The area of a square the Sq. cm. length of a side of which is I centimetre. [A]=[L]'. Volume, v. Density, d. Velocity, v. The volumes of similar solids The mass of a body is pro- Force, f. over I centimetre in a second. The acceleration of a body Cm. per sec. per [a]=[L][T]'. whose velocity is increas ing every second by 1 cm. pe: sec. sec. The work done by a dyne | Erg. when it has moved its point of application through 1 centimetre. |[W]=[M] [L]{T}~'. The pressure exerted when Dyne per sq. cm. [P]=[M] [L]-1 [T]. the force on every sq. cm. of area is 1 dyne. DERIVATION OF UNITS ON THE C. G.S. SYSTEM-continued. 1 See chaps. xvii. and xviii. The electrostatic system is not employed in the experiments described below. The C.G.S. System. The table, p. 18, shows the method of derivation of such absolute units on the C.G.S. system as we shall have occasion to make use of in this book. The first column contains the denominations of the quantities measured; the second contains the verbal expression of the physical law on which the derivation is based, while the third gives the expression of the law as a variation equation; the fourth and fifth columns give the definition of the C.G.S. unit obtained and the name assigned to it respectively, while the last gives the dimensional equation. This will be explained later (p. 24). The equations given in the third column are reduced to ordinary equalities by the adoption of the unit defined in the next column, or of another unit belonging to an absolute system based on the same principles. Some physical laws express relations between quantities whose units have already been provided for on the absolute system, and hence we cannot reduce the variation equations to ordinary equalities. This is the case with the formula for the gaseous laws already mentioned (p. 15). A complete system of units has thus been formed on the C.G.S. absolute system, many of which are now in practical use. Some of the electrical units are, however, proved to be not of a suitable magnitude for the electrical measurements most frequently occurring. For this reason practical units have been adopted which are not identical with the C.G.S. units given in the table (p. 20), but are immediately derived from them by multiplication by some power of 10. The names of the units in use, and the factors of derivation from the corresponding C.G.S. units are given in the following table : TABLE OF PRACTICAL UNITS FOR ELECTRICAL Measurement RELATED TO THE C.G.S. ELECTRO-MAGNETIC SYSTEM. To shorten the notation when a very small fraction or a very large multiple of a unit occurs, the prefixes micro- and mega- have been introduced to represent respectively division and multiplication by 106. Thus: Arbitrary Units at present employed. For many of the quantities referred to in the table (p. 18) no arbitrary unit has ever been used. Velocity, for instance, has always been measured by the space passed over in a unit of time. And for many of them the physical law given in the second column is practically the definition of the quantity; for instance, in the case of resistance, Ohm's law is the only definition that can be given of resistance as a measurable quantity. For the measurement of some of these quantities, however, arbitrary units have been used, especially for quantities which have long been measured in an ordinary way as volumes, forces, &c. Arbitrary units are still in use for the measurement of temperature and quantities of heat; also for light intensity, and some other magnitudes. We have collected in the following table some of the arbitrary units employed, and given the results of experimental determinations of their equivalents in the absolute |