Frank, Thank you for the tutorial. I believe I followed all the logic and steps. However, its your step 19 I am interested in. Any suggestions as to how to mark the inner surface with equal duration hours throughout the year?
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? -----Original Message----- From: Frank King [mailto:f...@cl.cam.ac.uk] Sent: Monday, October 16, 2017 11:12 AM To: Brad Thayer <wissenschaft...@verizon.net> Cc: sundial@uni-koeln.de; Frank King <f...@cl.cam.ac.uk> Subject: Re: Hemicyclium correction Dear Brad, You say: > I am looking to make a > hemicyclium-type sundial > (half-hemisphere) in a > metal working class. <snip> > Am I missing anything? Er, yes. Rather a lot alas... Before you start bashing metal it may be worth spending rather less effort on a prototype. > ...they are inaccurate... I am not sure where you got that from. There is no reason why they shouldn't be accurate provided you know what you can expect of one. > ...without being very clear > on the problem. I suspect the writer of your quote either didn't know what a hemicyclium was or had looked at one and noted that it didn't indicate the same time as his watch so it must be wrong. > It appears to me the only > issue is it needs to be > tilted so that the gnomon > aligns with the Earth's > rotation axis... Er, no. The polar-oriented gnomon wasn't invented for nearly 1500 years after the hemicyclium was in common use. What looks like a gnomon and may well be CALLED a gnomon is not what you think of as a gnomon. It is actually a "nodus support". Only the shadow of the tip is of interest. > I am also looking to use > an analemma-shaped gnomon > to cast the shadow on the > bowl... First, build a prototype. You can think about fancy upgrades later. Imagine the following... 1. Take an orange. 2. Cut it in half. Throw one half away. [OK, maybe eat it first.] 3. Then cut the half in half and throw one of these quarters away. 4. What you are left with is your half hemisphere. 5. This has one curved surface and two plane surfaces. 6. Arrange for one of the planes to be horizontal and the other to be vertical and facing due south (assuming you are in the northern hemisphere). 7. Now place a bead in the middle of the edge that is common to the two flat faces. THIS is the nodus. 8. Now imagine that all the space between the bead and the skin is replaced by a transparent medium. 9. You now have an embryonic hemicyclium. Let's think about some of its properties.... 10. At sunrise (and sunset) the sun is in the plane of the horizontal flat surface, and the shadow of the bead (in the winter half of the year) will fall on the inside rim of the horizontal element of skin. This rim is the "horizon line". 11. At an equinox the shadow of the bead during the course of a day will follow a great (half) circle on the inside surface of the skin. 12. At the winter solstice it will follow a small (less than half) circle on the inside surface and this will be above the equinoctial circle. 13. At the summer solstice you hit a minor snag. At sunrise the sun is north of due east and the shadow of the bead will not fall on the rim. Don't worry about this yet. [The Greeks DID cope with this but that's for later.] 14. Instead, pick up the path of the shadow starting from when the sun is due east and, by then, some way above the horizon. 15. You will again get a small (less than half) circle. 16. Now add lots of intermediate small circles for other times of year. 17. At this point you have a choice as to how you chop up each circle into hours... 18. The ancients chopped each part circle in the winter half into 12 parts, thus dividing the daylight period into unequal hours. You could label the spaces 1 to 12 if you like. The Greeks didn't have digits or even Roman Numerals and labelled the hours alpha, beta, gamma etc. 19. That's the way I would do it but if you insist on using iconoclastic new fangled equal hours then you can. You will find it rather harder! 20. That completes your prototype. Now have a long think about what you really want to do. Very best wishes Frank Frank H. King Cambridge, U.K. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
