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.