The art of drawing dials on any surface, plane or curved. On account of the limited utility of this art, from the causes before noticed, we shall confine ourselves to explaining the general principles of dialling, which may be aptly illustrated by the phenomena of a hollow or transparent sphere of glass. Then suppose a P B p to represent the earth as transparent, and its equator as divided into 24 equal parts, by so many meridian semicircles, a b c, etc, one of which is the geographical meridian of any given place, as London, which is supposed at the point a; and if the hour of 12 be marked upon that meridian, and upon the opposite one, and all the rest of the hours in succession on the other meridians, those meridians would be the hour circles of London; because, as the sun appears to move round the earth, which is in the centre of the visible heavens, in twenty-four hours, he will pass from one meridian to another in an hour. Then, if the sphere had an opaque axis as P e P, terminating in the poles P and P, the shadow of the axis, which is in the same plane with the sun and with each meridian, would fall upon every particular meridian and hour when the sun came to the plane of the opposite meridian, and would, consequently, show the time at London and at all other places on the same meridian.

If this sphere were cut through the middle by a solid plane ABCD in the rational horizon of London, one-half of the axis e P would be above the plane, and the other below it; and if straight lines were drawn from the centre of the plane to those points where its circumference is cut by the hour circles of the sphere, those lines would be the hour lines of an horizontal dial for London;■ for the shadow of the axis would fall upon each particular hour line of the dial when it fell upon the like hour circle of the sphere. Those who are further interested in the subject we would refer to Emerson's Dialling, and Ferguson's Lectures on Mechanics. Dr. Brewster, in the Appendix to his valuable edition of this latter work, has described an analemmatic dial, which sets itself. Many ingenious constructions of dials are also given in Dr. Hutton's Translation of Montucla's Recreations.