The New Physics and Its Evolution | Page 9

obtain actual measurements. But it is now becoming
more and more understood that to establish the relations which exist
between physical magnitudes, and to represent the variations of these
magnitudes by functions which allow us to use the power of
mathematical analysis, it is most necessary to express each magnitude
by a definite number.
Under these conditions alone can a magnitude be considered as
effectively known. "I often say," Lord Kelvin has said, "that if you can
measure that of which you are speaking and express it by a number you
know something of your subject; but if you cannot measure it nor
express it by a number, your knowledge is of a sorry kind and hardly
satisfactory. It may be the beginning of the acquaintance, but you are
hardly, in your thoughts, advanced towards science, whatever the
subject may be."
It has now become possible to measure exactly the elements which
enter into nearly all physical phenomena, and these measurements are
taken with ever increasing precision. Every time a chapter in science
progresses, science shows itself more exacting; it perfects its means of
investigation, it demands more and more exactitude, and one of the
most striking features of modern physics is this constant care for

strictness and clearness in experimentation.
A veritable science of measurement has thus been constituted which
extends over all parts of the domain of physics. This science has its
rules and its methods; it points out the best processes of calculation,
and teaches the method of correctly estimating errors and taking
account of them. It has perfected the processes of experiment,
co-ordinated a large number of results, and made possible the
unification of standards. It is thanks to it that the system of
measurements unanimously adopted by physicists has been formed.
At the present day we designate more peculiarly by the name of
metrology that part of the science of measurements which devotes itself
specially to the determining of the prototypes representing the
fundamental units of dimension and mass, and of the standards of the
first order which are derived from them. If all measurable quantities, as
was long thought possible, could be reduced to the magnitudes of
mechanics, metrology would thus be occupied with the essential
elements entering into all phenomena, and might legitimately claim the
highest rank in science. But even when we suppose that some
magnitudes can never be connected with mass, length, and time, it still
holds a preponderating place, and its progress finds an echo throughout
the whole domain of the natural sciences. It is therefore well, in order
to give an account of the general progress of physics, to examine at the
outset the improvements which have been effected in these
fundamental measurements, and to see what precision these
improvements have allowed us to attain.
§ 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.
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