Practical Electrical The unit of resistance that is employed almost universally in practical electrical work is the "ohm," which was named for G. S. Ohm, the distinguished physicist and discoverer of Ohm's law. This is defined as equal to 1,000,000,000 (or 10') C.G.S. electromagnetic units of resistance; the ideal standard that has precisely this resistance being called, for the sake of distinct identi fication, the true Many physicists have investigated the value of the ohm, as here de fined, and have constructed material standards for practical work, having a resistance of one ohm, as nearly as possible. A committee ap pointed by the British Association for the pur pose of investigating the value of the true ohm prepared a coil of German silver wire, which. at a certain definite temperature, was supposed to have a resistance of practically one ohm; and thin coil, from the time of its acceptance by the British Association in 1864 down to the year 1884, was the standard ohm of the world, being known, for as the "British Association ohm,* or, more briefly, as the "B.A. ohm." It is now customary to define the prac tical ohm in terms of the resistance of a col umn of mercury of stated dimensions and tem perature, as it is found that the resistance of a solid conductor depends not only upon the material of which the conductor is made, but also upon the physical state of that material with respect to internal stresses and other cir cumstances. The B.A. ohm of 1864 has a resistance equal to that of a column of pure mercury having a constant cross section of one square millimeter, and a length of 104.83 centi meters; the temperature of the mercury being 0 degrees C. This standard was subsequently found to be materially smaller than the true ohm, and the International Congress of Elec tricians at Paris, in 1884, adopted, as the equiv alent of the ohm, a column of mercury having a constant cross section of one square milli meter, and a length of 106 centimeters; the temperature of the mercury being 0 degrees C., as before. This standard is known as the "legal" or "congress" ohm. Several of the physicists present at that congress were of the opinion that the length of the column should be 106.2 or 106.25 centimeters; but the decimal being admittedly uncertain, it was finally agreed to disregard it entirely, until further experi mental evidence could be had. In August 1893 an International Congress of Electricians was held at Chicago; England, France, Germany, Italy, Austria, Switzerland, Sweden, Mexico, Canada and the United States being represented. This congress adopted another and (presum ably) better value of the ohm, the new standard being designated as the "International ohm." The International ohm, which has since been adopted by the nations represented at the con ference, was defined as "the resistance offered to an unvarying electrical current by a column of mercury (at the temperature of melting ice) 14.4521 grams in mass. of a constant cross sectional area, and of the length of 106.300 cen timeters." The conference preferred, it will be seen, to fix the sectional area by giving the mass of the column, rather than by stating the sectional area directly. The intention was, however, that the sectional area shall be sen sibly one millimeter; for a column of mercury 106.3 centimeters long and having a mass of 14.4521 grams, would have a sectional area, at 0. degrees C., of between 1 and 1.00003 square millimeters. The ohm thus defined by the Chi cago congress is probably very near to the true ohm.
The practical unit of current is the "ampere," named for the French physicist, A. M. Ampere. It is defined as equal to one-tenth of a C.G.S. electromagnetic unit of current. The Chicago International Congress of 1893, after consider ing the available experimental evidence, con cluded that the ampere can be defined, for prac tical purposes, as equal in magnitude to the unvarying current which will deposit 0.001118 gram of metallic silver every second from a solution of nitrate of silver in water. This particular estimate of the value of the true am pere is called, for definiteness, the "International ampere." The practical unit of electromotive force is the "volt,' which was named for the Italian physicist, Alessandro Volta, and which is defined as equal to 100,000,000 (or 10') C.G.S. electromagnetic units of difference of potential or as the electromotive force which is required in order to maintain a current of one ampere through a resistance of one ohm.
Of the remaining practical electrical units, j the coulomb, farad, joule, watt and henry call for special mention. The coulomb is the prac tical unit of electrical quantity. It may be de fined either as one-tenth of the C.G.S. electro magnetic unit of "quantity of electricity," or as the quantity of electricity conveyed by an am pere in one second. The farad (named for Faraday) is the practical unit of capacity, and may be defined either as the 1,000,000,000th part of a C.G.S. electromagnetic unit of capacity, or as the capacity of a condenser which holds one coulomb of electricity, when charged to a potential of one volt. The farad is much too large for convenience, and although it is called the "practical" unit of capacity, it is replaced, in practice, by the emicrofarad,x' which is equal to the millionth part of a farad. The condens ers which are in ordinary use are commonly made to have capacities of a microfarad, or of some decimal subdivision of a microfarad. The "joule" (named for James Prescott Joule) is the practical unit of work (or energy) in the electrical system of units, a joule being defined as 10,000,000 (or 10') ergs; and its practical convenience depends upon the fact that it is equal to the quantity of energy that is ex pended in one second by a current of one ampere acting through a resistance of one ohm.
