There's an excellend discussion and description of a measuring instrument made by the Moore Special Tool co. which is accurate to 0.1 second of arc. See the book: "Foundations of Mechanical Accuracy" by Wayne C. Moore published by the company in Bridgeport CT. in 1970. See:
The index and dividing tables are still made
 
Moore made  wonderful measuring machines built by hand scraping could measure anything in an approximate volume of 1' by l'-6"byl'-6" to  an accuracy of 25 millionths of an inch. The book described in beautiful detail how the measuring machines were made.
 
These days this type of measurement is done by laser and the measuring machines are much simpler. See for example:
 
Fred Jaggi

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