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The analemma

This is one of a series of articles written for "Clocks" magazine by the late Noel Ta'bois, and reproduced with permission here as a memorial to him.

This article originally appeared in Clocks in November 1986

The word 'analemma', originally derived from the Greek for a prop or support is Latin for the pedestal of a sundial and hence the sundial itself. Later meanings are an orthographic projection of the celestial sphere on to the plane of the meridian and a device for solving dialling problems. Nowadays it signifies the figure-of-eight pattern which relates the sun's declination to the Equation of Time.

The best way to understand this last meaning is to make an analemma for yourself. It will take a year to do so but the equipment is simple. A board about 15cm by 40cm is fixed horizontally, with its longer dimension running roughly north-south, on the inside sill of a window with a southerly aspect (northerly in the southern hemisphere). The window does not have to face due south (or north) but must be in sunlight at noon throughout the year, bearing in mind the seasonal variations in the height of the sun. It is surprising how the eaves of the house can obscure the summer sun, and trees or buildings quite a distance away the winter sun.

Mounted vertically on the board, close to the window is a metal strip about 11cm high. Near its top edge is a 1mm hole, counter-sunk if the metal is thick. Sizes and angles are not critical but it s important that everything is rigid and that nothing will move during the course of a year.

The sun shining through the hole on to the board produces a spot of light whose position varies with the position of the sun. The spot passes across the board from west to east in the hours around noon, is closest to the window at midsummer and furthest away at midwinter. At selected times (detailed below) the centre of this spot is marked and dated in pencil or in permanent waterproof ink; light will fade and condensation will dissolve some ball point and fibre tip inks.

If on a number of occasion between the solstices the spot position is marked when the sun is due south, and the marks joined they will produce a straight line (SN in the diagram) which lies in the plane of the meridian, ie it runs due north-south. This is one of the methods of finding south at a particular location.

One can determine when the sun is due south, ie when it is noon local solar time, by consulting an accurate clock and making allowances for longitude, the Equation of Time, and daylight saving time, as explained on this page in October 1985.

In addition to marking the position of the spot when the sun is on the meridian, mark it also at precisely noon by the clock, ie mean time noon, or 1.00pm when daylight saving time is in force. Thus you will mark two positions every day except if the sun is on the meridian at noon mean time when only one mark is needed. If true time (time by the sun) is fast, compared with mean time, the spot will be displaced to the east and if slow, to the west. Clouds and personal activities will prevent recording every day but do so as often as possible.

Because displacements to east and west caused by the Equation of Time follow two cycles in a year, and because displacements fore and aft caused by changes in the sun's declination follow only one cycle, joining up all the marks made at mean noon produce the analemma which will look like an elongated and distorted figure eight as shown in the diagram. If you live on or close to your time meridian the line SN will pass through the middle of the analemma. If your location is to the east or west of ;your time meridian then your analemma will be displaced to the east or west respectively. The diagram shows an analemma for a location about three degrees west of the time meridian. The date marks indicate the first of each month.

The analemma enable you to obtain noon mean time (ie clock time) by the sun; this will be when the light spot lies on the analemma. But be careful to pick the correct side of the analemma; the light spot crosses both sides every day.

Use the solid line curve shown in the diagram from 21st June to 21st December to 21st June.

By inserting the date when you marked each spot you will not only know which side of the analemma to read but also you will have made yourself a sun calendar! Incidentally, if you mark and join the spots at intervals as the spot crosses the board on the days when the sun enters signs of the Zodiac you will produce declination lines.

If you erected the perforated plate for the noon mark described last January you can use this without any alteration to make a vertical analemma. Being vertical it will be different: the two loops of one figure eight will be about the same size, the winter solstice will be at the top and the summer solstice at the bottom.

The French do not use the word analemma but refer to the figure as a mean time meridian, a term which makes sense - until it is abbreviated, as it often is, to just meridian or until it is drawn elsewhere than on the true meridian!

If an analemma is drawn on every hour line of a sundial, not just on the noon line, that dial will then read mean time instead of true time. The analemma is the basis of all mean time dials which is the topic for next month.