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.

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.