The principles of science

by William Stanley Jevons

Before we can measure the phenomena of nature, we require a third independent unit, which shall enable us to define the quantity of matter occupying any given space. All the changes of nature, as we shall see, are probably so many manifestations of energy; but energy requires some substratum or material machinery of molecules, in and by which it may be manifested. Observation shows that, as regards force, there may be two modes of variation of matter. As Newton says in the first definition of the Principia, “the quantity of matter is the measure of the same, arising from its density and bulk conjunctly.” Thus the force required to set a body in motion varies both according to the bulk of the matter, and also according to its quality. Two cubic inches of iron of uniform quality, will require twice as much force as one cubic inch to produce a certain velocity in a given time; but one cubic inch of gold will require more force than one cubic inch of iron. There is then some new measurable quality in matter apart from its bulk, which we may call density, and which is, strictly speaking, indicated by its capacity to resist and absorb the action of force. For the unit of density we may assume that of any substance which is uniform in quality, and can readily be referred to from time to time. Pure water at any definite temperature, for instance that of snow melting under inappreciable pressure, furnishes an invariable standard of density, and by comparing equal bulks of various substances with a like bulk of ice-cold water, as regards the velocity produced in a unit of time by the same force, we should ascertain the densities of those substances as expressed in that of water. Practically the force of gravity is used to measure density; for a beautiful experiment with the pendulum, performed by Newton and repeated by Gauss, shows that all kinds of matter gravitate equally. Two portions of matter then which are in equilibrium in the balance, may be assumed to possess equal inertia, and their densities will therefore be inversely as their cubic dimensions.

Unit of Mass.

Multiplying the number of units of density of a portion of matter, by the number of units of space occupied by it, we arrive at the quantity of matter, or, as it is usually called, the unit of mass, as indicated by the inertia and gravity it possesses. To proceed in the most simple manner, the unit of mass ought to be that of a cubic unit of matter of the standard density; but the founders of the metrical system took as their unit of mass, the cubic centimetre of water, at the temperature of maximum density (about 4° Cent.). They called this unit of mass the gramme, and constructed standard specimens of the kilogram, which might be readily referred to by all who required to employ accurate weights. Unfortunately the determination of the bulk of a given weight of water at a certain temperature is an operation involving many difficulties, and it cannot be performed in the present day with a greater exactness than that of about one part in 5000, the results of careful observers being sometimes found to differ as much as one part in 1000.‍[223]

Weights, on the other hand, can be compared with each other to at least one part in a million. Hence if different specimens of the kilogram be prepared by direct weighing against water, they will not agree closely with each other; the two principal standard kilograms agree neither with each other, nor with their definition. According to Professor Miller the so-called Kilogramme des Archives weighs 15432·34874 grains, while the kilogram deposited at the Ministry of the Interior in Paris, as the standard for commercial purposes, weighs 15432·344 grains. Since a standard weight constructed of platinum, or platinum and iridium, can be preserved free from any appreciable alteration, and since it can be very accurately compared with other weights, we shall ultimately attain the greatest exactness in our measurements of mass, by assuming some single kilogram as a provisional standard, leaving the determination of its actual mass in units of space and density for future investigation. This is what is practically done at the present day, and thus a unit of mass takes the place of the unit of density, both in the French and English systems. The English pound is defined by a certain lump of platinum, preserved at Westminster, and is an arbitrary mass, chosen merely that it may agree as nearly as possible with old English pounds. The gallon, the old English unit of cubic measurement, is defined by the condition that it shall contain exactly ten pounds weight of water at 62° Fahr.; and although it is stated that it has the capacity of about 277·274 cubic inches, this ratio between the cubic and linear systems of measurement is not legally enacted, but left open to investigation. While the French metric system as originally designed was theoretically perfect, it does not differ practically in this point from the English system.

Natural System of Standards.

Quite recently Professor Clerk Maxwell has suggested that the vibrations of light and the atoms of matter might conceivably be employed as the ultimate standards of length, time, and mass. We should thus arrive at a natural system of standards, which, though possessing no present practical importance, has considerable theoretical interest. “In the present state of science,” he says, “the most universal standard of length which we could assume would be the wave-length in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such a standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body.”‍[224] In the same way we should get a universal standard unit of time, independent of all questions about the motion of material bodies, by taking as the unit the periodic time of vibration of that particular kind of light whose wave-length is the unit of length. It would follow that with these units of length and time the unit of velocity would coincide with the velocity of light in empty space. As regards the unit of mass, Professor Maxwell, humorously as I should think, remarks that if we expect soon to be able to determine the mass of a single molecule of some standard substance, we may wait for this determination before fixing a universal standard of mass.

In a theoretical point of view there can be no reasonable doubt that vibrations of light are, as far as we can tell, the most fixed in magnitude of all phenomena. There is as usual no certainty in the matter, for the properties of the basis of light may vary to some extent in different parts of space. But no differences could ever be established in the velocity of light in different parts of the solar system, and the spectra of the stars show that the times of vibration there do not differ perceptibly from those in this part of the universe. Thus all presumption is in favour of the absolute constancy of the vibrations of light—absolute, that is, so far as regards any means of investigation we are likely to possess. Nearly the same considerations apply to the atomic weight as the standard of mass. It is impossible to prove that all atoms of the same substance are of equal mass, and some physicists think that they differ, so that the fixity of combining proportions may be due only to the approximate constancy of the mean of countless millions of discrepant weights. But in any case the detection of difference is probably beyond our powers. In a theoretical point of view, then, the magnitudes suggested by Professor Maxwell seem to be the most fixed ones of which we have any knowledge, so that they necessarily become the natural units.

In a practical point of view, as Professor Maxwell would be the first to point out, they are of little or no value, because in the present state of science we cannot measure a vibration or weigh an atom with any approach to the accuracy which is attainable in the comparison of standard metres and kilograms. The velocity of light is not known probably within a thousandth part, and as we progress in the knowledge of light, so we shall progress in the accurate fixation of other standards. All that can be said then, is that it is very desirable to determine the wave-lengths and periods of the principal lines of the solar spectrum, and the absolute atomic weights of the elements, with all attainable accuracy, in terms of our existing standards. The numbers thus obtained would admit of the reproduction of our standards in some future age of the world to a corresponding degree of accuracy, were there need of such reference; but so far as we can see at present, there is no considerable probability that this mode of reproduction would ever be the best mode.

Subsidiary Units.

Having once established the standard units of time, space, and density or mass, we might employ them for the expression of all quantities of such nature. But it is often convenient in particular branches of science to use multiples or submultiples of the original units, for the expression of quantities in a simple manner. We use the mile rather than the yard when treating of the magnitude of the globe, and the mean distance of the earth and sun is not too large a unit when we have to describe the distances of the stars. On the other hand, when we are occupied with microscopic objects, the inch, the line or the millimetre, become the most convenient terms of expression.