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THE EQUATION OF TIME
The Earth is tilted to the plane of its orbit around the sun by some 23 degrees. As it travels around its yearly course it appears to rock backwards and forwards on its axis (the polar axis), causing each hemisphere to pass closer to the sun. This is what causes the seasons. (Incidentally, because the Northern hemisphere is tilted away from the sun, the Southern hemisphere enjoys a warmer climate, being closer.) The result of this is that the days grow longer as we tilt towards the sun and shorter as we appear to tilt away.
The lengthening and shortening of the days causes a sundial to run slow or fast, since it takes varying lengths of time for the sun to move across the sky from where it rises in the East, to where it sets in the West, depending on the time of year.
Another factor affecting the varying lengths of the day is the Earths elliptical orbit around the sun. The Earth is further away from the sun during the summer months and closer in winter, the suns gravitational pull altering the days length.
If you put these two variables together the result is the Equation of time, usually represented by a graph, below, or a table, (see www.sundials.co.uk).
THE HORIZONTAL SUNDIAL
The horizontal sundial consists of a dial face and a gnomon. The gnomon casts the shadow onto the dial face, which is engraved with the days hours. In order to create the best geometric relationship with the passage of the sun across the sky, the gnomon is aligned with the polar axis, which will also be its angle of latitude. So a sundial made for a location in Cornwall will have a gnomon angled at 50 degrees, and a sundial made for Northern Scotland would have an angle of 58 degrees.The hour angles also change for different latitudes. Other common features on a horizontal dialface are: The Equation of time graph, (or table), a compass rose (the gnomon sits on the North/South axis and points North), a motto, dedication , or family crest. A date. The makers name and decoration and embellishments as requested. (Fluer de Lys, scrolls, etc.)

THE VERTICAL DIAL (WALL DIAL)
A vertical dial that is placed on a wall that faces due South looks like this:
The morning and afternoon hours are symmetrical and noon runs vertically dead centre.
This arrangement is perfect for 0 degrees longitude (Greenwich). However,in locations West of zero, this dial will run slow and East of zero, it will run fast. One degree of longitude equals four minutes of time, so in Celtenham, (2 degrees west of Greenwich), this dial will run 8 minutes slow, and in Great Yarmouth, (1.5 degrees East of Greenwich), the dial will run 6 minutes fast. A longitudinal correction can be applied to a walldial, during manufacture, to eliminate this problem: the hours are moved accordingly , and the dial assumes its accuracy. (Apart from the Equation of time).
THE ARMILLARY SPHERE
A Charlestown sundials armillary has six rings: the horizon ring, a vertical ring, the hour ring, the tropics of Cancer and Capricorn and a meridian ring. The meridian ring has a gap on the front to allow the passage of light at mid day.
The gnomon, a 4mm brass rod, is set to the angle of latitude of the sundials location, and lies parallel to the polar axis. The hour ring lies at 90 degrees to the gnomon, ( its co-latitude ) and has the hours engraved upon it at 15 degree intervals. The hour ring represents the Equator. The tropics lie parallel to the hour ring, the same as you would find on an Atlas. The horizon ring is not neccessary for dialling purposes, but represents our veiw of the horizon. A reference for us when observing the movement of the sun from AM to PM.
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