Fer J. de Vries wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >This answer to the question if a gnomon could be made for an equatorial >sundial which adjust for the equation of time isn't fully correct, >because such a gnomon can be made. > >One solution is a solid body shaped as the half of the EoT curve mounted >to the gnomon, one for each half year. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Well, approximately working solid body gnomons of this type can be made, sufficiently accurate for most of us (and they probably are not quite shaped as halves of the analemmic figure). But mathematically exact solid body gnomons do not exist. It is not very difficult to get parametric equations for the corresponding surfaces of revolution. Surprisingly, there are two singularities in these equations, at the times of the solstices. As a result, the two surfaces flare to infinity near the singularities and do not enclose solid bodies. The singularities get even more severe if, in addition to the EoT-correction, a correction for the local time zone and/or DST is included. And again much more severe if the dial is made horizontal. For the math and pictures, see my report (in ps/pdf) in ftp://ftp.cc.tut.fi/pub/math/ruohonen/Raportit/PRep9/ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >The other is a plate in which the EoT curve is cut out. >For this solution see Compendium, bulletin of NASS, vol. 5, >no. 4 dec. 199. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This approach works, the plate, facing sun, gives mathematically exact EoT-correction. The mathematical representation of this curve, as a curve of intersection of a conical-like surface and a plane, is again fairly easily obtained. Around the times of the solstices, reading this kind of dial might get difficult. Another answer to the original posting contained a web address for some nice pictures of a showy dial of this sort: http://netnow.micron.net/~petes/sundial/ Keijo Ruohonen %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%NULLIUS%IN%VERBA% Keijo Ruohonen Tampere University of Technology [EMAIL PROTECTED] Department of Mathematics Voice (+358) (3) 3652420 http://matwww.ee.tut.fi/ Tampere, FINLAND Fax (+358) (3) 3653549 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
