The New Physics and Its Evolution

by Lucien Poincaré

They represent, however, two essentially different things. Mass is the characteristic of a quantity of matter; it depends neither on the geographical position one occupies nor on the altitude to which one may rise; it remains invariable so long as nothing material is added or taken away. Weight is the action which gravity has upon the body under consideration; this action does not depend solely on the body, but on the earth as well; and when it is changed from one spot to another, the weight changes, because gravity varies with latitude and altitude.

These elementary notions, to-day understood even by young beginners, appear to have been for a long time indistinctly grasped. The distinction remained confused in many minds, because, for the most part, masses were comparatively estimated by the intermediary of weights. The estimations of weight made with the balance utilize the action of the weight on the beam, but in such conditions that the influence of the variations of gravity becomes eliminated. The two weights which are being compared may both of them change if the weighing is effected in different places, but they are attracted in the same proportion. If once equal, they remain equal even when in reality they may both have varied.

The current law defines the kilogramme as the standard of mass, and the law is certainly in conformity with the rather obscurely expressed intentions of the founders of the metrical system. Their terminology was vague, but they certainly had in view the supply of a standard for commercial transactions, and it is quite evident that in barter what is important to the buyer as well as to the seller is not the attraction the earth may exercise on the goods, but the quantity that may be supplied for a given price. Besides, the fact that the founders abstained from indicating any specified spot in the definition of the kilogramme, when they were perfectly acquainted with the considerable variations in the intensity of gravity, leaves no doubt as to their real desire.

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° 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. Macé de Lépinay 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.

§ 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.

We might have taken as the standard of time the duration of another natural phenomenon, which appears to be always reproduced under identical conditions; the duration, for instance, of a given luminous vibration. But the experimental difficulties of evaluation with such a unit of the times which ordinarily have to be considered, would be so great that such a reform in practice cannot be hoped for. It should, moreover, be remarked that the duration of a vibration may itself be influenced by external circumstances, among which are the variations of the magnetic field in which its source is placed. It could not, therefore, be strictly considered as independent of the earth; and the theoretical advantage which might be expected from this alteration would be somewhat illusory.