Schema for vertical declining dials as interpreted by Waugh in 1973.

• A semicircle is drawn, with a descending vertical.
• For a morning dial, or south-east decliner, a right angles triangle is drawn to the left with a top angle being the co-latitude.
• A second triangle is drawn to the right, with a top angle of D, the declination of the wall.

Finding SD- the substyle length

• The bottom bar of the left triangle represents cot Φ. The length is noted and using dividers copied over to the right triangle hypotenuse, and a further horizontal bar drawn. that will have the length of sin D. This is measured and and placed on the bottom bar of the left triangle. This sets the position M, and the substyle line (the term diallist use for the angle).

Finding SH - the substyle height

• The height of the right triangle is noted, and a line of this length is swung from point M, till it touches the circle. The angle from the origin to here, is the substyle height.(the term diallist use for the angle).

Drawing the hourlines

At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor).

• An arbitary point on the sub-style line is chosen. From here, a long-line, at right-angles to it, is drawn. A line is drawn at right angles from the substyle height, so that it passes through that point. Its length is noted.
• The length is copied from the point to O'. This will become the centre used by circular protractor. Draw a line from here to crossing of the vertical and the long-line.
• The circular protractor is aligned so that zero falls on the new line. Points are marked off and lines drawn through them to the long line. From each of these crossings. a final line is drawn back to the Origin at the top. These are the hour-lines. 12 is on the vertical, and the forenoon hours are to the left- and the afternoon hours (fewer in number) to the right.