A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2016 Dec 31, 07:09 -0800
Stan you wrote: "It seems to me that the only "perfect" Mercator chart is really a projection of the lines of latitude and longitude on a cylinder tangent to the equator (for the "normal" Mercator) from an Earth that is an oblate spheroid, not a sphere, where even the smallest unit of latitude increases continuously as you move further from the equator. Any other "Mercator" chart is derived mathematically."
My reaction to that was that the presence of the logarithm in the formula for Meridional Parts means that even the "normal" Mercator chart cannot be obtained by any purely geometric projection even on a sphere. If I'm wrong I'd be very interested in learning how it can be done.
Bowditch 2002 states
"305. Mercator Projection
Navigators most often use the plane conformal projection known as the Mercator projection. The Mercator projection is not perspective, and its parallels can be derived mathematically as well as projected geometrically. "
and shows a picture (Fig 304) of what looks like a Mercator chart wrapped around a globe. This picture serves only to define the classification of Mercator as a cylindrical projection but may give the misleading impression that direct geometric projection is possible.
By "as well as projected geometrically. " Bowditch is presumably referring to the graphical method described in the http://fer3.com/arc/imgx/AFM-51-40-Mercator-chart_0001.jpg that Gary provided.
All this begs the the question as to how did Gerardus Mercator (1512-1594) construct his chart prior to the advent of calculus. Presumably he must have used the "graphical method",