Bulletin 02.2 English summary

R. Hooijenga.

Contents of the May 2002 Bulletin, nr. 79

Meeting of 12 January 2002 Secretariat 1

There were twenty-one members present. – A discussion on definitions and signs in sundial calculations (e.g. azimuth reckoned from north or south; positive or negative solutions for arccos, etc.). – Chris Horikx and Dees Verschuuren will prepare a catalogue of all the sundial-related models by Jan Kragten. – Jan de Graeve will review Seeing the Light, The Sun in the Church as Solar Observations by J.L. Heilbron (1999). – Is an armillosphere an equatorial or a cylindrical polar dial? – H. Hollander shows his postcard dial. – Fer de Vries mentions an investigation that suggests that some "conical sundials" may turn out to be based on an elliptical cylinder instead of a cone.

This meeting, chaired by Fer de Vries, was attended by nineteen members. – There is no excursion subject yet (there was shortly after, see the Bulletin). – Chris Horikx would like to see more articles aimed at the beginner in the Bulletin. This is noted by the editors. – Ruud Hooijenga becomes member of the board because of his editorship, which he has taken from Secretary Fer de Vries. – The main subject is the presentation by Gerrit Sasbrink on his armillospheres, of which he has made over one hundred. He also explains his gilding technique. – Chris Doomernik wonders about the large excursions of his magnetometer. Rather than long term influences, aurora is likely to play a role. – One of Sasbrink’s hoops finds use in an explanation why the sun is not always due west at 6pm. – Hans de Rijk brought cigar boxes and colour prints for everyone to make sundials out of. – Fer de Vries brought a model of the Maddux spar dial. – Jacob Borsje made a shadow plane dial for a schoolyard.

Fer de Vries, the present secretary of the Society, has held that function since 1988. All that time he was editor of the Bulletin as well, a task that he has now transferred to Ruud Hooijenga (see also the Summaries header).

This year the excursion is in Utrecht, home of the oldest pole style dial (1464AD) still in operation. A walk takes us along several dials in the Museum Quarter. There will also be talks on bringing back a sundial to the Dom Tower and on a dial for the Hortus (Botanicus).

An abandoned horizontal sundial project. Only a meridian plus equinox point and the positions of the shadow of the gnomon tip at three o'clock and at five o'clock are left - these were recorded some two months after the equinox. Supposing everything else is unknown (including the location of the dial, or the gnomon height), reconstruct the entire sundial. What is really wanted is a graphical construction rather than a calculation. As a hint, one possible solution uses a special property of sundials that is known for over four hundred years, according to Italian sources.

The Ootmarsum Chronomium has acquired one of these recorders. A 95mm diameter glass sphere has its focal point on a strip of prepared paper, not quite 20mm behind the glass. It follows that the refractive index is 1.54, somewhat greater than for ordinary glass. The trace burned in the paper shows the times and durations of the sunshine. There are strips for the summer, winter, or autumn/spring seasons. They are graduated every whole and half hour, so the instrument could double as an equatorial sundial. – The author thinks the recorder reminds one of the Aristarchus skaphè.

The Genk Sundial Park has a realisation of Spanish Javier Moreno Bores’ idea for such a sundial. Fig. 1 shows the dial in principle. One property of such a dial is that the Italian and Babylonian hours are read on a shadow line, instead of just a shadow point as in ordinary point dials. I and B lines are obtained by the rotation of the horizontal plane about the polar axis. After every 15 degrees, the intersection between the rotated plane and the dial face forms the next hour line. The rotating plane described a cone, which consists of two halves, both of which are useable as shadow casters. Fig. 2c shows the lower half used with an inclined southing face.

Riccardo Anselmi of Italy realised that the tip of the cone does not have to be in the plane of the dial face. In fig.4, it looks as if the cone is placed on top of a gnomon. This enables one to construct the hour lines on the dial face as if for an ordinary point dial. Because at the winter solstice the two shadow line of the cone will be outside the pattern, it is useful to extend the hour lines.

Trying this for cones for lower latitudes, it becomes clear that the extended hour lines are all tangent to an ellipse, shown in fig. 6, or to a parabola or hyperbole, depending on latitude and dial face orientation. – The conical gnomon can also be used for sidereal time. Hour lines are obtained by rotating the plane of the ecliptic around the polar axis. The apex will always be 133 degrees, independent on latitude (fig.7 was missing). This should make it simple to make a universal sidereal time dial.

A box and two pieces of sewing thread make a point dial. Because the box projects the sky upside-down on its inside, the dial face (with furniture calculated by Fer de Vries) shows an upside-down version of the typical Dutch landscape.

This is a correction to a twenty-year old paper on the length of an elliptical arc. The top formula is wrong, the bottom one, starting boog CP =, is correct. Note that the integral cannot be solved analytically, only approximated numerically. The author suggests the trapezoid rule.

Wim Geerts built a bird feeder with three date lines and hourly analemmas etched on the inside of the glass roof, and a readout dot on the floor. He calculated the patterns with a homebrew Pascal program.

A good overview of his sundials. A description of the Sawyer Prize ceremony is on sundials.org/conference/2001/2001conf.htm

 Postcard dial by Sundialfactory H. Hollander 22

This elaborate sundial, once finished, shows local time, date lines, and longitude+EOT corrections.

Why do neither the Dom Tower nor the Cathedral have a sundial? The dark red dial with golden hour lines of St.Nicholas catches the eye immediately, and the Jacobi church even has two.

Dom Tower did have sundials. A drawing shows the 1525 situation, with a large style triangle near the Egmond chapel. A century later, in 1626, it must have been missing, for the town council ordered sundials to be placed on several buildings, among them the Dom Tower.

This dial did not survive either, and the 1838 model of the tower (now in Central Museum) by L. Koentz shows a small horizontal dial near the Egmond chapel. It was invisible from below. Probably this dial was last seen in 1966, but it vanished without trace.

A widespread misconception is that citizens read time on the sundial. They did not; they had the tower clock – which the tower keeper set to the sundial. A small dial was all that was necessary; but in many cases, if you were going to add a sundial to your church, it might as well be a nice one. They were difficult to maintain, however, and the Dom Tower reverted to just a small dial for the keeper.

Whether a large vertical, or a smaller horizontal dial is not yet decided, but this much is certain: In 2003, the Dom Tower will have a sundial once more.

Manuel Lombardero and Manuel Valdés of Spain, and Manfred Hüttig of Germany, think that some antique so-called conical sundials may not be conical in shape, but that the stone is cut along a cylinder with elliptical cross section. They tend to add a new class: that of the elliptical-cylinder dials.

Properties of the "usual" conical dials are:

The axis of the cone is parallel to the earth’s axis (j ); the apex is free (2e ); the intersection of the cut-out with the equatorial plane is a circle; the intersection of the cut-out with the horizontal plane is an ellipse (e <j ), a parabola (e =j ), or a hyperbole (e >j ), but never a circle; and the surface of the cut-out is straight like the mantle of a cone is straight: you could glue saté sticks to the surface, and they would all point towards the top of the cone. Especially the last three properties are easily checked, but this is hardly done. Gibbs mentions it only once, for the Leiden dial.

If a cylinder is to intersect two (non-parallel) planes along two circles, it must itself have an elliptical cross section and make an angle of 45º+0.5j with the horizontal. Saté sticks glued to the surface would now all be parallel.