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A sundial consists of two main components---a *gnomon*, being the rod
which
casts the shadow, and a *dial*, which can be laid either
horizontally---using
a spirit level---onto a table , or vertical mounted onto a wall.
Horizontal is more usual.

The gnomon lies in the plane of the meridian---North-South (use the Sun at your midday---12 UT) to find this, and angled towards the celestial pole---i.e., it should point due North at an angle to the dial which equals your geographical latitude (for the USA, between 28 and 48 degrees depending on which State you live in, but look up in an atlas!). This angle can be called "L." At or near Christmas Day, the Equation of time is nearly zero, so that the Sun at midday clock time will be at the meridian to within 1 or 2 minutes accuracy!

To find where to place the hour markings, first take a sheet of paper and
draw on it a circle of radius `MC = 1`

unit (perhaps 10--20 cm),
where 1 unit is the
radius of the metal circle from which you intend to make the actual dial---this
is the Larger Circle. Also mark the center of the circle, M, and draw a radius
MC; this will serve as the meridian line. When the gnomon is mounted on the
meridian line, it will not cast a shadow at midday.

Extend the radius MC beyond the circle to a point O, such that ```
OC = sine
L
```

. Then draw a semi circle, with its centre at O, and radius OC, so that
the two circles touch each other at C.

Draw a tangent line through C---this is the common tangent to the two circles.

Mark on the Smaller Circle, starting at OC, out to the tangent, the angles 0, 15, 30 45, 60, 75, etc degrees , corresponding to the full hours (the Sun appears to move through the sky at 15 degrees per hour).

Now draw from the centre of the Larger circle, M, the radii that "belong" to these angles, and extend them up to their intersection with the tangent to meet the angle lines from the smaller circle OC. Mark C as 12 hours and the other hours in a clockwise direction; set the dial so that C points to north at 12 noon. The gnomon is set at an angle of L pointing north, in the 12 hour/noon direction.

The Larger circle MC, thus marked, is your dial Having done all this on paper, and checked it out, apply /trace the markings onto your metal circular plate and etch/score in the angle lines and labels.

Once again do this geometry on tracing paper first until you feel you understand and can achieve the necessary alignments, and try it out in the garden. When satisfied do it in metal as the "hard copy". A good material would be lacquered brass, or failing that stainless steel. The plate could be set on a wooden, or even a brick, pier, at horizontal with the aid of a spirit level The gnomon could be set at angle L using a protractor to measure L then a wedge cut from wood or plastic to hold it onto the plate at point M while you weld/solder or superglue the gnomon to the plate's centre.

Reference:

Astronomy: A Handbook, 1975, ed. G. D. Roth (New York:
Springer-Verlag)

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