How to Lay Out a Sundial
Details of Dial
The sundial is an instrument for measuring time by using the shadow of the sun. They were quite common in ancient times before clocks and watches were invented. At the present time they are used more as an ornamentation than as a means of measuring time, although they are quite accurate if properly constructed. There are several different designs of sundials, but the most common, and the one we shall describe in this article, is the horizontal dial. It consists of a flat circular table, placed firmly on a solid pedestal and having a triangular plate of metal, Fig. 1, called the gnomon, rising from its center and inclined toward the meridian line of the dial at an angle equal to the latitude of the place where the dial is to be used. The shadow of the edge of the triangular plate moves around the northern part of the dial from morning to afternoon, and thus supplies a rough measurement of the hour of the day.
Table No. 1.
Height of stile in inches for a 5 in.
base, for various latitudes
| Latitude | Height |
| 25° | 2.33 |
| 26° | 2.44 |
| 27° | 2.55 |
| 28° | 2.66 |
| 30° | 2.89 |
| 32° | 3.12 |
| 34° | 3.37 |
| 36° | 3.63 |
| 38° | 3.91 |
| 40° | 4.20 |
| 42° | 4.50 |
| 44° | 4.83 |
| 46° | 5.18 |
| 48° | 5.55 |
| 50° | 5.96 |
| 52° | 6.40 |
| 54° | 6.88 |
| 56° | 7.41 |
| 58° | 8.00 |
| 60° | 8.66 |
The style or gnomon, as it always equals the latitude of the place, can be laid out as follows: Draw a line AB, Fig. 1, 5 in. long and at the one end erect a perpendicular BC, the height of which is taken from table No. 1. It may be necessary to interpolate for a given latitude, as for example, lat. 41°-30'. From table No. 1 lat. 42° is 4.5 in. and for lat. 40°, the next smallest, it is 4.2 in. Their difference is .3 in. for 2°, and for 1° it would be .15 in. For 30' it would be 1/2 of 1° or .075 in. All added to the lesser or 40°, we have 4.2+.15+.075 in.= 4.42 in. as the height of the line BC for lat. 41 °-30'. If you have a table of natural functions, the height of the line BC, or the style, is the base (5 in. in this case) times the tangent of the degree of latitude. Draw the line AD, and the angle BAD is the correct angle for the style for the given latitude. Its thickness, if of metal, may be conveniently from 1/8 to 1/4 in.; or if of stone, an inch or two, or more, according to the size of the dial. Usually for neatness of appearance the back of the style is hollowed as shown. The upper edges which cast the shadows must be sharp and straight, and for this size dial (10 in. in diameter) they should be about 7-1/2 in. long.
To lay out the hour circle, draw two parallel lines AB and CD, Fig. 2, which will represent the base in length and thickness. Draw two semi-circles, using the points A and C as centers, with a radius of 5 in. The points of intersection with the lines AB and CD will be the 12 o'clock marks. A line EF drawn through the points A and C, and perpendicular to the base or style, and intersecting the semicircles, gives the 6 o'clock points. The point marked X is to be used as the center of the dial. The intermediate hour and half-hour lines can be plotted by using table No. 2 for given latitudes, placing them to the right or left of the 12-o'clock points. For latitudes not given, interpolate in the same manner as for the height of the style. The 1/4-hour and the 5 and 10-minute divisions may be spaced with the eye or they may be computed.