THE GENERAL PRINCIPLES DIALLING, ILLUSTRATED BY THE TERRESTRIAL GLOBE. THE art of dialling is of very ancient origin, and was in former times cultivated by all who had any pretensions to science; and before the invention of clocks and watches it was of the highest import. ance, and is even now used to correct and regulate them. It teaches us by means of the sun's rays to divide time into equal parts, and to represent on any given surface the different circles into which, for convenience, we suppose the heavens to be divided, but principally the hour circles. The hours are marked upon a plane, and pointed out by the interposition of a body, which receiving the light of the sun, casts a shadow upon the plane. This body is called the axis, when it is parallel, to the axis of the world. It is called the style when it is so placed that only the end of it coincides with the axis of the earth; in this case, it is only this point which marks the hours. Among the various pleasing-and profitable amusements, which arise from the use of globes, that of dialling is not the least. By it the pupil will gain satisfactory ideas of the principles on which this branch of science is founded; and it will reward with abundance of pleasure, those that chuse to exercise themselves in the practise of it. If we imagine the hour circles of any place, as London, to be drawn upon the globe of the earth, and suppose this globe to be transparent, and to revolve round a real axis, which is opake, and casts a shadow; it is evident, that whenever the plane of any hour semicircle points at the sun, the shadow of the axis will fall upon the opposite semicircle.* Let aPCp, plate 13, Jig. 1, represent a transparent globe; abcdefg the hour semicircles, it is clear, that if the semicircle Pap points at the sun, the shadow of the axis will fall upon the opposite semicircle. If we imagine any plane to pass through the centre of this transparent globe, the shadow of half the axis will always fall upon one side or the other of this intersecting plane. Thus, let ABCD be the plane of the horizon of London; so long as the sun is above the horizon, * Long's Astronomy, vol. I. p. 82. tt the shadow of the upper half of the axis will fall somewhere upon the upper side of the plane ABCD; when the sun is below the horizon of London, then the shadow of the lower half of the axis E falls upon the lower side of the plane. When the plane of any hour semicircle points at the sun, the shadow of the axis marks the respective hour-line upon the intersecting plane. The hour-line is therefore a line drawn from the centre rf the intersecting plane, to that point where this plane is cut by the semicircle opposite to the hour semicircle. Thus let ABCD, plate 13, Jig, 1, the horizon of London, be the intersecting plane, when the meridian of London points at the sun, as in the present figure, the shadow of the half axis PE falls upon the line EB, which is drawn from E, the centre of the horizon, to the point where the horizon is cut by the opposite semicircle; therefore EB is the line for the hour of twelve at noon. By the same method the rest of the hour-lines are found, by drawing for every hour a line, from the centre of the intersecting plane, to that semicircle which is opposite to the hour semicircle. Thus plate 13, Jig. 2, shews the hour-lines drawn upon the plane of the horizon of London, with only so many hours as are necessary; that is, those hours during which the sun is above the horizon of London, on the longest day in summer. If, when the hour-lines are thus found, the semi I circles be taken away, as the scaffolding is when the house is built, what remains, as in Jig. 2, will be an horizontal dial for London. If instead of twelve hour circles, as above described, we take twice that number, we may by the points, where the intersecting plane is cut by them, find the lines for every half hour; if we take four times the number of hour circles, we may find the lines for every quarter of an hour, and so on progressively. We have hitherto considered the horizon of London as the intersecting plane, by which is seen the method of making an horizontal dial. If we take any other plane for the intersecting plane, and find the points where the hour semicircles pass through it, and draw the lines from the centre of the plane to those points, we shall have the hour-lines for that plane. Plate 13, Jig. 3, shews how the hour-lines are found upon a south plane, perpendicular to the horizon. Fig. 4, shews a south dial, with its hourlines without the semicircle, by means whereof they are found. The gnomon of every sun dial represents the axis of the earth, and is therefore always placed parallel to it; whether it be a wire, as in the figure before us, or the edge of a brass plate, as in a common horizontal dial. The whole earth, as to its bulk, is but a point, if compared to its distance from the sun; therefore, if a small sphere of glass be placed on any part of the earth's surface, so that its axis be parallel to the axis of the earth, and the sphere hav« such lines upon it, and such planes within it, as above described, it will shew the hour of the day as truly as if it were placed at the centre of the earth, and the shell of the earth were as transparent as glass. A wire sphere, with a thin flat plate of brass within it, is often made use of to explain the principles of dialling. From what has been said, it is clear that dialling depends on finding where the shadow of a straight wire, parallel to the axis of the earth, will fall upon a given plane, every hour, half hour, &c. the hourlines being found as above described, which we shall proceed to exemplify by the globe. Every dial plane (that is, the plane surface on which a dial is drawn) represents the plane of a great circle, which circle is an horizon to some country or other. The centre of the dial represents the centre of the earth ; and the gnomon which casts the shade represents the axis, and ought to point directly to the poles of the equator. The plane upon which dials are delineated may be either, 1. parallel to the horizon; 2. perpendi cular to the horizon; or, 3. cutting it at oblique angles. ,/ |