The distance from D to the "zodiacal circle" is arbitrary, because all you really are doing is fixing the angles of the line segments radiating out from D. You want the outer lines to be +/-23.5 degrees from the horizontal from D. The interior lines have angles derived for each zodiacal sign by the Manaeus constructed with a circle tangent to these outer lines as shown in the previous chapter of Drinkwater.
Now you measure from A and B to the hour line intersections at the radiating lines from D, not from the horizontal parallel lines within the circle as implied by the text. To demonstrate this, look at pages 140-143 of the Dover edition of Albert Waugh's _Sundials: Their Theory and Construction_. This is an equivalent method of constructing the OUTER two lines of solar declination (+/- 23.5 degrees). He would have had to make a Manaeus to get the intermediate lines. Here we could replace A<-->O, D<-->T, and E<-->S between Drinkwater and Waugh (although E is not shown in Drinkwater's second figure). Also, Waugh uses measures from O, not S, (A, not E) but they should produce the same result when marked off from that point (Hmmm, I'm not sure that's true--should the distances along the horizontal line from D been measured from A for the vertical dial??). Anyway, as you can see, it is the intersections with the radiating lines at the 23.5 degree angles that give you the outer lines of declination. Ron Doerfler
