Part 2 (1/2)
The same objections have been made to the definition of the kilogramme, at first considered as the ma.s.s 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. 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 ma.s.s, the legal prototype of the metrical system, is now the international kilogramme sanctioned by the Conference of Weights and Measures.
The comparison of a ma.s.s 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 surpa.s.sed; and progress would seem likely to be slow, for difficulties singularly increase when we get to such small quant.i.ties. 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 ma.s.s 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 s.e.xagesimal 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 circ.u.mstances, 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.
Perhaps in the future recourse may be had to very different phenomena.
Thus Curie pointed out that if the air inside a gla.s.s tube has been rendered radioactive by a solution of radium, the tube may be sealed up, and it will then be noted that the radiation of its walls diminishes with time, in accordance with an exponential law. The constant of time derived by this phenomenon remains the same whatever the nature and dimensions of the walls of the tube or the temperature may be, and time might thus be denned independently of all the other units.
We might also, as M. Lippmann has suggested in an extremely ingenious way, decide to obtain measures of time which can be considered as absolute because they are determined by parameters of another nature than that of the magnitude to be measured. Such experiments are made possible by the phenomena of gravitation. We could employ, for instance, the pendulum by adopting, as the unit of force, the force which renders the constant of gravitation equal to unity. The unit of time thus defined would be independent of the unit of length, and would depend only on the substance which would give us the unit of ma.s.s under the unit of volume.
It would be equally possible to utilize electrical phenomena, and one might devise experiments perfectly easy of execution. Thus, by charging a condenser by means of a battery, and discharging it a given number of times in a given interval of time, so that the effect of the current of discharge should be the same as the effect of the output of the battery through a given resistance, we could estimate, by the measurement of the electrical magnitudes, the duration of the interval noted. A system of this kind must not be looked upon as a simple _jeu d'esprit_, since this very practicable experiment would easily permit us to check, with a precision which could be carried very far, the constancy of an interval of time.
From the practical point of view, chronometry has made in these last few years very sensible progress. The errors in the movements of chronometers are corrected in a much more systematic way than formerly, and certain inventions have enabled important improvements to be effected in the construction of these instruments. Thus the curious properties which steel combined with nickel--so admirably studied by M.Ch.Ed. Guillaume--exhibits in the matter of dilatation are now utilized so as to almost completely annihilate the influence of variations of temperature.
-- 5. THE MEASURE OF TEMPERATURE
From the three mechanical units we derive secondary units; as, for instance, the unit of work or mechanical energy. The kinetic theory takes temperature, as well as heat itself, to be a quant.i.ty of energy, and thus seems to connect this notion with the magnitudes of mechanics. But the legitimacy of this theory cannot be admitted, and the calorific movement should also be a phenomenon so strictly confined in s.p.a.ce that our most delicate means of investigation would not enable us to perceive it. It is better, then, to continue to regard the unit of difference of temperature as a distinct unit, to be added to the fundamental units.
To define the measure of a certain temperature, we take, in practice, some arbitrary property of a body. The only necessary condition of this property is, that it should constantly vary in the same direction when the temperature rises, and that it should possess, at any temperature, a well-marked value. We measure this value by melting ice and by the vapour of boiling water under normal pressure, and the successive hundredths of its variation, beginning with the melting ice, defines the percentage. Thermodynamics, however, has made it plain that we can set up a thermometric scale without relying upon any determined property of a real body. Such a scale has an absolute value independently of the properties of matter. Now it happens that if we make use for the estimation of temperatures, of the phenomena of dilatation under a constant pressure, or of the increase of pressure in a constant volume of a gaseous body, we obtain a scale very near the absolute, which almost coincides with it when the gas possesses certain qualities which make it nearly what is called a perfect gas.
This most lucky coincidence has decided the choice of the convention adopted by physicists. They define normal temperature by means of the variations of pressure in a ma.s.s of hydrogen beginning with the initial pressure of a metre of mercury at 0 C.
