Dialing scales

Dialing scales are used to layout the face of a sundial geometrically. They were proposed by Samuel Foster in 1638, and produced by George Serle and Anthony Thompson in 1658 on a ruler . There are two scales the latitude scale and the hour scale. They can be used to draw all gnomonic dials- and reverse engineer existing dials to discover their original intended location. [1]

Description

The traditional scales (Foster scales) are drawn on a ruler. The hour scale shows $\sin t \over \sin t + \cos t$ the latitude scale shows $\sin \varphi \over \sqrt {1+ \sin^2 \varphi}$. Other scales are in existence. [2]

Usage

A right-angle is drawn on the dial-face and the latitude scale indicates a construction point on the x-axis. This is used to place the hour line to form a hypotenuse, each of the hour points are copied over to the dial face- a straight edge is used to connect them to the origin thus drawing the hour lines for that location. They can be used to draw all gnomonic dials- and reverse engineer existing dials to discover their original intended location. [1]

References

1. ^ a b Sawyer, Fred (1995). "Serle's Dialing Scales". Compendium (Glastonbury, CT,USA: North American Sundial Society) 2 (2): 5.
2. ^ Sawyer, Fred (2003). "A Note on the origin of Dialing Scales". Compendium (Glastonbury, CT,USA: North American Sundial Society) 10 (1): 21.