to the Bureau, and their values in grammes were found to be respectively 453.59135, 453.58924, 453.58738. -Travaux et Mémoires, tome IV. In the following tables, cm. denotes centimetre or centimetres, gm. denotes gramme or grammes. The numbers headed "reciprocals" are the factors for reducing from C.G.S. measures. The value of g assumed in the following tables is 1 kilogramme, The ratio of the poundal to the dyne is independent of g. 1 joule, = 107 The value of the foot-poundal in ergs is independent of g. Various Measures of Length, in centimetres. French foot, 32·484 (= 12 inches = 144 lines). Toise, 194 904 (=6 feet). Rhenish or Prussian foot, 31.385; Austrian foot, 31.611; Bavarian, 29.186; Hanoverian, 29.209; Saxon, 28.319; Hessian, 28 770; Wurtemburg, 28 649; Baden, 30 000; Russian foot, 30.47945. The Russian sagène or sashen is 7 feet. Verst, 106678 (=500 sashen). Prussian mile, 753250 (= 24000 feet). Austrian mile, 758666 ( = 24000 feet). Geographical mile as understood in Germany, 742040. Various Measures of Mass, in grammes. Zollverein pound, 500; Prussian pound, 467-711; Austrian, 560 012; Russian, 409.52. Each of these pounds is divided into 32 loth or lot, and 100 pounds make one centner. CHAPTER I. GENERAL THEORY OF UNITS. Units and Derived Units. 1. THE numerical value of a concrete quantity is its ratio to a selected magnitude of the same kind, called the unit. Thus, if L denote a definite length, and the unit is a ratio in the strict Euclidean sense, and is called the numerical value of L. The numerical value of a concrete quantity varies directly as the concrete quantity itself, and inversely as the unit in terms of which it is expressed. 2. A unit of one kind of quantity is sometimes defined by reference to a unit of another kind of quantity. For example, the unit of area is commonly defined to be the area of the square described upon the unit of length ; and the unit of volume is commonly defined as the volume of the cube constructed on the unit of length. The units of area and volume thus defined are called derived units, and are more convenient for calculation than independent units would be. For example, when the above A definition of the unit of area is employed, we can assert that [the numerical value of] the area of any rectangle is equal to the product of [the numerical values of] its length and breadth; whereas, if any other unit of area were employed we should have to introduce a third factor which would be constant for all rectangles. 3. Still more frequently, a unit of one kind of quantity is defined by reference to two or more units of other kinds. For example, the unit of velocity is commonly defined to be that velocity with which the unit length would be described in the unit time. When we specify a velocity as so many miles per hour, or so many feet per second, we in effect employ as the unit of velocity a mile per hour in the former case, and a foot per second in the latter. These are derived units of velocity. Again, the unit acceleration is commonly defined to be that acceleration with which a unit of velocity would be gained in a unit of time. The unit of acceleration is thus derived directly from the units of velocity and time, and therefore indirectly from the units of length and time. 4. In these and all other cases, the practical advantage of employing derived units is, that we thus avoid the introduction of additional factors, which would involve needless labour in calculating and difficulty in remembering.* 5. The correlative term to derived is fundamental. * An example of such needless factors may be found in the rules commonly given in English books for finding the mass of a body when its volume and material are given. "Multiply the volume in cubic feet by the specific gravity and by 62'4, and the product will be the mass in pounds;" or "multiply the volume in cubic |