1. Take a convenient point A, and through A draw the meridian, or XII o'clock line, AB; and at the distance Aa, equal to the thickness of the stile, draw ab parallel to AB.

2. Make the angle BAD equal to the complement of the latitude of the place. Assume a point E in the line AD, and draw EF perpendicular to AB. Draw EG per

-pendicular

pendicular to AD, and through G draw the contingent line HI perpendicular to AB, representing the equinoctial.

3. Make GK, gk, each equal to GE, and with any radius, as GK, and K, k, as centres, describe the quadrants CL, gl, and divide each into six equal parts, Through the points of division draw lines from the centres K, k, cutting HI in the hour points m, m; n, n, &c. Then lines, drawn from the centres A, a, through the points m, m; h, n, &c. will be the hour lines; and are to be numbered I, II, III, &c. from XII toward the east.

NOTE 1. The stile may be a triangular plate similar to AEF, placed perpendicular to the plane of the dial on AGga. Or it may be a perpendicular pin erected at F, and equal in height to FE.

NOTE 2. This dial is set up with the face toward the south; IH being horizontal from east to west, and BA vertical, with the end A upward.

NOTE 3. This dial shews the time while the sun is on the south side of the prime vertical.

PROBLEM

PROBLEM VIII.

To draw geometrically an erect direct north dial.

1. Proceed as in drawing a south dial, except with respect to the hour lines, which must be those, that may be shewn while the sun is on the north side of the prime vertical, and the numbering of them from the substile must be in the contrary direction, or toward the west.

2. Then turn it upside down, setting the face directly northward, or making the stile point to the north pole; and it will be the dial required.

1. Draw the horizontal line AB; and assume a point C on the right, through which draw the contingent line CD, making the angle ACD equal to the elevation of the equator, or complement of the latitude.

2. Through any point D of the line DC draw FDG perpendicular to DC, and through d at the distance Dd, equal to the thickness of the stile, draw fdg parallel to FDG, for the VI o'clock hour line and the substile.

3. On FG, fg, také DG, dg, each equal to the height of the stile; and with the centres G, g, and any radius, as DG, describe the quadrants DH, dh, and divide each into six equal parts. Through the points of division draw lines from the centres G, g, cutting CD in the hour points m, m; n, n, &c. Then through the points m, m; n, n, &c. draw lines parallel to DF; numbering them VII, VIII, &c. from the substile toward the north or right, the hours before VI being toward the south or left; and they will be the hour lines required.

NOTE I. The stile may be a plate in form of a parallelogram, placed perpendicular to the dial plane on the substile, its thickness being equal to Dd, and its height equal to MK DG.

NOTE 2.

This dial shews the time of the forenoon.

PROBLEM