaginary celestial equator, for he knows just how high above the horizon this is situated, and when his clock points out 6h and 10m, he looks into the telescope and sees the newly discovered object. Thus the precise position occupied by any star, or planet, in the heavens, can be mapped down, using right ascensions and declinations in the same manner as terrestrial longitudes and latitudes. We should like to say a great deal more on this subject, but the nature of our work forbids. Our ordinary clocks and watches, are adjusted to keep mean solar time. It would, at first, be supposed, that the interval from moon to noon, although longer than a Siderial day, would, nevertheless, be an equal period, so that if a clock was adjusted to show 24 hours during the interval of the sun's leaving the meridian at any particular season of the year, to his return to it the next day, it would always indicate an interval of 24h, for any similar revolution. This is not the case, and we think we can show, very plainly, why it is not. The instant when the sun is actually on the meridian, is called the time of apparent noon, or 12 o'clock apparent time, although, a'clock regulated to keep what is called mean time, or mean solar time, may then show but 11h, 45m. The difference between apparent time and mean solar time, is called the equation of time, i.e. the correction which must be applied in order to determine true time, from the time indicated by the sun. It is evident that Sun-Dials will indicate apparent . time, and we will, therefore, devote the remainder of this chapter

Sun-dials. 71

to a description of the principles of dialing, and then proceed to illustrate the causes, which make the discrepancy observed between the times indicated by a clock supposed to run with an uniform motion, and a good sun-dial. We do this the more willingly, for we intend our book to be of some advantage to the reader, and we trust that after its attentive perusal, he will feel sufficiently interested to either erect a good dial, or Ameridian mark, in order to determine his local time with something more of accuracy than suffices for the ordinary wants of life. We mean by local time, the correct solar time for the place, in distinction from Greenwich time, or Siderial time. Chronometers, which are accurate, but portable, time-keepers, are often set to Greenwich time, i. e. they are adjusted so as to show, wherever they are carried, the actual time then indicated by the clock at Greenwich, the difference between this and the time indicated by the clock at any other place, or the local time will give, by simple inspection, the difference of longitude.

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Let P A B C, be the earth, and E the position of a spectator upon it, and let F Gobe the horizon, or a horizontal circle, and let C H A be the plane of a great circle parallel to the small circle F G, and let P B be the axis of the earth inclined to the diameter

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CA of the great circle C H A, according to the latitude of the spectator E. Now as the earth turns once on its axis in 24 hours, it is evident that the several meridians P, PI, PII, PIII, &c., will come successively under the sun at exact intervals of 1 hour, if they are all 15° apart, for 24 multiplied into 15 gives 360, the whole number of degrees to the circle. Suppose, for a moment, fhat instead of the earth turning up on its axis, once in 24 hours, that the sun moves around the earth in this time, the effect will be the same If the sphere of the earth was transparent, but its axis PD B opaque, then PD would, as the sun passed around, cast a shadow in the directions D A, DI, DII, DIII, &c., when the sun was in the opposite direction, and the progress of this shadow would mark the hour, according to the meridian in which it should fall. It will be observed, that the intervals A-I, I-II, IIIII, are not equal intervals, but vary, because the circle C H A, cuts the meridians obliquely. Now the sun is so far distant, that if the observer at E should locate a horizontal plane, which, of course, would be parallel to the large plane C H A, and describe on it a small circle, and then divide this circle in proportion as the meridians divide the large circle C H A, and should, likewise, erect from its centre a gnomon, or shadow stick, inclined so as to point to the north star, or in other words, to be parallel to PD, the progress of this shadow would mark the hour. We have here,

then, the principle of the horizontal Sun-dial, and all that is necessary to construct one, is, to graduate it proportionally according to the latitude. This can easily be done by calculation, which, however, would involve more of mathematical skill than we shall suppose the reader to possess; we will, therefore, show how it may be done experimentally, and thus any one, with the least ingenuity, can construct a horizontal dial. Referring back

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DIALING. 73

to the figure, page 71, it will not be difficult to perceive that if the circle C H A, had been the equator, then all the angles of the hour lines D A, D I, DII, &c., would have been measured by equal arcs, each 15°. The same would be true of any small circle, IK, parallel to the equator, the meridians, 15° apart, would divide it into 24 equal parts. Now, if on a globe, we should divide any parallel of latitude, such as I K, before alluded to, into 24 equal parts, and then pass a plane, a sheet of paper for example, through each of these divisions and the centre of the globe, then, wherever this plane intersected the plane of any other circle, C H A for example, it would mark out the directions of the hour lines D A, D I, DII, DIII. &c. Take, now, a flat board, on which a sheet of paper is fastened, and describe a circle whose centre is O, as in the diagram below, and let O B be a metallic

rod, inclined to the line A C, drawn on the paper to represent a meridian line, at an angle equal to the latitude of the place, let D E be a small circle, so fixed on O B, that its plane is everywhere perpendicular to it, or in other words, so that the distance from the point B to the circumference of the circle, may be the same throughout. Let this smaller circle be graduated into 24 equal parts, and subdivided into halves, and quarters, and if desired, still smaller spaces. Take, now, a fine thread, or a straight edge, and carry it from B through each division of the little circle, successively, down to the plane of the paper below, taking care, if a thread is used, not to crook it against the edge of the little circle, but simply passing it straight down. Through the points F, G, H,

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I, &c., thus indicated on the paper, and the centre of the circle A, draw the hour-lines A F, A G, A H, &c., extending, however, only to the circumference of the circle, and we have a dial ready for use, after adding the figures. Of course the little circle must be so adjusted that when the line is passed by some one of its graduations, it will reach the horizontal plane at a point in the meridian line A C. Instead of a wire for the gnomon, we may use an inclined plane, so that our dial will now be not unlike this

figure. In order to use it, we must next determine the north and south line, or a meridian line, and place the line on our dial which marks XII, to correspond therewith. This may be ascertained by means of a surveyor's compass, provided the variation of the needle from true north is known; or, at the time of the solstices, mid-summer or mid-winter, when the sun's declination is changing very slowly, a number of circles may be traced upon a horizontal plane, having a common centre, over which centre a plumb-line must be suspended, having two or three knots tied in it. Upon marking where the shadow of these knots falls, successively, on the circles, in the forenoon and afternoon, and then bisecting the space so measured on each circle, and drawing a line through the centre and these points of bisection, a pretty exact meridian line may be laid down. The use of several circles, is simply to ensure greater accuracy in the result. We will now suppose the dial constructed, and located in a window facing to the south. We may here observe, that there will be no use in graduating the dial all the way round, as that portion only can be used over which the shadow passes during the day, say from 5 o'clock to 5 o'clock, on each side, viz: from V, on the western side, through VI, VII, VIII, IX, X, XI, to XII, and from XII, to V, on the eastern side. When the sun rises before 6 o'clock, say

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