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.
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. Macé de Lépinay 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.
For the moment, however, the need of any change in the definition of the unit is in no way felt; we must, on the contrary, hope that the use of the unit adopted by the physicists of the whole world will spread more and more. It is right to remark that a few errors still occur with regard to this unit, and that these errors have been facilitated by incoherent legislation. France herself, though she was the admirable initiator of the metrical system, has for too long allowed a very regrettable confusion to exist; and it cannot be noted without a certain sadness that it was not until the 11th July 1903 that a law was promulgated re-establishing the agreement between the legal and the scientific definition of the metre.
Perhaps it may not be useless to briefly indicate here the reasons of the disagreement which had taken place. Two definitions of the metre can be, and in fact were given. One had for its basis the dimensions of the earth, the other the length of the material standard. In the minds of the founders of the metrical system, the first of these was the true definition of the unit of length, the second merely a simple representation. It was admitted, however, that this representation had been constructed in a manner perfect enough for it to be nearly impossible to perceive any difference between the unit and its representation, and for the practical identity of the two definitions to be thus assured. The creators of the metrical system were persuaded that the measurements of the meridian effected in their day could never be surpassed in precision; and on the other hand, by borrowing from nature a definite basis, they thought to take from the definition of the unit some of its arbitrary character, and to ensure the means of again finding the same unit if by any accident the standard became altered. Their confidence in the value of the processes they had seen employed was exaggerated, and their mistrust of the future unjustified. This example shows how imprudent it is to endeavour to fix limits to progress. It is an error to think the march of science can be stayed; and in reality it is now known that the ten-millionth part of the quarter of the terrestrial meridian is longer than the metre by 0.187 millimetres. But contemporary physicists do not fall into the same error as their forerunners, and they regard the present result as merely provisional. They guess, in fact, that new improvements will be effected in the art of measurement; they know that geodesical processes, though much improved in our days, have still much to do to attain the precision displayed in the construction and determination of standards of the first order; and consequently they do not propose to keep the ancient definition, which would lead to having for unit a magnitude possessing the grave defect from a practical point of view of being constantly variable.
We may even consider that, looked at theoretically, its permanence would not be assured. Nothing, in fact, proves that sensible variations may not in time be produced in the value of an arc of the meridian, and serious difficulties may arise regarding the probable inequality of the various meridians.
For all these reasons, the idea of finding a natural unit has been gradually abandoned, and we have become resigned to accepting as a fundamental unit an arbitrary and conventional length having a material representation recognised by universal consent; and it was this unit which was consecrated by the following law of the 11th July 1903:—
"The standard prototype of the metrical system is the international metre, which has been sanctioned by the General Conference on Weights and Measures."
§ 3. THE MEASURE OF MASS
On the subject of measures of mass, similar remarks to those on measures of length might be made. The confusion here was perhaps still greater, because, to the uncertainty relating to the fixing of the unit, was added some indecision on the very nature of the magnitude defined. In law, as in ordinary practice, the notions of weight and of mass were not, in fact, separated with sufficient clearness.