Article of the month May

Sundial transformations

If on an equatorial plane one draws Babylonian and Italian hour lines, there results a pattern of lozenge-shaped figures (blue).
The side corners of every lozenge, as seen from the centre, subtend fifteen degrees, equal to the hour angle for one hour.
The long diagonals read the whole hours, the side corners the half-hours.
We will use the lozenges to construct other sundials.

The example below shows twice as many, and overlapping, lozenges. The long diagonals read the half hours, and the quarters are read in between.
This is still an equatorial sundial.

We will now distort the equatorial sundial to make it into a vertical south dial for 45 degrees latitude.
The style height is therefore 45 degrees. We compress the figure horizontally, using a multiplier equal to the sine of 45 degrees, or 0.707.
Our south dial is ready.

This principle is much more generally applicable if one also allows rotations of the figure.
As an example, we show a random sundial for a latitude of 52 degrees.
This sundial has an inclination of 100 degrees (it leans forward 10 degrees out of the vertical)and a declination of -30 degrees (30 degrees towards east from south).
The starting point is again the equatorial sundial built from lozenges.