Part 2 (2/2)
A particular speed, for instance, is in reality nothing else but a speed, and it is only by the peculiar choice of unit that we can say that it is the s.p.a.ce covered during the unit of time. In the same way, a quant.i.ty of electricity is a quant.i.ty of electricity; and there is nothing to prove that, in its essence, it is really reducible to a function of ma.s.s, of length, and of time.
Persons are still to be met with who seem to have some illusions on this point, and who see in the doctrine of the dimensions of the units a doctrine of general physics, while it is, to say truth, only a doctrine of metrology. The knowledge of dimensions is valuable, since it allows us, for instance, to easily verify the h.o.m.ogeneity of a formula, but it can in no way give us any information on the actual nature of the quant.i.ty measured.
Magnitudes to which we attribute like dimensions may be qualitatively irreducible one to the other. Thus the different forms of energy are measured by the same unit, and yet it seems that some of them, such as kinetic energy, really depend on time; while for others, such as potential energy, the dependency established by the system of measurement seems somewhat fict.i.tious.
The numerical value of a quant.i.ty of energy of any nature should, in the system C.G.S., be expressed in terms of the unit called the erg; but, as a matter of fact, when we wish to compare and measure different quant.i.ties of energy of varying forms, such as electrical, chemical, and other quant.i.ties, etc., we nearly always employ a method by which all these energies are finally transformed and used to heat the water of a calorimeter. It is therefore very important to study well the calorific phenomenon chosen as the unit of heat, and to determine with precision its mechanical equivalent, that is to say, the number of ergs necessary to produce this unit. This is a number which, on the principle of equivalence, depends neither on the method employed, nor the time, nor any other external circ.u.mstance.
As the result of the brilliant researches of Rowland and of Mr Griffiths on the variations of the specific heat of water, physicists have decided to take as calorific standard the quant.i.ty of heat necessary to raise a gramme of water from 15 to 16 C., the temperature being measured by the scale of the hydrogen thermometer of the International Bureau.
On the other hand, new determinations of the mechanical equivalent, among which it is right to mention that of Mr. Ames, and a full discussion as to the best results, have led to the adoption of the number 4.187 to represent the number of ergs capable of producing the unit of heat.
In practice, the measurement of a quant.i.ty of heat is very often effected by means of the ice calorimeter, the use of which is particularly simple and convenient. There is, therefore, a very special interest in knowing exactly the melting-point of ice. M.
Leduc, who for several years has measured a great number of physical constants with minute precautions and a remarkable sense of precision, concludes, after a close discussion of the various results obtained, that this heat is equal to 79.1 calories. An error of almost a calorie had been committed by several renowned experimenters, and it will be seen that in certain points the art of measurement may still be largely perfected.
To the unit of energy might be immediately attached other units. For instance, radiation being nothing but a flux of energy, we could, in order to establish photometric units, divide the normal spectrum into bands of a given width, and measure the power of each for the unit of radiating surface.
But, notwithstanding some recent researches on this question, we cannot yet consider the distribution of energy in the spectrum as perfectly known. If we adopt the excellent habit which exists in some researches of expressing radiating energy in ergs, it is still customary to bring the radiations to a standard giving, by its const.i.tution alone, the unit of one particular radiation. In particular, the definitions are still adhered to which were adopted as the result of the researches of M. Violle on the radiation of fused platinum at the temperature of solidification; and most physicists utilize in the ordinary methods of photometry the clearly defined notions of M. Blondel as to the luminous intensity of flux, illumination (_eclairement_), light (_eclat_), and lighting (_eclairage_), with the corresponding units, decimal candle, _lumen_, _lux_, carcel lamp, candle per square centimetre, and _lumen_-hour.[4]
[Footnote 4: These are the magnitudes and units adopted at the International Congress of Electricians in 1904. For their definition and explanation, see Demanet, _Notes de Physique Experimentale_ (Louvain, 1905), t. iv. p. 8.--ED.]
-- 7. MEASURE OF CERTAIN PHYSICAL CONSTANTS
The progress of metrology has led, as a consequence, to corresponding progress in nearly all physical measurements, and particularly in the measure of natural constants. Among these, the constant of gravitation occupies a position quite apart from the importance and simplicity of the physical law which defines it, as well as by its generality. Two material particles are mutually attracted to each other by a force directly proportional to the product of their ma.s.s, and inversely proportional to the square of the distance between them. The coefficient of proportion is determined when once the units are chosen, and as soon as we know the numerical values of this force, of the two ma.s.ses, and of their distance. But when we wish to make laboratory experiments serious difficulties appear, owing to the weakness of the attraction between ma.s.ses of ordinary dimensions.
