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Nicol�s de Hilster wrote:

> There are two ways to construct those diagonals:
> 1) Using a tilted cutting plate (I think that is how they were constructed)
> 2) Using a very long beam compass

Interesting.  I only knew of the method of Philippe de La Hire described 
in Maurice Daumas' "Scientific Instruments of the 17th and 18th 
Centuries and their Makers".  (It's a good book on general instruments, 
including navigation - I found an English translation of the original 
French book in a second-hand bookstore for $45 years ago - a bargain 
considering the content and how often I refer to it.)

La Hire uses a system based on circular arcs.

> the diagonals are no arcs but clothoids. 

That's interesting to know.

> John Bird and had as 
> disadvantage that they grew and shrunk with temperature and humidity 
> (these problems have been described by him in a book, I believe it was 
> 'The Method of Dividing Astronomical Instruments', dated 1767).

Daumas mentions that beam compass techniques (I don't remember if they 
include Bird's) included only marking the instruments at certain times 
of the year (spring and autumn so the weather is moderate) and leaving 
the instruments with the workpieces overnight so they are the same 
temperature and humidity as the work the next morning.


Mike


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