But formerly, when watches did not exist, the tracing of the I, II, III, &c., o'clock lines was done by calculating the angle which each of these lines would make with the XII o'clock line. Now, except in the simple cases of a horizontal dial or of a vertical dial facing a cardinal point, this would require long and intricate calculations, or elaborate geometrical constructions, implying considerable mathematical knowledge, but also introducing increased chances of error. The chief source of error would lie in the uncertainty of the data; for the position of the dial-plane would have to be found before the calculations began,—that is, it would be necessary to know exactly by how many degrees it declined from the south towards the east or west, and by how many degrees it inclined from the vertical. The ancients, with the means at their disposal, could obtain these results only very roughly.
Dials received different names according to their position:—
Horizontal dials, when traced on a horizontal plane;
Vertical dials, when on a vertical plane facing one of the cardinal points;
Vertical declining dials, on a vertical plane not facing a cardinal point;
Inclining dials, when traced on planes neither vertical nor horizontal (these were further distinguished as reclining when leaning backwards from an observer, proclining when leaning forwards);
Equinoctial dials, when the plane is at right angles to the earth's axis, &c. &c.
Dial Construction.—A very correct view of the problem of dial construction may be obtained as follows:—
| Fig. 1 |
Conceive a transparent cylinder (fig. 1) having an axis AB parallel to the axis of the earth. On the surface of the cylinder let equidistant generating-lines be traced 15° apart, one of them XII ... XII being in the meridian plane through AB, and the others I ... I, II ... II, &c., following in the order of the sun's motion.