Microscopic forces, so to speak, have to be observed, and therefore all the causes of errors have to be avoided which would be unimportant in most other physical researches. It is known that Cavendish was the first who succeeded by means of the torsion balance in effecting fairly precise measurements. This method has been again taken in hand by different experimenters, and the most recent results are due to Mr Vernon Boys. This learned physicist is also the author of a most useful practical invention, and has succeeded in making quartz threads as fine as can be desired and extremely uniform. He finds that these threads possess valuable properties, such as perfect elasticity and great tenacity. He has been able, with threads not more than 1/500 of a millimetre in diameter, to measure with precision couples of an order formerly considered outside the range of experiment, and to reduce the dimensions of the apparatus of Cavendish in the proportion of 150 to 1. The great advantage found in the use of these small instruments is the better avoidance of the perturbations arising from draughts of air, and of the very serious influence of the slightest inequality in temperature.
Other methods have been employed in late years by other experimenters, such as the method of Baron Eotvos, founded on the use of a torsion lever, the method of the ordinary balance, used especially by Professors Richarz and Krigar-Menzel and also by Professor Poynting, and the method of M. Wilsing, who uses a balance with a vertical beam.
The results fairly agree, and lead to attributing to the earth a density equal to 5.527.
The most familiar manifestation of gravitation is gravity. The action of the earth on the unit of ma.s.s placed in one point, and the intensity of gravity, is measured, as we know, by the aid of a pendulum. The methods of measurement, whether by absolute or by relative determinations, so greatly improved by Borda and Bessel, have been still further improved by various geodesians, among whom should be mentioned M. von Sterneek and General Defforges. Numerous observations have been made in all parts of the world by various explorers, and have led to a fairly complete knowledge of the distribution of gravity over the surface of the globe. Thus we have succeeded in making evident anomalies which would not easily find their place in the formula of Clairaut.
Another constant, the determination of which is of the greatest utility in astronomy of position, and the value of which enters into electromagnetic theory, has to-day a.s.sumed, with the new ideas on the const.i.tution of matter, a still more considerable importance. I refer to the speed of light, which appears to us, as we shall see further on, the maximum value of speed which can be given to a material body.
After the historical experiments of Fizeau and Foucault, taken up afresh, as we know, partly by Cornu, and partly by Michelson and Newcomb, it remained still possible to increase the precision of the measurements. Professor Michelson has undertaken some new researches by a method which is a combination of the principle of the toothed wheel of Fizeau with the revolving mirror of Foucault. The toothed wheel is here replaced, however, by a grating, in which the lines and the s.p.a.ces between them take the place of the teeth and the gaps, the reflected light only being returned when it strikes on the s.p.a.ce between two lines. The ill.u.s.trious American physicist estimates that he can thus evaluate to nearly five kilometres the path traversed by light in one second. This approximation corresponds to a relative value of a few hundred-thousandths, and it far exceeds those hitherto attained by the best experimenters. When all the experiments are completed, they will perhaps solve certain questions still in suspense; for instance, the question whether the speed of propagation depends on intensity. If this turns out to be the case, we should be brought to the important conclusion that the amplitude of the oscillations, which is certainly very small in relation to the already tiny wave-lengths, cannot be considered as unimportant in regard to these lengths. Such would seem to have been the result of the curious experiments of M. Muller and of M. Ebert, but these results have been recently disputed by M. Doubt.
In the case of sound vibrations, on the other hand, it should be noted that experiment, consistently with the theory, proves that the speed increases with the amplitude, or, if you will, with the intensity. M.
Violle has published an important series of experiments on the speed of propagation of very condensed waves, on the deformations of these waves, and on the relations of the speed and the pressure, which verify in a remarkable manner the results foreshadowed by the already old calculations of Riemann, repeated later by Hugoniot. If, on the contrary, the amplitude is sufficiently small, there exists a speed limit which is the same in a large pipe and in free air. By some beautiful experiments, MM. Violle and Vautier have clearly shown that any disturbance in the air melts somewhat quickly into a single wave of given form, which is propagated to a distance, while gradually becoming weaker and showing a constant speed which differs little in dry air at 0 C. from 331.36 metres per second. In a narrow pipe the influence of the walls makes itself felt and produces various effects, in particular a kind of dispersion in s.p.a.ce of the harmonics of the sound. This phenomenon, according to M. Brillouin, is perfectly explicable by a theory similar to the theory of gratings.
CHAPTER III
PRINCIPLES
-- 1. THE PRINCIPLES OF PHYSICS
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