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UNITS OF MEASUREMENT. When any physical quantity is to be measured, it is necessary to select a unit in terms of which the magnitude of the quantity is to be ex pressed. We may, if we choose, select an entirely arbitrary unit for each different kind of quantity to be meastired; or we may select certain arbitrary fundamental units as a basis and construct upon these a consistent system of derived units. The first method is employed (for every-day purposes) in English-speaking countries, and the second in those countries which employ the metric system. In scientific measurements, the second, or "logicaP system is also employed, in practically all civilized coun tries at the present time.

In any system of units of measurement, it is necessary to select at least three units that are entirely arbitrary. It is customary (though not at all essential) to select, as the three fundamental units, the units for measuring length, mass and time. In the English system, the fundamental unit of length is the yard. It is said that the yard was originally defined, by royal decree, as the length of the arm of King Henry I. The United States yard is de fined as III? metres; the metre being the fun damental unit of length. The British yard is the distance, at between two lines on a bronze bar kept at the Standards Office, West minster, London. The •relation of the British yard to the metre, as nearly as it can be deter mined is 1 yard (British)=u}$ ihu metres.

The foot is then defined as the third part of a yard, and the inch as the 12th part of a foot. In the British system, the unit of mass is the avoirdupois pound, which is defined as the mass of a certain cylinder of platinum in the possession of the British government, which is marked °P. S. 1844" ; the letters "P. S." signi fying "Parliamentary Standard.° In the United States the unit of mass is the pound defined as /./trayin kilograms, the kilogram being the fundamental unit of mass. The British pound is a mass of platinum iridium deposited in the Standards Office, London. The United States pound and the British pound are ectual as nearly as can be determined. In all civilized countries the fundamental unit of time is the second; the second being defined as the 86,400th part of a mean solar day, or the 86,400th part of the average interval between two successive passages of the tun across the meridian of any given place. In the metric system the funda mental unit of length is the metre; the metre being defined as the distance, at C., between two marks on a certain bar of platin-iridium in the possession of the International Bureau of Weights and Measures, at Sevres, France.

The fundamental unit of mass, in the metric system, is the kilogram, which is defined as the mass of a certain piece of platin iridium in the possession of the International Bureau of Weights and Measures. The kilo gram was intended to be (and is, very nearly), equal to the mass of a cubic decimetre of water, at the temperature (about 4° C.) at which water has its greatest density.

Secondary Units.— The various units that are employed in measurement, in addition to the fundamental units described above, are de fined, for the sake of precision, in terms of those fundamental units. The United States gallon is defined as a, volume of 231 cubic inches. Measures made to contain this volume are usually standard at either 4° C. or C. (68° F.). That is, they are made to hold a vol ume of 231 cubic inches at one of these tem peratures. State standard gallon measures are of brass and are standard at C. Glass ca pacity measures are usually standard at 20° C. The British Imperial gallon is defined as the volume of 10 pounds of water at 62° F. when weighed in air at F. with brass weights and with the barometer at 30 inches. The volume of the British gallon is 277274 cubic inches. Many of the secondary units that are used in English-speaking countries are as arbitrary as the gallon; but others are derived from the funda mental units in a perfectly definite way. The unit of work and of energy, for example, in English and American engineering practice, is the foot-pound; the foot-pound being defined as the work that must be done in order to over come, through a distance of one foot, a force equal to the attraction that the earth exerts upon a pound of matter. (See FORCE; MECHAN ICS). The attractive force that the earth exerts upon a pound of matter is often called a 'pound.* This is incorrect, however, for the pound (like the gram or the kilogram) is a unit of mass, and not of force. The °poundal° is the logical unit of force in the system of units in common use in English-speaking coun tries• the poundal being defined as the force which, when acting for one second upon a body having a mass of one pound, will communicate to that mass a velocity of one foot per second. The poundal is not in general use, however, because in scientific work, where precision of statement and a high degree of numerical ac curacy are of paramount importance, the "cen timeter-gram-second' system of units is now almost universally employed.