matter acting upon that matter during one second, produces a final velocity of 32·1889 feet per second or about 32 units of velocity. Although from its perpetual action and approximate uniformity we find in gravity the most convenient force for reference, and thus habitually employ it to estimate quantities of matter, we must remember that it is only one of many instances of force. Strictly speaking, we should express weight in terms of force, but practically we express other forces in terms
We still require the unit of energy, a more complex notion. The momentum of a body expresses the quantity of motion which belongs or would belong to the aggregate of the particles; but when we consider how this motion is related to the action of a force producing or removing it, we find that the effect of a force is proportional to the mass multiplied by the square of the velocity and it is convenient to take half this product as the expression required. But it is shown in books upon dynamics that it will be exactly the same thing if we define energy by a force acting through a space. The natural unit of energy will then be that which overcomes a unit of force acting through a unit of space; when we lift one kilogram through one metre, against gravity, we therefore accomplish 9·80868... units of work, that is, we turn so many units of potential energy existing in the muscles, into potential energy of gravitation. In lifting one pound through one foot there is in like manner a conversion of 32·1889 units of energy. Accordingly the unit of energy will be in the English system, that required to lift one pound through about the thirty-second part of a foot; in terms of metric units, it will be that required to lift a kilogram through about one tenth part of a metre.
Every person is at liberty to measure and record quantities in terms of any unit which he likes. He may use the yard for linear measurement and the litre for cubic measurement, only there will then be a complicated relation between his different results. The system of derived units which we have been briefly considering, is that which gives the most simple and natural relations between quantitative expressions of different kinds, and therefore conduces to ease of comprehension and saving of laborious calculation.
It would evidently be a source of great convenience if scientific men could agree upon some single system of units, original and derived, in terms of which all quantities could be expressed. Statements would thus be rendered easily comparable, a large part of scientific literature would be made intelligible to all, and the saving of mental labour would be immense. It seems to be generally allowed, too, that the metric system of weights and measures presents the best basis for the ultimate system; it is thoroughly established in Western Europe; it is legalised in England; it is already commonly employed by scientific men; it is in itself the most simple and scientific of systems. There is every reason then why the metric system should be accepted at least in its main features.
Provisional Units.
Ultimately, as we can hardly doubt, all phenomena will be recognised as so many manifestations of energy; and, being expressed in terms of the unit of energy, will be referable to the primary units of space, time, and density. To effect this reduction, however, in any particular case, we must not only be able to compare different quantities of the phenomenon, but to trace the whole series of steps by which it is connected with the primary notions. We can readily observe that the intensity of one source of light is greater than that of another; and, knowing that the intensity of light decreases as the square of the distance increases, we can easily determine their comparative brilliance. Hence we can express the intensity of light falling upon any surface, if we have a unit in which to make the expression. Light is undoubtedly one form of energy, and the unit ought therefore to be the unit of energy. But at present it is quite impossible to say how much energy