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Colleagues, In consideration of several off-list discussions, I clarify the geometry of this map’s projection. As a conformal conic with 75° standard parallel, its fault is: • A constant 7-mm shift of parallels downward along the meridians. The parallel spacing matches within 1.5-mm for all of the 10° parallels. As a stereographic, its faults are: • A constant 3% compression of angles between meridians. • A constant 12-mm shift of parallels downward along the meridians. The parallel spacing matches within 1-mm for all of the 10° parallels. In other words, the map is much closer to a conformal conic than it is to a stereographic. But, I think it is more likely to be a poorly drafted stereographic, as Vladimiro Valerio also suggested, because this explanation avoids the very difficult questions I point out below. I can think of specific mistakes the mapmaker might have made in order to result in a (partial) stereographic with these faults. I had not discovered the shift along the meridians when I posted my first inquiry. This error in construction probably arose because the projection’s geometry was never drafted out all the way to the pole. In any case, that is the reason I did not notice the discrepancy in the first place. Hopefully this takes care of any lingering questions and we can consider the matter resolved. Regards, — daan Strebe > Vladimiro: > > Thanks again for your comments. In short, I think you are right. I had > discarded the stereographic from consideration because I do not expect > meridional compression to arise out of its usual construction technique. But > as I wrote to Waldo Tobler last night, the map as a conformal conic does not > add up in too many ways: > > • The mathematics were not available; > • The concept of conformality was not available; > • The motivation to produce a conformal conic at this scale, for this map and > no other, is obscure; > • The standard parallel is inapt for the territory; something like 45° or 50° > would be more reasonable. > > And, as I found last night: > • While the parallel spacing and the cone constant fit a conformal conic, the > parallels are shifted a constant 10-mm downward along the meridians. > > In the face of the contextual anomalies, the physical evidence for the > conformal conic must be unassailable. It is not, given this last discovery. > That led me to reexamine the stereographic. Even as a stereographic, the map > suffers from constant parallel shift along the meridians, though the extent > is harder to characterize because of the other major problem: the improbable > compression of meridional spacing. While the fit to a stereographic is > considerably poorer than to a conformal conic, the stereographic would not be > an anachronism. > > As Vladimiro suggests, the map was likely stereographic in intent. It is just > drafted particularly poorly, probably the result of taking some measurements > from an existing map rather than starting from the basic geometry. We see > plenty of examples of careless projection construction in maps of the period. > > Thanks, all, for the help. I am still interested to know when this map’s > archetype appeared, and in what publication. > > Regards, > — daan Strebe >
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