the length of the arm of an English king, Henry I. After this unit became established as a standard, it is probable that the foot was arbitrarily chosen as one third of the yard. In view of such an origin it will be clear why no agreement existed among the units in use in different countries. 3. Relations between different units of length. It has also been true, in general, that in a given country the different units of length in common use (such, for example, as the inch, the hand, the foot, the fathom, the rod, the mile, etc.) have been derived either from the lengths of different members of the human body or from equally unrelated magnitudes, and in consequence have been connected with one another by different, and often by very awkward, multipliers. Thus, there are 12 inches in a foot, 3 feet in a yard, 5 yards in a rod, 1760 yards in a mile, etc. 4. Relations between units of length, area, volume, and mass. A similar and even worse complexity exists in the relations of the units of length to those of area, volume, and mass. Thus, there are 272 square feet in a square rod, 57 cubic inches in a quart, and 31 gallons in a barrel. Again, the pound, instead of being the mass of a cubic inch or a cubic foot of water, or of some other common substance, is the mass of a cylinder of platinum, of inconvenient dimensions, which is preserved in London. 5. Origin of the metric system. At the time of the French Revolution the extreme inconvenience of existing weights and measures, together with the confusion arising from the use of different standards in different localities, led the National Assembly of France to appoint a commission to devise a more logical system. The result of the labors of this commission was the present metric system, which was introduced into France in 1793 and has since been adopted by the governments of most civilized nations except those of Great Britain and the United States; and even in these countries its use in scientific work is practically universal. The World War did much to speed its adoption in these countries. 6. The standard meter. The standard length in the metric system is called the meter (m.). It is the distance, at the freezing temperature, between two transverse parallel lines Exact size of the cross section FIG. 1. The standard meter ruled on a bar of platinum-iridium (Fig. 1), which is kept at the International Bureau of Weights and Measures at Sèvres, near Paris. This distance is 39.37 inches (Fig. 2). FIG. 2. Metric units in comparison with the old unstandardized units In order that this standard length might be reproduced if lost, the commission attempted to make it one ten-millionth of the distance from the equator to the north pole, measured on the meridian of Paris. But since later measurements have thrown some doubt upon the exactness of the commission's determination of this distance, we now define the meter not as any particular fraction of the earth's quadrant, but simply as the distance between the scratches on the bar mentioned above. On account of its more convenient size the centimeter (one one-hundredth of a meter) is universally used, for scientific purposes, as the fundamental unit of length. 7. Metric standard capacity. The standard unit of capacity is called the liter (1.). It is the volume of a cube which is one tenth of a meter (about 4 inches) on a side. The liter is therefore equal to 1000 cubic centimeters (cc.). It is equivalent to 1.057 quarts. A liter and a quart are therefore roughly equivalent measures (Fig. 2). 8. The metric standard of mass. In order to establish a connection between the unit of length and the unit of mass, the commission directed a committee of the French Academy to prepare a cylinder of platinum which should have the same weight as a liter of water at its temperature of greatest density; namely, 4° centigrade (39° Fahrenheit). An exact equivalent of this cylinder, made of platinum-iridium and kept at Sèvres with the standard meter, now represents the standard of mass in the metric system. It is called the standard kilogram (kg.) and is equivalent to about 2.2 pounds. One one-thousandth of this mass was adopted as the fundamental unit of mass and was named the gram (g.). For practical purposes, therefore, the gram may be taken as equal to the mass of 1 cubic centimeter of water. 9. The other metric units. The three standard units of the metric system - the meter, the liter, and the gram- have decimal multiples and submultiples, so that every unit of length, volume, or mass is connected with the unit of next higher denomination by an invariable multiplier; namely, ten. The names of the multiples are obtained by adding the Greek prefixes deka (ten), hecto (hundred), kilo (thousand); the submultiples are formed by adding the Latin prefixes deci (tenth), centi (hundredth), and milli (thousandth). Thus: The most common of these units, with the abbreviations which will be used for them in this book, are the following: meter (m.) centimeter (cm.) millimeter (mm.) liter (1.) cubic centimeter (cc.) gram (g.) 10. Relations between the English and metric units. The following table, which is inserted for reference only, gives the relation between the most common English and metric units: The relations 1 in. = 2.54 cm., 1 m. = 39.37 in., 1 kilo (kg.) = 2.2 lb., 1 km. = .62 mi., should be memorized. Portions of a centimeter and of an inch scale are shown together in Fig. 3. It will be seen from Fig. 3 that 1 inch = 2.54 centimeters. 11. The standard unit of time. The second is taken among all the civilized nations as the standard unit of time. It is 6400 part of the time from noon to noon; that is, of the mean solar day. 86 12. Measurement of length. Measuring the length of a body consists simply in comparing its length with that of the standard meter bar kept at the International Bureau. In order that this may be done conveniently, great numbers of rods of the same length as this standard meter bar have been made and distributed all over the world. They are our common meter sticks. They are divided into 10, 100, or 1000 equal parts. Great care is taken to have all the parts of exactly the same length. FIG. 4. A set of weights 13. Measurement of mass. Similarly, measuring the mass of a body consists in comparing its mass with that of the standard kilogram. In order that this might be done conveniently it was first necessary to construct bodies of the same mass as this kilogram, and then to make a whole series of bodies whose masses were à, 10, 180, 1000, etc. of the mass of this kilogram; in other words, to construct a set of standard masses commonly called a set of weights (Fig. 4). B With the aid of such a set of standard masses the determination of the mass of an unknown body is made by placing the body upon the pan B (Fig. 5), counterpoising by adding shot, paper, etc. to the pan A, and then replacing the unknown body at B by as many of the standard masses as are required to bring the pointer back to O again. The mass of the body is equal to the sum of these standard masses. This rigorously correct method of weighing is called the method of substitution. FIG. 5. The simple balance If a balance is well constructed, however, a weighing may usually be made with sufficient accuracy by simply placing the unknown body upon one pan and finding the sum of the |