nd us had become larger, that we ourselves had
become taller, and that the distance travelled by light in the
duration of a vibration had become greater, we should not hesitate to
think ourselves the victims of an illusion, that in reality all these
distances had remained fixed, and that all these appearances were due
to a shortening of the rule which we had used as the standard for
measuring the lengths.

From the mathematical point of view, it may be considered that the two
hypotheses are equivalent; all has lengthened around us, or else our
standard has become less. But it is no simple question of convenience
and simplicity which leads us to reject the one supposition and to
accept the other; it is right in this case to listen to the voice of
common sense, and those physicists who have an instinctive trust in
the notion of an absolute length are perhaps not wrong. It is only by
choosing our unit from those which at all times have seemed to all men
the most invariable, that we are able in our experiments to note that
the same causes acting under identical conditions always produce the
same effects. The idea of absolute length is derived from the
principle of causality; and our choice is forced upon us by the
necessity of obeying this principle, which we cannot reject without
declaring by that very act all science to be impossible.

Similar remarks might be made with regard to the notions of absolute
time and absolute movement. 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.