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Histers,
A question for all you projection fans....????
I am currently finishing up a very long article for the 20th Century volume of the "History of Cartography" called "Mathematics and Cartography". The article highlights the entrance into cartography of results and theorems from pure mathematics like existence theorems, modular form, fractals, differential topology etc, etc....
I am having trouble verifying the appearance in cartographic literature of Abelian Integrals. C.S. Pierce published an account of a conformal projection of a sphere in a square in 1889 and this followed the work of E. Guyou who solved a related projection in 1887. Both of these are based on the use of Elliptic Integrals. In 1925 Oscar Adams of the Coast and Geodetic Survey published a small booklet called 'Elliptic Functions Applied to Conformal Maps' where he extends this theory of elliptic integrals using Abelian functions developed in series solutions. This is an important historical development because it represents some of the most interesting applications of the theory of functions of a complex variable in cartography. Is this the first and nearly last use of Abelian functions for cartographic purposes...????
Thanks..
John W. Hessler
Fellow of the Royal Geographical Society Senior Cartographic Librarian
Geography and Map Division Library of Congress Washington DC 202-707-7223 What any picture, of whatever form, must have in common
with reality in order to depict it--correctly or incorrectly-- in any way at all, is logical form, i.e. the form of reality. --Wittgenstein Tractatus Logico-Philosophicus |
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