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.
It is allowable for a scientific man to introduce a new unit in any branch of knowledge, provided that it assists precise expression, and is carefully brought into relation with the primary units. Thus Professor A. W. Williamson has proposed as a convenient unit of volume in chemical science, an absolute volume equal to about 11·2 litres representing the bulk of one gram of hydrogen gas at standard temperature and pressure, or the equivalent weight of any other gas, such as 16 grams of oxygen, 14 grams of nitrogen, &c.; in short, the bulk of that quantity of any one of those gases which weighs as many grams as there are units in the number expressing its atomic weight.18 Hofmann has proposed a new unit of weight for chemists, called a crith, to be defined by the weight of one litre of hydrogen gas at 0° C. and 0°·76 mm., weighing about 0·0896 gram.19 Both of these units must be regarded as purely subordinate units, ultimately defined by reference to the primary units, and not involving any new assumption.
Derived Units.
The standard units of time, space, and mass having been once fixed, many kinds of magnitude are naturally measured by units derived from them. From the metre, the unit of linear magnitude follows in the most obvious manner the centiare or square metre, the unit of superficial magnitude, and the litre that is the cube of the tenth part of a metre, the unit of capacity or volume. Velocity of motion is expressed by the ratio of the space passed over, when the motion is uniform, to the time occupied; hence the unit of velocity is that of a body which passes over a unit of space in a unit of time. In physical science the unit of velocity might be taken as one metre per second. Momentum is measured by the mass moving, regard being paid both to the amount of matter and the velocity at which it is moving. Hence the unit of momentum will be that of a unit volume of matter of the unit density moving with the unit velocity, or in the French system, a cubic centimetre of water of the maximum density moving one metre per second.
An accelerating force is measured by the ratio of the momentum generated to the time occupied, the force being supposed to act uniformly. The unit of force will therefore be that which generates a unit of momentum in a unit of time, or which causes, in the French system, one cubic centimetre of water at maximum density to acquire in one second a velocity of one metre per second. The force of gravity is the most familiar kind of force, and as, when acting unimpeded upon any substance, it produces in a second a velocity of 9·80868 . . metres per second in Paris, it follows that the absolute unit of force is about the tenth part of the force of gravity. If we employ British weights and measures, the absolute unit of force is represented by the gravity of about half an ounce, since the force of gravity of any portion of