Hmm. I'll try again. Imagine a vertical sundial declining almost due east - say 90 degrees and 1 second if we're in the northern hemisphere or 89 degrees 59 minutes and 59 seconds in the southern hemisphere. Its gnomon points due north-south, of course, so, viewed from above, the gnomon will be seen to stick out of the dial by only a very small angle. This angle is so small that the gnomon has to be extremely long if it is to be usable. In fact if the dial were 20 km wide (and as tall as needed depending on your latitude) the bottom of the gnomon would stick out just 10cm. In practice, the way to make the gnomon length manageable is to cut off and discard the top 19.9999 km, leaving the familiar direct east dial, but for this mental exercise imagine that it had not been cut off. We have a 20km sundial ! All morning, up to just before noon, the shadow of the gnomon will fall very close to the style, and will seem to be almost parallel to the gnomon, although it is not quite parallel, as they converge at the top of the dial. As noon approaches, the sun gets almost into the plane of the dial, and the gnomon's shadow rushes away. At exactly noon, the shadow is a vertical line, passing through the point of attachment of the gnomon to the dial - in other words 20km away from the bottom of the gnomon. If you still doubt it, all you have to do is build a dial with a gnomon around 20km long, wait for noon, stand well back and watch. Regards Chris
-----Original Message----- From: Fernando Cabral [SMTP:[EMAIL PROTECTED] Sent: 17 October 1998 17:23 To: [email protected] Subject: Re: Help! a novice is knocked down <snip> 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
