To all, 1 or 2 days ago a question about Foster Lambert sundials was on this list. In september 1997 there also was a discussion about this subject. At that time I sent an e-mail to this list and I made a page with pictures accompanying the message. I repeat the e-mail in this message and I replaced the pictures at http://www.iaehv.nl/users/ferdv/foster.htm After some time I will remove the page from the net.
Also look at the page http://www.iaehn.nl/users/ferdv/projdial.htm where you find an article by J.A.F. de Rijk, (Bruno Ernst) about projection dials. Fer de Vries. ------------------------- Text september 1997 To all, Last week we had a discussion about the Foster Lambert sundials on this list and some question still are open. Now I will try to give some basic informations for such dials. Several names are used for these types as Foster, hybride, Lambert, Parent, analemmatic, elliptical, circular, linear and combinations of these words. They all can be seen as a projection of the ( self orietating ) ( universal ) equatorial ring dial, so let us start with this one. For figures look at http://www.iaehv.nl/users/ferdv/foster.htm Equatorial ring sundial. This dial consists of : - a polestyle - a knob K ( or hole ) on that polestyle, movable according the date - an equatorial ring with radius R and with the center C on the polestyle and with equiangular hourpoints. See fig 0 and 1. The distance CK = R tan(decl) so on the polestyle we have a scale of date. When K is placed according the date the shadow ( or light spot ) is always running across the equatorial ring. All we now have to do to make an elliptic, circular or linear sundial is : project the equatorial dial onto our sundial plane in a direction of free choice. That's all...... Let us explain some simple cases. We project the equatorial dial onto the horizontal plane and we only use a style which is in the vertical north-south plane, in the local meridian. At first we make an analemmatic or elliptical sundial. The style is vertical and points to the zenith. The projection direction thus is from zenith to the horizontal plane. In fig. 2 you see how this is done. The circle transforms into an ellipse ( if lat isn't 90, -90 or 0 ) and that is the ellipse for our dial. Each hourpoint is projected in this way and forms the corresponding hourpoint on the final sundial. Also all the wanted points of the scale of date is projected in this way. As second example we choose a style which is just between the vertical line and the polestyle. The angle to the horizontal plane then is ( lat + 90 ) / 2 So we must have a style with that angle to the horizontal plane. Project the equatorial dial into this direction and, surprise, we get a circle, the same as the equatorial circle. So this is an example of a circular sundial ( or Foster Lambert dial )( The left one in fig 3 ). Also when we use a style with angle to the horizontal plane of ( 90 - lat ) / 2 we get the same circle, but another scale for the date. Both are drawn in fig. 3. It is nice to see how the shadow on both dials runs in opposite directions. To get a linear sundial we choose a style which lies in the equatorial plane. Again we project the equatorial dial into this direction onto the horizontal plane as you can see in fig. 4. The equatorial circle transforms into a simple line. In fig 5 all the styles I have used now are drawn. In fact we can project the equatorial sundial into any direction we like and we can project onto any plane we want, so there are infinit possibilities to make analemmatic sundials or what name you give them. Even on an irregular body we can make such a dial. Start with making a model of the equatorial sundial. With the help of a dia projector or even with the help of the lights of your car ( on reasonable distance ) project your model onto your sundial plane and draw the pattern. What a fun, isn't it? The special case of the dial in Cambridge you also can look at as is drawn in fig. 6. This is a vertical projection onto such a plane that the circle is projected as a circle. You see the dial's plane now is no longer horizontal, but in this special case it is a mirrored plane of the equatorial plane. I do hope this explanation will help all who had questions about these dials. All comment is welcome. As I told in one of my earlier messages it is also possible to use a central projection for such dials. Who knows more about this projection dials? ( The page with the figures will be deleted after some time. ) Fer de Vries, Netherlands.
