there is in any particular amount of light. The question then arises,—Are we to defer the measurement of light until we can assign its relation to other forms of energy? If we answer Yes, it is equivalent to saying that the science of light must stand still perhaps for a generation; and not only this science but many others. The true course evidently is to select, as the provisional unit of light, some light of convenient intensity, which can be reproduced from time to time in the same intensity, and which is defined by physical circumstances. All the phenomena of light may be experimentally investigated relatively to this unit, for instance that obtained after much labour by Bunsen and Roscoe.20 In after years it will become a matter of inquiry what is the energy exerted in such unit of light; but it may be long before the relation is exactly determined.
A provisional unit, then, means one which is assumed and physically defined in a safe and reproducible manner, in order that particular quantities may be compared inter se more accurately than they can yet be referred to the primary units. In reality the great majority of our measurements are expressed in terms of such provisionally independent units, and even the unit of mass, as we have seen, ought to be considered as provisional.
The unit of heat ought to be simply the unit of energy, already described. But a weight can be measured to the one-millionth part, and temperature to less than the thousandth part of a degree Fahrenheit, and to less therefore than the five-hundred thousandth part of the absolute temperature, whereas the mechanical equivalent of heat is probably not known to the thousandth part. Hence the need of a provisional unit of heat, which is often taken as that requisite to raise one gram of water through one degree Centigrade, that is from 0° to 1°. This quantity of heat is capable of approximate expression in terms of time, space, and mass; for by the natural constant, determined by Dr. Joule, and called the mechanical equivalent of heat, we know that the assumed unit of heat is equal to the energy of 423·55 gram-metres, or that energy which will raise the mass of 423·55 grams through one metre against 9·8... absolute units of force. Heat may also be expressed in terms of the quantity of ice at 0° Cent., which it is capable of converting into water under inappreciable pressure.
Theory of Dimensions.
In order to understand the relations between the quantities dealt with in physical science, it is necessary to pay attention to the Theory of Dimensions, first clearly stated by Joseph Fourier,21 but in later years developed by several physicists. This theory investigates the manner in which each derived unit depends upon or involves one or more of the fundamental units. The number of units in a rectangular area is found by multiplying together the numbers of units in the sides; thus the unit of length enters twice into the unit of area, which is therefore said to have two dimensions with respect to length. Denoting length by L, we may say that the dimensions of area are L × L or L2. It is obvious in the same way that the dimensions of volume or bulk will be L3.
The number of units of mass in a body is found by multiplying the number of units of volume, by those of density. Hence mass is of three dimensions as regards length, and one as regards density. Calling density D, the dimensions of mass are L3D. As already explained, however, it is usual to substitute an arbitrary provisional unit of mass, symbolised by M; according to the view here taken we may say that the dimensions of M are L3D.
Introducing time, denoted by T , it is easy to see that the dimensions of velocity will be L / T or LT