John,Hi Dave: I know you wrote the list asking for answers, not questions. But I don't understand the whole basis of the Britannica instructions.They say: A horizontal dial designed for Chicago's latitude radiates as a42 deg ellipse. For this example we use a 42 deg ellipse to determine the hour lines' radiation on a horizontal dial at 42 deg latitude.I've never heard of using an ellipse to construct a horizontal dial. Neither Mayall or Waugh use this "ellipse method". And I've never heard of an ellipse being described in terms of "degrees". What in the world is a 42 deg ellipse?
I think I can help you on this. They use a very elegant method to draw a sundial based on geometrical
affinity that traces back to our High School days:
1. Draw two concentrical circles : one of radius r and the other one of radius r*sin(Lat)
2. Now draw a sheaf of 24 equispaced lines from its center as if it were an equatorial dial.
3. These lines intersect the circles at points I' and I'', II' and II'', and so on up to XXIV' and XXIV''.
4. Now trace horizontal lines from the inner points and vertical lines from the outer points. Let's call
I the point where the lines from I' and I'' intersect, II the point for II' and II'', and so on.
5. If we connect these points we just have the analemmatic ellipse, right? Well, but if we trace lines
from the center to these points we get a horizontal dial for that latitude. Isn't that nice?
Maybe somebody more skilled for drawing than me could make a sketch of this smart construction.
Best regards,
Anselmo
