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 a meridian 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.

Let PA B C, be the earth, and E the position of a spectator upon it, and let F G be the horizon, or a horizontal circle, and let CH 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

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, P III, &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, that 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 P D 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 P D, 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

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, D II, &c., would have been measured by equal arcs, each 15°. The same would be true of any small circle, I K, 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 HA for example, it would mark out the directions of the hour lines DA, DI, D II, D III, &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 DE 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,

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

DIALS AND CLOCKS.

75 at 5 o'clock, it will then be shown at V, by the shadow on the western side of the dial, and the shadow cannot be observed on the dial to advantage much later than 5 o'clock, Suppose, then, the dial located, and that when the shadow indicates XII, or apparent noon, a well regulated clock is started, the hands of which also indicate XII, and this on the 24th day of December, for, as we shall soon see, this is one of the four days in the year when the clock and dial agree, then, although for a few days, the clock and dial will appear to indicate the hour of noon together, it will soon be observed, that the clock begins to gain on the dial, and after an interval of one month, the clock will show 12h, 13m, when the dial indicates noon, or 12 o'clock apparent time. This difference will go on increasing, until February 10th, or 11th, when the clock will appear to lose time, and by the 25th of March will be only 6m. faster than the dial, and on the 15th day of April they will again correspond. The clock, after this, will continue, apparently, to lose time until about May 15th, at which time it will only indicate 11h, 56m, when the dial shows noon; after this, its rate seems to increase, and on the 16th day of June they again come together. The clock now continues to gain on the dial until July 25th, when it is about 6m, 4s, faster, after which, its rate apparently decreases, until at August 31, they again coincide. On the 2d of November, the clock shows 11h, 43m, 46s, when the dial says it is noon; this is the greatest difference of all, being 16m, 14s, after this they begin to come together, and on December 24th, again correspond. Now, can it be that the sun's motion in the heavens, or rather the earth's motion, is thus irregular? We might, at first, suspect our clocks, and watches, but the utmost pains have been bestowed on these, and when their rates of going have been ascertained, by means of the stars, and a transit instrument, as already described, they are found to go perfectly uniform, or very nearly so. Hence we are forced to admit, that the discrepancy between the dial and the clock, is to be sought for in the movements of the earth, and we shall fully show, in our next chapter, what these are.

Thus far we hope we have succeeded in explaining the phenomena of the heavens due to the movements of the earth, and