Thanks to studies thus systematically pursued, we have succeeded in the course of a hundred years in increasing the precision of measures in the proportion of a thousand to one, and we may ask ourselves whether such an increase will continue in the future.  No doubt progress will not be stayed; but if we keep to the definition of length by a material standard, it would seem that its precision cannot be considerably increased.  We have nearly reached the limit imposed by the necessity of making strokes of such a thickness as to be observable under the microscope.

It may happen, however, that we shall be brought one of these days to a new conception of the measure of length, and that very different processes of determination will be thought of.  If we took as unit, for instance, the distance covered by a given radiation during a vibration, the optical processes would at once admit of much greater precision.

Thus Fizeau, the first to have this idea, says:  “A ray of light, with its series of undulations of extreme tenuity but perfect regularity, may be considered as a micrometer of the greatest perfection, and particularly suitable for determining length.”  But in the present state of things, since the legal and customary definition of the unit remains a material standard, it is not enough to measure length in terms of wave-lengths, and we must also know the value of these wave-lengths in terms of the standard prototype of the metre.

This was determined in 1894 by M. Michelson and M. Benoit in an experiment which will remain classic.  The two physicists measured a standard length of about ten centimetres, first in terms of the wave-lengths of the red, green, and blue radiations of cadmium, and then in terms of the standard metre.  The great difficulty of the experiment proceeds from the vast difference which exists between the lengths to be compared, the wave-lengths barely amounting to half a micron;[3] the process employed consisted in noting, instead of this length, a length easily made about a thousand times greater, namely, the distance between the fringes of interference.

[Footnote 3:  I.e. 1/2000 of a millimetre.—­ED.]

In all measurement, that is to say in every determination of the relation of a magnitude to the unit, there has to be determined on the one hand the whole, and on the other the fractional part of this ratio, and naturally the most delicate determination is generally that of this fractional part.  In optical processes the difficulty is reversed.  The fractional part is easily known, while it is the high figure of the number representing the whole which becomes a very serious obstacle.  It is this obstacle which MM.  Michelson and Benoit overcame with admirable ingenuity.  By making use of a somewhat similar idea, M. Mace de Lepinay and MM.  Perot and Fabry, have lately effected by optical methods, measurements of the greatest precision, and no doubt further progress may still be made.  A day may perhaps come when a material standard will be given up, and it may perhaps even be recognised that such a standard in time changes its length by molecular strain, and by wear and tear:  and it will be further noted that, in accordance with certain theories which will be noticed later on, it is not invariable when its orientation is changed.