M.P. Chappuis, in some very precise experiments conducted with much method, has proved that at ordinary temperatures the indications of such a thermometer are so close to the degrees of the theoretical scale that it is almost impossible to ascertain the value of the divergences, or even the direction that they take. The divergence becomes, however, manifest when we work with extreme temperatures. It results from the useful researches of M. Daniel Berthelot that we must subtract +0.18 from the indications of the hydrogen thermometer towards the temperature -240 C, and add +0.05 to 1000 to equate them with the thermodynamic scale. Of course, the difference would also become still more noticeable on getting nearer to the absolute zero; for as hydrogen gets more and more cooled, it gradually exhibits in a lesser degree the characteristics of a perfect gas.
To study the lower regions which border on that kind of pole of cold towards which are straining the efforts of the many physicists who have of late years succeeded in getting a few degrees further forward, we may turn to a gas still more difficult to liquefy than hydrogen.
Thus, thermometers have been made of helium; and from the temperature of -260 C. downward the divergence of such a thermometer from one of hydrogen is very marked.
The measurement of very high temperatures is not open to the same theoretical objections as that of very low temperatures; but, from a practical point of view, it is as difficult to effect with an ordinary gas thermometer. It becomes impossible to guarantee the reservoir remaining sufficiently impermeable, and all security disappears, notwithstanding the use of recipients very superior to those of former times, such as those lately devised by the physicists of the _Reichansalt_. This difficulty is obviated by using other methods, such as the employment of thermo-electric couples, such as the very convenient couple of M. le Chatelier; but the graduation of these instruments can only be effected at the cost of a rather bold extrapolation.
M.D. Berthelot has pointed out and experimented with a very interesting process, founded on the measurement by the phenomena of interference of the refractive index of a column of air subjected to the temperature it is desired to measure. It appears admissible that even at the highest temperatures the variation of the power of refraction is strictly proportional to that of the density, for this proportion is exactly verified so long as it is possible to check it precisely. We can thus, by a method which offers the great advantage of being independent of the power and dimension of the envelopes employed--since the length of the column of air considered alone enters into the calculation--obtain results equivalent to those given by the ordinary air thermometer.
Another method, very old in principle, has also lately acquired great importance. For a long time we sought to estimate the temperature of a body by studying its radiation, but we did not know any positive relation between this radiation and the temperature, and we had no good experimental method of estimation, but had recourse to purely empirical formulas and the use of apparatus of little precision. Now, however, many physicists, continuing the cla.s.sic researches of Kirchhoff, Boltzmann, Professors Wien and Planck, and taking their starting-point from the laws of thermodynamics, have given formulas which establish the radiating power of a dark body as a function of the temperature and the wave-length, or, better still, of the total power as a function of the temperature and wave-length corresponding to the maximum value of the power of radiation. We see, therefore, the possibility of appealing for the measurement of temperature to a phenomenon which is no longer the variation of the elastic force of a gas, and yet is also connected with the principles of thermodynamics.
This is what Professors Lummer and Pringsheim have shown in a series of studies which may certainly be reckoned among the greatest experimental researches of the last few years. They have constructed a radiator closely resembling the theoretically integral radiator which a closed isothermal vessel would be, and with only a very small opening, which allows us to collect from outside the radiations which are in equilibrium with the interior. This vessel is formed of a hollow carbon cylinder, heated by a current of high intensity; the radiations are studied by means of a bolometer, the disposition of which varies with the nature of the experiments.
It is hardly possible to enter into the details of the method, but the result sufficiently indicates its importance. It is now possible, thanks to their researches, to estimate a temperature of 2000 C. to within about 5. Ten years ago a similar approximation could hardly have been arrived at for a temperature of 1000 C.
-- 6. DERIVED UNITS AND THE MEASURE OF A QUANt.i.tY OF ENERGY
It must be understood that it is only by arbitrary convention that a dependency is established between a derived unit and the fundamental units. The laws of numbers in physics are often only laws of proportion. We transform them into laws of equation, because we introduce numerical coefficients and choose the units on which they depend so as to simplify as much as possible the formulas most in use.