History of curvilinear coordinates
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A brief document dated 11.17.10 and initialed PhL, so it appears to be Phil's own note. It comments on Lamé, Heine, Mathieu and Weber, who worked on elliptic coordinate problems, and links to Morris Kline's Mathematical Thought from Ancient to Modern Times, Volume 2. It also includes excerpts on curvilinear coordinates, apparently as images, and a section headed From Byerly.
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History of curvilinear coordinates PhL 11.17.10
This book has some comments on Lamé and Heine and Mathieu and Weber all of whom did elliptic things. They were amazed at what you could do with "curvilinear coordinates".
http://books.google.com/books?id=aO-v3gvY-I8C&printsec=frontcover#v=onepage&q&f=false
Mathematical thought from ancient to modern times, Volume 2
By Morris Kline // some excerpts on history of curvilinears.
From Byerly: