They have been put in evidence and set
forth very forcibly by a learned and profound mathematician, M.
Painleve.
On the particularly clear example of the measure of length, it is
interesting to follow the evolution of the methods employed, and to
run through the history of the progress in precision from the time
that we have possessed authentic documents relating to this question.
This history has been written in a masterly way by one of the
physicists who have in our days done the most by their personal
labours to add to it glorious pages. M. Benoit, the learned Director
of the International Bureau of Weights and Measures, has furnished in
various reports very complete details on the subject, from which I
here borrow the most interesting.
We know that in France the fundamental standard for measures of length
was for a long time the _Toise du Chatelet_, a kind of callipers
formed of a bar of iron which in 1668 was embedded in the outside wall
of the Chatelet, at the foot of the staircase. This bar had at its
extremities two projections with square faces, and all the _toises_ of
commerce had to fit exactly between them.
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