A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2020 May 5, 06:41 -0700
A couple of observations:
1) Since the usual altitude formula used to derive the tables is symmetric in latitude, L, and declination, δ, the altitude, h. can be calculated (in the form Lars Bergman wrote) as
tan U = cot L cos t; sin h = sin L sec U sin( δ + U )
tan U = cot δ cos t; sin h = sin δ sec U sin( L + U )
The Latitude column in Smart & Shearme tables could have just as well been labelled as Declination. Entering the tables using hour angle and declination seems more natural to me in that they are both properties of the object being sighted and not the observer. Off hand I can't think of a good reason why latitude was used. Can anyone else?
2) The expression for U and the formulas that Lars gave yesterday are just crying out for evaluation using a Bygrave.