Peter Tandy writes: >I am trying to make a model of a Berossus type dial using a conical section >rather than a hemisphere. None of the references I have looked at (e.g >Cousins, "Sundials"; Rohr, "Sundials: Theory & Practice" etc) >specifically state the shape of the cone. My >intuition tells me that it should have an apical angle of 47 degrees (i.e. >2 x 23.5 degrees), and the drawings in the two references cited above >concur with this, but I cannot prove this to myself. Can anyone out there >CONFIRM that this is so ? I also take it that the axis of the cone , which >points to the Pole Star, must be at an angle with the horizontal equal to >the lattitude of the place it is for.
I dug through my copy of Sharon L. Gibbs' book, _Greek and Roman Sundials_ (1976) and found some information. I assume you are referring to the predominant form of conical dial, a South-facing conical dial with the vertex above the horizontal top surface (a virtual point out in space). The tip of a horizontal gnomon extending horizontally from the top surface lies on the central axis of the right circular cone, and it is the shadow point of this tip alone (not an edge) that indicates the time. Also, you are probably aware that this dial marks equal hours for a given day, but that these equal hours are different for different days of the year (seasonal hours), so it's not too "practical." You are correct that the axis of the cone is at an angle with the horizontal equal to the latitude. However, it seems that the angle at the vertex between the axis and the cone surface (which I'll call W and is half of what you describe) can be any value. Much of Gibbs' analysis of these dials concerns how to take such a dial and find the latitude and, independently, the angle W for the dial. With the gnomon usually missing, and the vertex located in space somewhere, you have to measure the lines for the solstice, the equinox and the individual hours and calculate these values. Looking at the data for actual conical dials in the book, I see calculated values of W of 36.5, 21, 45.5, 30.2, 43.5, 36, 30, 33.5, 26, 41.5, 27.3, etc. degrees for 109 ancient dials, mostly from Greece. The minimum seems to be 8 degrees. I didn't see any "rule of thumb" given for how to pick an angle. Perhaps others have thoughts on this. Given that there is such a wide range of angles for a single region (Greece), I can't imagine it depends directly on the latitude. Perhaps it is a limiting factor in that you have a certain size block of stone, and a given latitude will affect where the hour lines will have to lie on the conical surface of the block. Ron Doerfler
