Analemmatic sundials can be considered as a projection of an auxiliary armillary (equatorial) sundial. The style is the line of projection of the active point (the point on the style of the equatorial dial which is active on a given date). To correct the equatorial sundial for the equation of time, all that is needed is to turn the equatorial circle around the polar axis by an angle corresponding to the equation of time. If this is positive (sun is slow), the circle must be turned anticlockwise as viewed from the north side.
The problem of the correction for the equation of time by a movement of the style of an analemmatic sundial can be stated thus:
Given an analemmatic sundial marked for a certain value of the equation of time (zero, for instance), does there exist a projection which uses the same markings for all other values of the equation (for which the auxiliary circle will have been rotated, consequently)? Note that it is the orientation of the circle which is fixed, and not its position or its radius which can be changed if need be. The style will be positioned taking account of the new geometry of the auxiliary dial and of the associated projection.
One solution consists of turning, at the same time as the auxiliary circle, the directions of projection and of the dial surface. This solution can be applied, for example, to Parent's dial as it is easy to see how to turn its dial. But, in reality, one has merely changed the problem, as the original idea was to move only the style !...
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Date written: 18 November 97
Date translated: 18 February 98