Declining Dial

The vertical sundial declining has its vertical table, but not making vis-a-vis one cardinal points. The style is parallel to the axis of the Earth.

If one notes $\ Delta$ the angle which one turns the table of a southernmost dial ( $\ Delta<0$ towards the East, $\ Delta>0$ towards the West), the angle between under-stylaire and the line of midday (vertical) are defined by:

$\ tan \ theta= \ frac {\ sin \ Delta} {\ tan \ phi}, \,$

where $\ phi$ represents the latitude of the place. It is also about the slope compared to the horizontal one of the line of variation the days of equinox.

The angle between the time line H and the line of midday is given by

$\ tan \ gamma_H= \ frac {\ cos \ phi} {\ cos \ Delta \ cot H+ \ sin \ Delta \ sin \ phi} \.$

Note:: $H<0 \ Leftrightarrow \ gamma_H<0$ corresponds in the morning (left of the dial), whereas $H>0 \ Leftrightarrow \ gamma_H>0$ corresponds to the afternoon (right of the dial).

It is checked that for $\ Delta=0$ , one finds the relation of the vertical Cadran simple (Southerner or septentrional).

For $\ Delta=- \ pi/2$ , one obtains a Eastern Cadran, and for $\ Delta= \ pi/2$ , one obtains a Western Cadran.

See too

External bonds

Claude Garino. Sundials: Their calculation and their construction. Bull. One. Prof Phys. Chim., 83 (710): 35-68, January 1989.
Orlando DIVIDED INTO VOLUMES. Sundials and the astrolabe planispheric without the use of spherical trigonometry. Bull. One. Prof Phys. Chim., 98 (868 (1)) : 1523-1576, November 2004.

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