A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2016 Jan 20, 04:09 -0800
The diagram in question is a form of nomogram designed to evaluate or solve the second equation in the pdf file. It does not rely on or assume any particular projection. In a standard nomogram a line is drawn between 2 scales and the value where it intersects a third scale is the required result. In this nomogram the result is obtained by connecting points on the 2 scales and measuring the direction of the resulting line. Eq.(1.1) is simply the statement of that requirement.
"The fifth equation has x=0, so it must be the straight line up the centre."
Yes with values that increase like tan(L2) - exactly as seen on the chart.
"does that mean you’ve tried putting equations four and five into a function drawing programme to see what comes out?
That is indeed what it means,