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 1000.16
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