Dear Brad, I'm delighted that you enjoyued my "tutorial"...
> However, its your step 19 I am > interested in. Ah yes. That's where I mention marking out equal hours. I thought you would be most interested in that step :-) You add... > And if I do tilt the hemispherium > so that the horizon line is now > instead parallel to the earth's > axis, does that solve any of the > issues? This is like taking an aircraft as your inspiration for designing a car and not appreciating what the wings are for. The absolutely key feature of the hemicyclium design is that, at its top, there is a FLAT HORIZONTAL surface. It isn't like that just so the Greek user could put his Retsina glass on it. It is like that in order to be parallel to the plane of the horizon and... That is important because it echos the position of the sun at sunrise and sunset and... That is important because the principal purpose of this dial was to divide the day into equal intervals of time starting at sunrise and ending at sunset. These unequal hours may not be to your taste but this is the scheme that was in widespread use for thousands of years! Why not educate your friends? Why not educate yourself? OK, I'll get round to what you really want shortly but, meantime, I am going to stick to the original purpose... In my previous message I was simplifying matters by saying that you should cut the sphere (the orange) into quarters. The problem with using a quarter of a sphere (and this also applies if you insist on equal hours) is that you can't represent sunrise and sunset in the summer months. A real hemicyclium was rather more than a quarter of a sphere. Take a look at: http://www.sundials.co.uk/leicester/fig04.jpg You can see the horizontal surface easily enough and you can also see a forward-sloping face at the front. The slope, relative to the vertical, matches the local latitude. This is about 37 degrees off the vertical in Greece but 50+ in the U.K. By leaning forward this allows the horizontal surface to grow so that its inside rim is no longer a semi-circle. It is now much more of a circle. The tip of the spike serves as the nodus and this is at the centre of the rim circle. The two "wings" are way beyond this tip. If you look at the markings you can see the three main constant-declination arcs. The middle one is a great circle and the tip of the spike is the centre of this circle too. The upper arc is for the winter solstice and the lower is for the summer solstice. These are small circles. If you hold one end of a piece of string on the tip of the spike and run the other end round either of these circles you would see the string sweeps out a cone, not a disc. OK, once you have this elegant hollow shape you can make cardboard templates which exactly fit these three circular arcs. The template for the equinoctial arc will be an exact semi-circle. The other two have a slightly smaller radius than the equinoctial circle. Clearly, the template for the summer solstice is more than a semi-circle and that for the winter solstice is less than a semi-circle. If you fit the two together you should get a perfect circle. Can you see why? Now all you have to do is to divide the rims of each of these three circles into 12 equal parts. This gives you the unequal hours of the day exactly as in fig 4. Of course, what you really want are new-fangled equal hours... Well, you make the same three templates as before and then, on each, mark the centre point on the rim. This is the noon point. You then mark off at 15-degree intervals either side of this point. This is easy for the equinoctial template. For the other two I suggest you butt them together so you can see the centre of the common circle. It is then a case of joining the dots to get the equal hour lines. You will find that several hour lines run up to the rim and abruptly stop. With the unequal hours ALL the lines run from the winter solstice arc to the summer solstice arc as in fig 4. As a refinement, I don't care for the way the Greeks mounted their spikes! I would allow you to improve on that... I suggest you drill a hole at the point where the noon line and equinoctial arc intersect. You now need a rod whose exposed length matches the radius of your sphere. Fix the hidden part in the hole and fix a small ball at the outer end to serve as the nodus. Make sure it is at the centre of the main horizontal rim. This means that at noon on the day of an equinox, the shadow of the nodus falls at the foot of the support rod. If you REALLY want a polar-oriented gnomon then you drill a hole through the nodus that is at right-angles to the support rod and insert the gnomon into this new hole. Make sure it is oriented towards the north celestial pole. I regard this as serious uglification. Best of luck with your efforts. Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
