Editing Sundial (section)

===Vertical sundials===
[[File:Houghton Hall Norfolk UK 4-face sundial.jpg|thumb|Two vertical dials at [[Houghton Hall]] [[Norfolk]] [[UK]] {{Coord|52.827469|0.657616|type:landmark|format=dms|name=Houghton Hall vertical sundials}}. The left and right dials face south and east, respectively. Both styles are parallel, their angle to the horizontal equaling the latitude. The east-facing dial is a polar dial with parallel hour-lines, the dial-face being parallel to the style.]]

In the common ''vertical dial'', the shadow-receiving plane is aligned vertically; as usual, the gnomon's style is aligned with the Earth's axis of rotation.<ref>{{harvp|Rohr|1996|pp=46–49}}; {{harvp|Mayall|Mayall|1994|pp= 557–58, 102–107, 141–143}}; {{harvp|Waugh|1973| pp= 52–99}}</ref> As in the horizontal dial, the line of shadow does not move uniformly on the face; the sundial is not ''equiangular''. If the face of the vertical dial points directly south, the angle of the hour-lines is instead described by the formula:<ref>{{harvp|Rohr|1996|p=65}}; {{harvp|Waugh|1973| p=52}}</ref>

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

where {{mvar|L}} is the sundial's geographical [[latitude]], <math>\ H_V\ </math> is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and {{mvar|t}} is the number of hours before or after noon. For example, the angle <math>\ H_V\ </math> of the 3&nbsp;{{sc|p.m.}} hour-line would equal the [[inverse trigonometric function|arctangent]] of {{nobr| [[trigonometric function|cos]] {{mvar|L}} ,}} since {{nobr|{{math| tan 45° {{=}} 1 }} .}} The shadow moves ''counter-clockwise'' on a south-facing vertical dial, whereas it runs clockwise on horizontal and equatorial north-facing dials.

Dials with faces perpendicular to the ground and which face directly south, north, east, or west are called ''vertical direct dials''.<ref>{{harvp|Rohr|1996|pp=54–55}}; {{harvp|Waugh|1973| pp= 52–69}}</ref> It is widely believed, and stated in respectable publications, that a vertical dial cannot receive more than twelve hours of sunlight a day, no matter how many hours of daylight there are.<ref>{{harvp|Waugh|1973| p=83}}</ref> However, there is an exception. Vertical sundials in the tropics which face the nearer pole (e.g. north facing in the zone between the Equator and the Tropic of Cancer) can actually receive sunlight for more than 12&nbsp;hours from sunrise to sunset for a short period around the time of the summer solstice. For example, at latitude 20° North, on June&nbsp;21, the sun shines on a north-facing vertical wall for 13&nbsp;hours, 21&nbsp;minutes.<ref name="Sunrise">{{cite web |last=Morrissey |first=David |title=Worldwide Sunrise and Sunset map |url=http://www.sunrisesunsetmap.com/ |url-status=live |access-date=28 October 2013 |archive-url=https://web.archive.org/web/20210210004115/https://sunrisesunsetmap.com/  |archive-date=10 February 2021}}</ref> Vertical sundials which do ''not'' face directly south (in the northern hemisphere) may receive significantly less than twelve hours of sunlight per day, depending on the direction they do face, and on the time of year. For example, a vertical dial that faces due East can tell time only in the morning hours; in the afternoon, the sun does not shine on its face. Vertical dials that face due East or West are ''polar dials'', which will be described below. Vertical dials that face north are uncommon, because they tell time only during the spring and summer, and do not show the midday hours except in tropical latitudes (and even there, only around midsummer). For non-direct vertical dials – those that face in non-cardinal directions – the mathematics of arranging the style and the hour-lines becomes more complicated; it may be easier to mark the hour lines by observation, but the placement of the style, at least, must be calculated first; such dials are said to be ''declining dials''.<ref>{{harvp|Rohr|1996|pp=55–69}}; {{harvp|Mayall|Mayall|1994|p=58}}; {{harvp|Waugh|1973| pp= 74–99}}</ref>

[[File:Nové Město nad Metují sundials 2011 3.jpg|thumb|170px|"Double" sundials in [[Nové Město nad Metují]], Czech Republic; the observer is facing almost due north.]]

Vertical dials are commonly mounted on the walls of buildings, such as town-halls, [[cupola]]s and church-towers, where they are easy to see from far away. In some cases, vertical dials are placed on all four sides of a rectangular tower, providing the time throughout the day. The face may be painted on the wall, or displayed in inlaid stone; the gnomon is often a single metal bar, or a tripod of metal bars for rigidity. If the wall of the building faces ''toward'' the south, but does not face due south, the gnomon will not lie along the noon line, and the hour lines must be corrected. Since the gnomon's style must be parallel to the Earth's axis, it always "points" [[true north]] and its angle with the horizontal will equal the sundial's geographical latitude; on a direct south dial, its angle with the vertical face of the dial will equal the [[colatitude]], or 90° minus the latitude.<ref>{{harvp|Waugh|1973| p=55}}</ref>