Editing Sundial (section)

==Nodus-based sundials==
[[File:057Cracow.JPG|thumb|170px|upright| Kraków. {{Coord|50.0614|19.9400|type:landmark|format=dms|name=Kraków sundial}} The shadow of the cross-shaped nodus moves along a [[hyperbola]] which shows the time of the year, indicated here by the zodiac figures. It is 1:50&nbsp;{{sc|p.m.}} on 16&nbsp;July, 25&nbsp;days after the [[summer solstice]].]]

Another type of sundial follows the motion of a single point of light or shadow, which may be called the ''nodus''. For example, the sundial may follow the sharp tip of a gnomon's shadow, e.g., the shadow-tip of a vertical [[obelisk]] (e.g., the ''[[Solarium Augusti]]'') or the tip of the horizontal marker in a shepherd's dial. Alternatively, sunlight may be allowed to pass through a small hole or reflected from a small (e.g., coin-sized) circular mirror, forming a small spot of light whose position may be followed. In such cases, the rays of light trace out a [[Cone (geometry)|cone]] over the course of a day; when the rays fall on a surface, the path followed is the intersection of the cone with that surface. Most commonly, the receiving surface is a geometrical [[plane (geometry)|plane]], so that the path of the shadow-tip or light-spot (called ''declination line'') traces out a [[conic section]] such as a [[hyperbola]] or an [[ellipse]]. The collection of hyperbolae was called a ''pelekonon'' (axe) by the Greeks, because it resembles a double-bladed ax, narrow in the center (near the noonline) and flaring out at the ends (early morning and late evening hours).
[[File:Sundial solstice declination lines for different latitudes - slow.gif|thumb|left|Declination lines at solstices and equinox for sundials, located at different latitudes]]
There is a simple verification of hyperbolic declination lines on a sundial: the distance from the origin to the equinox line should be equal to [[harmonic mean]] of distances from the origin to summer and winter solstice lines.<ref>{{cite journal | last = Belk | first = T. | date = September 2007 | title = Declination lines detailed | journal = BSS Bulletin | volume = 19 | issue = iii  | pages = 137–140 | url = http://www.sundialsoc.org.uk/Bulletin/Bulletin-19iii-Belk.pdf | url-status = dead | archive-url = https://web.archive.org/web/20121018080432/http://sundialsoc.org.uk/Bulletin/Bulletin-19iii-Belk.pdf | archive-date = 2012-10-18 }}</ref>

Nodus-based sundials may use a small hole or mirror to isolate a single ray of light; the former are sometimes called ''aperture dials''. The oldest example is perhaps the antiborean sundial (''antiboreum''), a spherical nodus-based sundial that faces [[true north]]; a ray of sunlight enters from the south through a small hole located at the sphere's pole and falls on the hour and date lines inscribed within the sphere, which resemble lines of longitude and latitude, respectively, on a globe.<ref>{{harvp|Rohr|1996|p=14}}</ref>

===Reflection sundials===
[[Isaac Newton]] developed a convenient and inexpensive sundial, in which a small mirror is placed on the sill of a south-facing window.<ref>{{harvp|Waugh|1973|pp=116–121}}</ref> The mirror acts like a nodus, casting a single spot of light on the ceiling. Depending on the geographical [[latitude]] and time of year, the light-spot follows a conic section, such as the hyperbolae of the pelikonon. If the mirror is parallel to the Earth's equator, and the ceiling is horizontal, then the resulting angles are those of a conventional horizontal sundial. Using the ceiling as a sundial surface exploits unused space, and the dial may be large enough to be very accurate.