Why the Sawyer Equant works, and where the lily pad shape comes from:

Here is a horizontal dial designed for 37 degrees latitude. The hour lines are not equally spaced. Rotating the design would advance some hours more than others.
Here are equally spaced (Equant) hour lines. Rotating this design advances all hours the same amount. Unfortunately, this design would not tell time as a sundial.
Here the two designs are overlapped. The intersection of matching hour lines are noted with red circles. At these points the design works both as a sundial and as equally spaced (blue) hour lines.
Here the black curve traces the intersection not only of the hours, but of the minutes as well, showing the derivation of the lily pad shape. Rotating the equant blue lines about their origin allows the blue time scale to be adjusted for the date and daylight savings, and still keep time accurately if read where it crosses the "lily pad".


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