CHAPTER II UNITS OF MEASUREMENT Fundamental units, 15. Derived units, 16. Units of length, 17. Units of mass, 18. Units of time, 19. Units of force, 20. In any kind of quantitative work it is a great advantage to have a convenient system of units. The common British system of weights and measures is a glaring example of what not to have. In this system there are a great many different units for measuring the same thing, and, what is worse, there is often no simple way of changing from one to another. For example, to measure volume we may use cubic inches, cubic feet, cubic yards, bushels, barrels, gallons, quarts, pecks, etc. Of some of these there are two kinds; for example, the wet gallon and the dry gallon. The difficulty sometimes encountered of changing from one of these to another is shown by the work necessary to change cubic feet to bushels, a not uncommon computation. The use of different units for measuring the same quantity is not objectionable provided the relationship of the units is simple. No one has trouble in reducing dollars to cents, owing to the simplicity of the decimal system. This system is so satisfactory that it is used the world over in scientific units. 15. Fundamental units. In any system it is necessary at the beginning to assume certain units arbitrarily. In each of the commonly used systems there are three of these fundamental units. The fundamental quantities in the international scientific system are length, mass, and time. The units of these are, respectively, the centimeter, the gram, and the second. The initial letters of the units give the name to the system, which is known as the C.G.S. system. In the British Engineering (B.E.) system the fundamental quantities are length, force, and time. The units of these are the foot, the pound, and the second. It should be noticed that while mass is a fundamental quantity in the C.G.S. system, force is the fundamental quantity in the British Engineering system. The difference between mass and force, and the important reasons for making a distinction, will be discussed later. The C.G.S. system is used in scientific work in all countries. Engineers in English-speaking countries generally use the British Engineering system, although the use of metric units is constantly increasing. The electrical and magnetic units used by engineers are based on C.G.S. units. 16. Derived units. Frequently the unit of a quantity is obtained from other units. For example, the cubic foot is a unit of volume obtained from the unit of length; a foot-pound is a unit of work derived from the units of length and force. Such units are called derived units. A liter is a volume equal to 1000 cubic centimeters. It is a derived unit based on the unit of length-the centimeter. In the C.G.S. system nearly all the units are derived. In general it is simpler to use derived units than arbitrary ones. For example, if one knows the dimensions of a bin in feet, it is easier to compute the volume in cubic feet, a derived unit, than in bushels, an arbitrary unit. An arbitrary unit is one chosen without regard to the other existing units. 17. Units of length. The international meter was defined as the distance between the ends of a platinum bar, the mètre des Archives, made by Borda and preserved in the national archives of France. Between 1875 and 1887 the International Bureau of Weights and Measures, with headquarters in a suburb of Paris, made thirty-one copies of the Borda meter. Each of these was made of an alloy of 90 per cent platinum and 10 per cent iridium. In each case the meter was the distance between two fine parallel lines ruled on the surface of the bar. The one which agreed most closely with Borda's meter was declared to be the International Prototype Meter. The others were distributed among the governments which participated in the support of the Bureau. The United States secured two of these, Nos. 21 and 27. They are preserved in the Bureau of Standards in Washington. The one-hundredth part of the meter is the centimeter, the basic unit of length in the C.G.S. system. For small distances the millimeter (one tenth of the centimeter) is often used, while for large distances the kilometer (1000 meters) is used. In special cases other units of length are used in scientific work. For example, in measuring microscopic distances the micron (one millionth of a meter) is used. But in all cases the unit used should be some decimal multiple of the meter. In the United States the meter is the legal standard for both metric and common units. The yard was defined in terms of the meter by an act of Congress, July 28, 1866: From this, 1 yd. (U.S.) = m. 1 m. = 39.37 in. The British imperial yard is defined in a different way, but for nearly all purposes the United States and British yards may be regarded as equal. 18. Units of mass. The gram is approximately the mass of 1 cubic centimeter of water at 4° C. The precise value of the gram is defined as being the one-thousandth part of the standard kilogram, a mass carefully preserved by the International Bureau of Weights and Measures. The United States government obtained two accurate copies of the standard kilogram about the time the two meters were delivered. 19. Units of time. There are two different time systems used. The basis of one of these is the time of revolution of the earth on its axis. This is called the sidereal day, and 1/86400 of it is called the sidereal second. The more common system is based on the apparent motion of the sun. When the sun is on the meridian, it is said to be solar noon. The time between two successive solar noons is the solar day. As solar days at different seasons are not of the same length, the mean solar day is used, and the mean solar second is 1/86400 of this. The mean solar second is about 13 sidereal seconds. In all the various systems of scientific units the mean solar second is used as the unit of time. 20. Units of force. The pound in the United States is legally defined as the weight of 1/2.204622 kilogram. The weight of this mass varies slightly from place to place on the earth's surface. For this reason it is customary in very accurate work to use as the standard the weight at a place where a falling body would gain in one second a velocity of 32.1739 feet per second. This is approximately the velocity acquired at sea level at 45 degrees latitude. In the C.G.S. system the unit of force is the dyne, a derived unit. It will be defined later. The weight of various masses can be used as force units. Sometimes the weight of a kilogram is used as a unit of force. But this unit should never be called a kilogram. It is better to say the weight of a kilogram, or a kilogram-weight. The kilogram is a mass unit (not a force unit) in the systems used in this country. CHAPTER III Three forms of matter, 21. Pressure and force, 22. Some facts regarding pressures in liquids, 23. Derivation of the pressure-depth formulas, 24. The hydrostatic paradox, 25. Units for measuring pressure, 26. Transmission of pressure; Pascal's principle, 27. Archimedes' principle, 28. Theoretical proof of Archimedes' principle, 29. Examples of Archimedes' principle, 30. Specific gravity; density, 31. Measurement of the specific gravity of solids, 32. The specific gravity of liquids, 33. The compressibility of liquids, 34. 21. Three forms of matter. Matter exists in three forms: solids, liquids, and gases. Sometimes the last two of these are grouped under the term fluids. The property possessed by solids that differentiates them from liquids and gases is called rigidity, the tendency to maintain shape. There is no hard and fast line of separation between solids and liquids, for some solids if left alone long enough exhibit properties of liquids; thus pitch and some of the waxes will flow if given time enough. Many substances change freely from one form to another. We are familiar with water in the three forms, solid, liquid, and gaseous, but it is not so commonly known that many other substances can exist in the different forms. Metals, such as iron, copper, and lead, when raised to sufficiently high temperatures become gases. On the other hand, all known gases have been changed into liquids at low temperatures and, with the exception of helium, have been solidified at still lower temperatures. In reading over the discussion of the familiar properties of liquids and gases the student should avoid confusing a knowledge of the facts with an understanding of the fundamental principles involved. In scientific work a knowledge of the facts is only the first step. When the principles are understood and the ability to use them is acquired, it will be found not only that it is easier to |