The same objections have been made to the definition of the kilogramme, at first considered as the mass of a cubic decimetre of water at 4 deg.  C., as to the first definition of the metre.  We must admire the incredible precision attained at the outset by the physicists who made the initial determinations, but we know at the present day that the kilogramme they constructed is slightly too heavy (by about 1/25,000).  Very remarkable researches have been carried out with regard to this determination by the International Bureau, and by MM.  Mace de Lepinay and Buisson.  The law of the 11th July 1903 has definitely regularized the custom which physicists had adopted some years before; and the standard of mass, the legal prototype of the metrical system, is now the international kilogramme sanctioned by the Conference of Weights and Measures.

The comparison of a mass with the standard is effected with a precision to which no other measurement can attain.  Metrology vouches for the hundredth of a milligramme in a kilogramme; that is to say, that it estimates the hundred-millionth part of the magnitude studied.

We may—­as in the case of the lengths—­ask ourselves whether this already admirable precision can be surpassed; and progress would seem likely to be slow, for difficulties singularly increase when we get to such small quantities.  But it is permitted to hope that the physicists of the future will do still better than those of to-day; and perhaps we may catch a glimpse of the time when we shall begin to observe that the standard, which is constructed from a heavy metal, namely, iridium-platinum, itself obeys an apparently general law, and little by little loses some particles of its mass by emanation.

Sec. 4.  THE MEASURE OF TIME

The third fundamental magnitude of mechanics is time.  There is, so to speak, no physical phenomenon in which the notion of time linked to the sequence of our states of consciousness does not play a considerable part.

Ancestral habits and a very early tradition have led us to preserve, as the unit of time, a unit connected with the earth’s movement; and the unit to-day adopted is, as we know, the sexagesimal second of mean time.  This magnitude, thus defined by the conditions of a natural motion which may itself be modified, does not seem to offer all the guarantees desirable from the point of view of invariability.  It is certain that all the friction exercised on the earth—­by the tides, for instance—­must slowly lengthen the duration of the day, and must influence the movement of the earth round the sun.  Such influence is certainly very slight, but it nevertheless gives an unfortunately arbitrary character to the unit adopted.