It was discovered in very early times that a vertical rod could not throw a shadow that would accurately denote time, and the correct inclination of such a rod or the stile of a sun-dial was evidently a matter of experiment and approximation before the ancient astrono mers fixed the angle by calculation. This sur mise is borne out by the various inclinations found in ancient dials. Some of these were constructed arbitrarily at 45°, an angle having no relation whatever to the latitude of its location.
The first historic sun-dial dates from about 1000 B.C. It was found in Rhodesia, and is be lieved to be of Semitic origin. Sun-dials are referred to in Grecian literature in 560 B.C., and a certain sun-dial is specifically spoken of as having been set up at Athens by the astronomer Meton in 433 B.C. It is said of the Turks that wherever they build a mosque they place a sun-dial. In China they are every where, and small ones which may be carried in the pocket are very common. The correct use of these portable dials depends, of course, upon their accurate orientation when reading them.
Sun-dials have been classified under three headings, according to their superficial form: spherical, cylindrical and plane. The spherical form is the most ancient. It consists of a hemispherical hollow cut into a rock or built up in that form, the flat of the hemisphere being horizontal. An upright rod was set in the centre of the hemisphere, pointing to the zenith. The hour marks were cut into the hol low surface. A variation of this type was the cutting away of the front half of the hemi sphere. This form of necessity can mark only the hours from 6 A.M. to 6 P.M. An old Roman dial is in the form of a spherical shell of which about two-thirds have been cut away, held upon the shoulders of a herculean figure. Cylindrical dials have the hollow in the shape of a semi-cylinder cut through lengthwise. A rod in the position of the axis of the cylinder throws the shadow. A variation of this form is a semi-cone cut through its axis. The plane dials are too well known to need description.
In the placing of sun-dials another classifi cation comes into play; they may be horizontal or vertical. Many of the latter type are set into or carved upon the walls of churches or other buildings or on stone blocks set upon pillars or pedestals. As a rule, the vertical sun-dials are set to face directly south. Where this is not feasible the gnomon may extend toward the south at the angle of a corner of a building, the hour lines being partly on one façade and partly on the other. In some of the odd pillar types the stone block at the top is cut with many facets like a crystal, with a gnomon on each facet.
The leading principles of dialing may be made intelligible to general readers by the following simple illustration: Let P B p D represent the earth as a hollow transparent sphere, having an axis P E p, of which P and p are the poles. Let the equator be divided into 24 equal parts and through these divisions draw the meridians, a, b, c, d, etc. Let one of these meridians pass through any given place for which a dial is required to be made, and where that meridian cuts the equator let it be numbered XII. The opposite meridian must likewise be numbered XII, the other meridians being numbered as shown in the cut. This being done, these meridians will be the hour circles of the place on the first meridian; so that if the axis P E p were opaque, the sun in his (apparent) motion round the earth in 24 hours will pass from one merid ian to another in one hour, and cause the shadow of the axis to fall on the hour on the plane D C B A. This diagram has been drawn for the latitude of Glasgow, 55° 52', and the plane in its present position would form a horizontal dial for that place; but we may suppose it capable of moving round its axis A C, so as to assume different positions in the sphere. If it move round so as to be
come vertical, that is, at right angles to its position in the figure, we then obtain an erect south dial. The plane may also be made to incline from the meridian either toward the east or west. Thus we have dials of different kinds dependent on the position of the plane with regard to the first meridian, the position of the hour lines of which are all determined by the meridians of the sphere cutting the plane.
We have been considering the earth as the sphere, in our illustration of the nature of dials, but the earth's magnitude is so small compared with the distance of the sun, that no appreciable error will follow in considering a small glass sphere similar to that above described, but placed on the surface of the earth with its axis parallel to that of the earth; then will the sphere show the hour of the day in the manner before specified. The only things absolutely essential for a dial are the axis and the plane, the places of the hour lines having been once determined. Dials may have various forms, many of which are exceed ingly curious and intricate, and require for their construction the application of complicated trigonometrical formulae. We shall confine our attention here to the most common, and, at the same time, most useful form, that is, the plane horizontal dial. On the proposed plane, which may be either of marble, slate or brass, draw a straight line P H S for the meridian or 12 o'clock line, and parallel to this draw 12, h S, leaving a space between them equal to the thickness of the gnomon.
The gnomon is a thin triangu lar plate of metal, somewhat similar in shape to the figure A E B, the side A B being fixed into the plate of the dial, so that the gnomon shall stand perpendicularly, the line A E being directly north and south.
The line A E is called the style, and the angle E A B is made equal to the latitude of the place for which the dial is constructed. In the case of a vertical dial the angle E A B must be the complement of the latitude, the line A B the top of the gnomon and the line B E affixed to the dial.
We return again to the consideration of Fig. 2. Draw 6 H 6 perpendicular to 12 H S, and it will be the six o'clock hour line; make the angle 12 H F equal to the latitude of place, and draw 12 F perpendicular to H F; con tinue S 12 to P, making 12 P equal to 12 F. The line 12 1 2 3 4 is drawn parallel to the line 6 H 6. From the point P draw the lines P 1, P 2, P 3, etc., terminating in the line 12 1 2 3 4, making angles with the line 12 P at the point P of 30°, 45°, etc., increasing by 15° each line. Next from the centre H draw the lines H 1, H 2, H 3, etc., and thus the hour lines of 1, 2, 3, 4 and 5 P.M. will be found. The hour lines on the other side of the style should now be formed by taking a tracing of the side al ready formed; the hours are of course num bered differently, and both sides will stand thus, the hour line of both sides corresponding: 1, 2, 3, 4, 5, 6, 7, 8, 12, 11, 10, 9, 8, 7, 6, 5, 4.
Here we have carried the hours beyond 6, which was the extent of the construction but to find the hour lines for 4 and 5 in the morning we have only to produce the hour lines of 4 and 5 in the evening, and in like manner for the hour lines of 7 and 8 in the afternoon, produce the hour lines of 7 and 8 in the morning. The dial gives solar time, and, therefore, the time, according to it, will only agree four days in the year with a well-regulated clock. See EQUA