PHYSICAL UNITS. In order that our acquaintance with any part of nature may become exact we must have not merely a qualitative but a quantitative knowledge of facts. Hence the moment that any branch of science begins to develop to any extent, attempts are made to measure and evaluate the quantities and effects found to exist. To do this we have to select for each measurable magnitude a unit or standard of reference, by com parison with which amounts of other like quantities may be nu merically defined. There is nothing to prevent us from selecting these fundamental quantities, in terms of which other like quanti ties are to be expressed, in a perfectly arbitrary and inde pendent manner, and, as a matter of fact, this is what is generally done in the early stages of every science. We may, for instance, choose a certain length, a certain volume, a certain mass, a cer tain force or power as our units of length, volume, mass, force or power, which have no simple or direct relation to each other. Similarly we may select for more special measurements any arbi trary electric current, electromotive force, or resistance, and call them our units. The progress of knowledge, however, is greatly assisted if all the measurable quantities are brought into relation with each other by so selecting the units that they are related in the most simple manner, each to the other and to one common set of measurable magnitudes ca:led the fundamental quantities.
The progress of this co-ordination of units has been greatly aided by the discovery that forms of physical energy can be con verted into one another, and that the conversion is by definite rule and amount. (See ENERGY.) Thus the mechanical energy associated with moving masses can be converted into heat, hence heat can be measured in mechanical energy units. The amount of heat required to raise one gramme of water through I° C in the neighbourhood of o° C is equal to about 42 million ergs, the erg being the kinetic energy or energy of motion associated with a mass of 2 grammes when moving uniformly, without rotation, with a velocity of I cm. per second. This number is commonly called the "mechanical equivalent of heat," but would be more exactly described as the "mechanical equivalent of the specific heat of water at re C." Again, the fact that the maintenance of an electric current requires energy, and that when produced its energy can be wholly utilized in heating a mass of water, en ables us to make a similar statement about the energy required to maintain a current of one ampere through a resistance of one ohm for one second, and to define it by its equivalent in the energy of a moving mass. Physical units have therefore been selected with the object of establishing simple relations be tween each of them and the fundamental mechanical units. Meas
urements based on such relations are called absolute measure ments. The science of dynamics, as far as that part of it is con cerned which deals with the motion and energy of material sub stances, starts from certain primary definitions concerning the measurable quantities involved. In constructing a system of phy sical units, the first thing to consider is the manner in which we shall connect the various items. What, for instance, shall be the unit of force, and how shall it be determined by simple reference to the units of mass, length and time? The modern absolute system of physical measurement is founded upon dynamical notions, and originated with C. F. Gauss. The postulate which lies at the base of the study of physics is that in the ultimate issue we can describe all phenomena in terms of mechanical data. Our fundamental scientific notions are those of length, time, and mass. Hence, in selecting units for physical measurements, we have first to choose units for the above three quantities.