Editing Sundial (section)

===Vertical declining dials===
[[File:Verticalezonnewijzers-en.jpg|thumb|600px|center|Effect of declining on a sundial's hour-lines. A vertical dial, at a latitude of 51°&nbsp;N, designed to face due south (far left) shows all the hours from 6&nbsp;{{sc|a.m.}} to 6&nbsp;{{sc|p.m.}}, and has converging hour-lines symmetrical about the noon hour-line. By contrast, a West-facing dial (far right) is polar, with parallel hour lines, and shows only hours after noon. At the intermediate orientations of [[Boxing the compass|south-southwest, southwest, and west-southwest]], the hour lines are asymmetrical about noon, with the morning hour-lines ever more widely spaced.]]
{{Clear}}
<!-- [[File:MootHallSundial.JPG|upright|thumb|SSW facing, vertical declining sundial on Moot Hall, [[Aldeburgh]], Suffolk, England.]]  Logically better place-->
[[File:Vertical Sundial at Fatih Mosque.jpg|upright|thumb|Two sundials, a large and a small one, at [[Fatih Mosque]], [[Istanbul]] dating back to the late 16th&nbsp;century. It is on the southwest facade with an azimuth angle of 52° N.]]
A ''declining dial'' is any non-horizontal, planar dial that does not face in a cardinal direction, such as (true) [[north]], [[south]], [[east]] or [[west]].<ref>{{harvp|Rohr|1996|pp=55–69}}; {{harvp|Mayall|Mayall|1994|pp= 58–112, 101–117, 1458–146}}; {{harvp|Waugh|1973| pp= 74–99}}</ref> As usual, the gnomon's style is aligned with the Earth's rotational axis, but the hour-lines are not symmetrical about the noon hour-line. For a vertical dial, the angle <math>\ H_\text{VD}\ </math> between the noon hour-line and another hour-line is given by the formula below. Note that <math>\ H_\text{VD}\ </math> is defined positive in the clockwise sense w.r.t. the upper vertical hour angle; and that its conversion to the equivalent solar hour requires careful consideration of which quadrant of the sundial that it belongs in.<ref name="harvp|Rohr|1996|p=79">{{harvp|Rohr|1996|p=79}}</ref>

:<math> \tan H_\text{VD} = \frac{\cos L}{\ \cos D\ \cot(\ 15^{\circ} \times t\ ) - s_o\ \sin L\ \sin D\ } </math>

where <math>\ L\ </math> is the sundial's geographical [[latitude]]; {{mvar|t}} is the time before or after noon; <math>\ D\ </math> is the angle of declination from true [[south]], defined as positive when east of south; and <math>\ s_o\ </math> is a switch integer for the dial orientation. A partly south-facing dial has an <math>\ s_o\ </math> value of {{nobr|{{math| +1 }} ;}} those partly north-facing, a value of {{nobr|{{math| −1 }}.}} When such a dial faces south (<math>\ D  = 0^{\circ}\ </math>), this formula reduces to the formula given above for vertical south-facing dials, i.e.

:<math>\ \tan H_\text{V}  = \cos L\ \tan(\ 15^{\circ} \times t\ )\ </math>

When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle <math>\ B\ </math> between the substyle and the noon hour-line is given by the formula<ref name="harvp|Rohr|1996|p=79"/>

:<math> \tan B = \sin D\ \cot L </math>

If a vertical sundial faces trUe south Or north (<math>\ D = 0^{\circ}\ </math> or <math>\ D  = 180^{\circ}\ ,</math> respectively), the angle <math>\ B  = 0^{\circ}\ </math> and the substyle is aligned with the noon hour-line.

The height of the gnomon, that is the angle the style makes to the plate, <math>\ G\ ,</math> is given by :
:<math>\ \sin G = \cos D\ \cos L  ~</math><ref>{{harvp|Mayall|Mayall|1994|p= 138}}</ref>