Sec. 2. THE MEASURE OF LENGTH
To measure a length is to compare it with another length taken as
unity. Measurement is therefore a relative operation, and can only
enable us to know ratios. Did both the length to be measured and the
unit chosen happen to vary simultaneously and in the same degree, we
should perceive no change. Moreover, the unit being, by definition,
the term of comparison, and not being itself comparable with anything,
we have theoretically no means of ascertaining whether its length
varies.
If, however, we were to note that, suddenly and in the same
proportions, the distance between two points on this earth had
increased, that all the planets had moved further from each other,
that all objects around 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.
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