NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Henry Halboth
Date: 2015 Jan 18, 23:26 -0500
I don't get what the last few posts are trying to accomplish. The equation for LHA by John in post g30016 gives the longitude (via the LHA) on the LOP for the given latitude. With no iterations that lat & lon is an exact position on the LOP. That's all that possible to know from a single Ho observation. And of course you can compute as many of those exact points as you wish -- even to the point of ploting the whole circular LOP by lats and lons. No AP is needed.
The point of the St. Hilaire method is that it gives the unique point on the LOP that is nearest to an Assigned Point, the AP. Historically. this point has been called the assumed postion, but that is a bad, and misleading, name for it. We assume nothing when we assign a point for the AP. This is discussed more in my book where the designation AP is used solely to correspond with previous writings.
J Karl