axis of the gnomon agi, and from g let fall the perpendicular gi upon the meridian line ai, and there will be a triangle made, whose sides are ag, gi, and ia; if a plate similar to this triangle be made as thick as the distance between the lines ac and bd, and be set upright between them, touching at a and b, the line ag will, when it is truly set, be parallel to the axis of the world, and will cast a shadow on the hour of the day. The trouble of dividing the two quadrants may be saved, by using a line of chords, which is always placed upon every scale belonging to a case of instruments.* PROBLEM XLI. To delineate a direct south dial for any given latitude, by the globe. Let us suppose a south dial for the latitude of London. Elevate the pole to the co-latitude of your place, 38° 30′, and proceed in all respects as above taught for the horizontal dial, from VI in the morning to VI in the afternoon, only the hours must be reversed, as in plate 13, fig. 3; and the hypothenuse ag, fig. 4. of the gnomon agf, must make an angle with the dialplane equal to the co-latitude of the place. As the sun can shine no longer than from VI in the morning to VI in the evening, there is no occasion for having more than twelve hours upon this dial. * Or much more so by an appropriate set of dialling lines, placed on a 14-inch box scale, which is sold at our shop, in Holborn. EDIT. In solving this problem, we have considered our vertical south dial for the latitude of London, as an horizontal one for the complement of that latitude, or 38 deg. 30 min. all direct vertical dials may be thus reduced to horizontal ones in the same manner. The reason of this will be evident, if the globe be elevated to the latitude of London; for, by fixing the quadrant of altitude to the zenith, and bringing it to intersect the horizon in the east point, it will point out the plane of the proposed dial. This plane is at right angles to the meridian, and perpendicular to the horizon; and, it is clear, from the bare inspection of the globe, thus elevated, that its axis forms an angle with this plane, which is just the complement of that which it forms with the horizon, and is therefore just equal with the co-latitude of the place; and that, therefore, it is most simple to rectify the globe to that co-latitude. The north vertical dial is the same with the south, only the style must point upwards, and that many of the hours, from its direction can be of no use. PROBLEM XLII. To make an erect dial, declining from the south towards the east or west. Elevate the pole to the latitude of the place, and screw the quadrant of altitude to the zenith. Then, if your dial declines towards the east, (which we shall suppose in the present instance) count in the horizon the degrees of declination from the east point towards the north, and bring the lower end of the quadrant to coincide with that degree of declination at which the reckoning ends. Then bring the first meridian under the graduated edge of the strong brass meridian, which strong meridian will serve as the horary index. Now turn the globe westward, and observe the degrees cut in the quadrant of altitude by the first meridian, while the hours XI, X, IX, &c. in the forenoon, pass successively under the brazen one; and the degrees thus cut on the quadrant by the first meridian are the respective distances of the forenoon hours, from XII on the plane of the quadrant. For the afternoon hours, turn the quadrant of altitude round the zenith, until it comes to the degree in the horizon, opposite to that where it was placed before, namely, as far from the west towards the south, and turn the globe eastward; and as the hours I, II, III, &c. passes under the strong brazen meridian, the first meridian will cut on the quadrant of altitude the number of degrees from the zenith that each of the hours is from XII on the dial. When the first meridian goes off the quadrant at the horizon, in the forenoon, the hour index will shew the time when the sun comes upon this dial; and when it goes off the quadrant in the afternoon, it points to the time when the sun leaves the dial. Having thus found all the hour distances from XII, lay them down upon your dial-plane, either by dividing a semicircle into two quadrants, or by the line of chords. In all declining dials, the line on which the gno mon stands, makes an angle with the twelve o'clock line, and falls among the forenoon hour-lines, if the dial declines towards the east; and among the afternoon hour-lines, when the dial declines towards the west; that is, to the left-hand from the twelve o'clock line in the former case, and to the right-hand from it in the latter. To find the distance of this line from that of twelve. This may be considered, 1. If the dial declines from the south towards the east, then count the degrees of that declination in the horizon, from the east point towards the north, and bring the lower end of the quadrant to that degree of declination where the reckoning ends; then turn the globe, until the first meridian cuts the horizon in the like number of degrees, counted from the south point towards the east, and the quadrant and first meridian will cross one another at right angles, and the number of degrees of the quadrant, which are intercepted between the first meridian and the zenith, is equal to the distance of this line from the twelve o'clock line. The numbers of the first meridian, which are intercepted between the quadrant and the north pole, is equal to the elevation of the style above the plane of the dial. The second case is, when the dial declines westward from the south. Count the declination from the east point of the horizon towards the south, and bring the quadrant of altitude to the degree in the horizon at which the T PROBLEMS. falls among the forenoon hour-lines, if the Sands, makes an angle with the twelve o'clock and among towards the east; lines, when the dial declines towards ormer case, and to the right-hand of this line from that of the globe, the like oint end of the quadrant to coincide with that degr that ea W re the sl |