At 7:34 PM -0500 10/17/98, Mac Oglesby wrote: >Greetings all, > >I have an opportunity to design and install an analemmatic dial at a nearby >elementary school. But first the staff would like to know more about the >project and has asked for a presentation at an upcoming (soon) staff >meeting. I feel comfortable describing the dial and how it would be >constructed. However, I don't remember (if I ever knew) why such a dial is >called "analemmatic."
> >Someone is bound to ask me, so I'm asking you, "Why is an analemmatic dial >called an analemmatic dial?" Mac: Be grateful that I never throw away anything useful. I dug this out of my Email archives. Ray Quote: Mac Oglesby asks for an English translation of Yvon Masse's Web pages. Having read them in French, I am convinced that they are well worthy of translation, so have undertaken that task. This email includes the first two of the three pages. I cannot currently load the third page, but will translate it as soon as I can. Fans of the Foster-Lambert school should be sure to read this. My translation is fairly literal, so that you can easily relate it back to the original, except for some idioms. I have added one or two explanations in parentheses where I thought the English might be unclear. One expression eluded me: Is "le sens trigonometrique" clockwise or (as I believe) anticlockwise? Please see the original Web pages for all diagrams. I am happy to offer the following to the group. If Yvon wishes to add it to the Web site, I should be honoured. http://www.union-fin.fr/usr/ymasse/anlegprc.htm Title: Two Mean-Time Analemmatic Sundials SUMMARY: Analemmatic sundials have the peculiarity of having a style which must be moved throughout the year as the declination of the sun changes. This action by the user can be put to good use: by changing the orientation of the style at the same time, the equation of time can be allowed for, so that the dial shows mean time. Two types of sundial which achieve this are analysed here. Analammatic sundials can be considered as a projection of an auxilliary 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. If this is positive (sun is slow) , the circle must be turned anticlockwise ("le sens trigonometrique") as viewed from the north side. The problem of the correction of 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, for all other values of the equation, (for which the auxilliary circle will have been rotated, consequently,) a projection which gives the same markings? Note that it is the orientation of the circle which is important, 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 auxilliary dial and of the associated projection. One solution consists of turning, at the same time as the auxilliary circle, the directions of projection and of the dial surface. This solution can be applied, for example, to a Parent 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!... (Translator's note: I have not come across the Parent dial before, but it seems to be the same as the first sundial described below, but without any adjustment for the equation of time and with the direction of projection chosen to be due East-West. (see http://www.union-fin.fr/usr/ymasse/analprc.htm) ==================================================================== http://www.union-fin.fr/usr/ymasse/anleg1.htm Title: Two Mean-Time Analemmatic Sundials Subtitle: First sundial Here, then, is the first type of sundial which solves the problem. It is characterised by a direction of projection parallel to the equator. The projection of the auxilliary circle is reduced to a line segment. Figure 1 shows the auxilliary circle (A) with centre C in the equatorial plane. The circle is oriented for zero equation of time. Figure 1 here The intersection of the planes of the equator and of the dial surface is represented by the line (I). (D) is the freely chosen direction of projection and SS' is the segment of (I) corresponding to the projection of the auxilliary circle. H is the hour mark on the circle which is projected onto S and t is the angle HCS; t is also the angle between (D) and the perpendicular to (I). Note that CHS is a right angle. The choice of the length s=CS of the half-segment SS' can be seen to force the auxilliary circle's radius to be r0 = s.cos t. The projection of another hour mark such as M, at an angle MCH=h from H, gives the point M' on segment SS'. The distance from M' to C is: M'C = r0.cos h / cos t M'C = s.cos h This is negative when M' is between S' and C. A line parallel to the earth's axis passes through C, perpendicular to the plane of the figure. The active (shadow-casting) point P of the auxilliary dial is on this axis at a distance PC from C, where: PC = r0.tan d0 PC = s.cos t.tan d0 where d0 is the sun's declination for the particular date when the equation of time is zero. The style must therefore be positioned through P and parallel to (D). For a value E of the equation of time, when the circle has been turned by this value, the way to achieve the same projection SS' is to turn the direction of projection by the same angle, so that it remains at right angles to CH (see figure 2). Figure 2 here. The radius of the auxilliary circle must be changed to r=s.cos(t+E) and we find that M', the projection of M is still at a distance from C given by: M'C = r.cos h / cos(t+E) M'C = s.cos h As for the style, it must be moved along the polar axis by a distance PC = s.cos(t+E).tan d ,d being the sun's declination, then turned by an angle E so that it is again parallel to HS. (Translator's note: This is brilliant! Sorry, couldn't contain myself.) In practice, making such a sundial is made difficult because of this positioning of the style. The ideal support is along the polar axis as the style always passes through it at right angles. Unfortunately, for a plane dial, the active point on the polar axis is above the plane of the dial for only half the year. It's possible for the polar axis to be in the plane of the dial, which is the case, for example, for the Parent dial. For this, one can imagine a system of markings which show the correct orientation for the style as it moves up and down the polar axis. Another difficulty inherent in this type of dial is that each point of the segment SS' corresponds to two different times, and there is no simple rule to tell them apart. Finally, the summarise, let's see how to modify a Parent dial to show mean time. Starting from the initial position, you must: o Turn the style around the polar axis by an angle given by: a = lo + 15.fh + E/4 degrees where: lo: Longitude of sundial, positive if west of Greenwich fh: time zone, in hours E: Equation of time, in minutes, positive if mean time is in advance of sun-time (sun is 'slow') If a is positive, rotate the style anticlockwise as viewed from the north pole. o Reduce the distance from the style to the equatorial line by the factor f: f = cos (lo + 15.fh + E/4) f = cos a ==================================================================== http://www.union-fin.fr/usr/ymasse/anleg2.htm Title: Two Mean-Time Analemmatic Sundials Subtitle: Second sundial Translation to follow. Chris Lusby Taylor Ray Bates Newfane, VT 05345 (802)365 7770 http://www.thebritishclockmaker.com
