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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: My plotting board
From: Frank Reed
Date: 2015 May 9, 13:43 -0700

Bill Morris, you wrote:
"So, Frank, what should we call this (see attachment)? Did the Hydrographer get it wrong when calling it a "Mercatorial plotting sheet"? The scale of latitude in any part seems to be proportional to the sec LAT of that part."

Of course, there are, in fact, legitimately labeled Mercator projection plots out there. The majority of common plotting sheets which are labeled "Mercator" are not actually Mercator projections, but that doesn't imply that all things labeled "Mercator" (or in the case you posted "Mercatorial") are not Mercator projections. You say that the spacing of the latitude lines on that chart appear to be proportional to 1/cos(Lat). The latitude range shown in the title is from latitude 36° to 39°. Using the middle latitude of each pair (e.g. 36.5° for the spacing between 36° and 37°), I get 1/cos(Lat) values of 1.24, 1.26, and 1.28. That is, the spacing should grow by about 2% per degree of latitude --a very small, but measurable difference. Does that match what you see on that plotting chart? And if it does show that slightly-increasing spacing, would it matter much in practice if we replaced the chart with one whose spacing was 1.26 for all three degrees? That is, even if this is a Mercator projection, does it matter?

Most small plotting sheets are labeled Mercator plotting sheets when they are simply longitude-scaled (or latitude-scaled if you flip it around). They cover a band of latitude of one degree, more or less, and there's no reason to call this a Mercator projection. They are locally conformal, which is a common property of numerous projections. For a more user-friendly name, why not just call them "bird's-eye view" projections? This habit of calling simple plotting sheets "Mercator plots" seems to have originated during or after the Second World War, around the same time as the example that you posted here. Celestial navigation is in no way dependent on Mercator plots or the Mercator projection despite the labels on the sheets.

I would suggest that what we are seeing here is nothing more than the decades-long, even centuries-long, infatuation with and misunderstanding of the traditional Mercator projection. Navigators and non-navigators, too, have been taught culturally, outside the classroom and the textbooks, that the Mercator projection is the "navigators' map". It's a kind of magic name. And I suggest that this lore has led publishers to label any old plotting sheet as a "Mercator chart".

Frank Reed

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