Chris Lusby Taylor wrote: > PS -- Both Abert Waugh and Rene R. J. Rohr say that in a vertical dial > the 12 o'clock line is always vertical. Nevertheless, I've noticed this > is not the case for a vertical direct west (or east) dial. Have I found > a hint here? > > [Chris Lusby Taylor] I think you are wrong. A vertical direct east or west > dial does not have a 12 o'clock line! At 12 o'clock the sun is in the plane > of the dial, so the shadow of the gnomon does not fall on the dial. > A very very nearly direct east or west dial does, in principle, have a 12 > o'clock line, and it is vertical, passing through the point where the > gnomon touches the dial. Unfortunately the gnomon is almost in the plane of > the dial, so it protrudes only a very small amount and it is not very > practical. This is why direct east and west declining dials are always made > with the gnomon held away from the dial.
I feel so bad when I am caught saying things so negligently... You are completely right. Let me try to fix what said and meant. I wonder if I can still mend my reputation ;-) I am completely uncapable of mentally creating solids in the space. Of course, this spells big trouble when you thy to see with the eyes of your mind how the angles and shadows move as you, say, rotate a vertical plane to "see" the results. Alas, I cannot do that without resorting to some drawing and models. My thinking was: in a vertical direct east dial you have a gnomon that makes with the horizontal an angle equals to the latitude. The hour-lines are all paralell with the gnomon as well as to each other. The hour lines are put further apart as you go from 6 o'clock to a hyphothetical 12 o'clock line. Of course, I clearly understand both physically as well as mathmathically that this 12 o'clock line does not exist. Now I am approching the point I made my error. I can accept this, but I can not "see" it. Let me go a little further: At least theorethically, we can get as close to the 12 o'clock line as we like. Say, to 89 59' 59" or even closer. That hour-line, no matter how far from the gnomon, is still parallel to it. Let's also consider that our dial is set for a latitude of 60 degrees South. This means that the hour line for 12 o'clock minus "a very small delta" still makes an angle of 60 degrees with the horizontal. Let's say, just for the sake of argument, that now we twist our vertical plane just a very very small amount. Something very very close to 0. In this moment, that line jumps abruptly from its 60 degrees to 90 degrees with the vertical. That's the part I can not follow with my mind's eyes. Although I can still see that it probabily has to do with the tangent of the angle when when the angles varies from very close to 90 degrees to 90 degrees. By now I think I have fixed my original description, replacing 12 o'clock line by almost 12 o'clock line. Also, I certainly can understand the discontinuity of a function. I still can not make the dial work! - fernando -- Fernando Cabral Padrao iX Sistemas Abertos mailto:[EMAIL PROTECTED] http://www.pix.com.br mailto:[EMAIL PROTECTED] Fone: +55 61 321-2433 Fax: +55 61 225-3082 15º 45' 04.9" S 47º 49' 58.6" W 19º 37' 57.0" S 45º 17' 13.6" W