The "watt" (named for James Watt) is the corresponding unit of power, and is defined either as the expenditure of 10,000,000 efgs per second, or as the rate at which energy is expended when a current of one ampere flows through a resistance of one ohm. In dealing with the large currents that occur in modern electrical power-houses, the watt is an incon veniently small unit, and the kilowatt is almost invariably used in its place; a kilowatt being equal to 1,000 watts. A horse power is equal to 746 watts, or to 0.746 of a kilowatt. The "henry" (named for Joseph Henry) is the prac tical unit of inductance, and it is defined as the induction in a circuit, when an electro motive force of one volt is induced in this circuit while the inducing current varies at the rate of one ampere per second.
Dimensions.—A surface is said to have ex tension in two.dimensions, and a solid is simi larly said to have extension in three dimensions. The volume of a cube, for example, is found by multiplying together the length, width and height of the cube; and hence we may say that the volume in question is of three "dimen sions" in terms of L, the unit of length em ployed. This mode of expression has been extended to other units besides units of length, and the idea has proved itself quite useful in numerous ways. For example, a velocity is found by dividing a length by a time; so that if L represents a length and T a time, we may write and we say that velocity is of dimension + 1 in length, and — 1 in time. Sim ilarly, force is measured by the change of momentum that it produces, in a given mass, per unit of time. That is, it is found by multi plying a mass (which we may represent by M) by a velocity, and dividing the product by a time. That is, F MV/T. But we already know that V = LT—', and hence the equation becomes and we say that force is of dimensions + 1 in mass and in length, and of —2 in time. The equations here given are called °dimensional equations,* since in writ ing them we pay no attention to the actual nu merical magnitudes of the quantities involved, but only to the "dimensions* of those quantities. As a further illustration of the °dimensions* of a physical quantity, let us consider the case of work. This is defined as the product of a force by a distance, and hence we have W =FL =-- ML and we say that work is of dimensions + 1 in mass, + 2 in length and —2 in time. Kinetic energy is found by taking half the product of a mass and the square of a velocity. Omitting the numer ical factor (since it does not affect the di mensions of the energy in any way), we have E = = --= -2 so that ki netic energy is of dimensions + 1 in mass, 2 in length and —8 in time. That is, it is of the same dimensions in all respects as work; which is evidently correct, since work and kinetic energy are mutually convertible. As an illus tration of the determination of the dimensions of a quantity when the result is far less ob vious, consider the dimensions of a "quantity of electricity,* as expressed in electrostatic units. Let Q denote a charge of electricity, as expressed in electrostatic units. Then if a similar charge were brought near to the first one, the repulsion between the two would be found by dividing . the product of the two charges by the square of the distance between them. Hence the dimensions of the repulsion between the two charges would be But this repulsion, being a force, must be of the dimensions F = and hence we have ; whence Q= That is, °quantity of electricity,* as expressed in the electrostatic system, is of the dimensions in mass, # in length and — I in time. For the dimensions of other electrical magnitudes, and for the interesting facts that are known con cerning the ratios of the dimensions of the va rious electrical units, special works on these subjects must be consulted. Maxwell pointed out that in any equation that expresses a fact in nature, the several terms that are added to gether, or equated to one another, must be all of the same dimensions; a fact of which use has been made above, in determining the di mensions of °quantity of electricity.° As an illustration of the kind of information that can sometimes be had from dimensional equations, in constructing a formula of which we know the general but not the precise form, let us consider the case of the pendulum. Let us suppose that we know that the time of oscil lation of a pendulum, through a small arc, varies as some power of the length of the pendulum, multiplied by some power of the in tensity of gravity at the place where the experi ment is made, and let us seek to find what the unknown exponents are. Representing the in tensity of gravity by g, and the unknown ex ponents by x and y, respectively, the forego ing assumption with respect to the general form of the dependence of the period upon the length of the pendulum and the intensity of gravity gives us an expression of the form gzLv, for the time of oscillation of the pendulum. Now g, being an acceleration, is of the dimensions so that the foregoing expression is of the dimensions Lv; but this, being the expression for the time of oscillation of the pendulum, must itself be of the dimen sions T. Hence we have or Lx+v = T. This being an identity, we have, by equating the exponents of T, — 2x = I.
or x And since we also have x y =0.
we see that y Hence the time of vibra tion of the pendulum varies directly as the square root of the length of the pendulum, and inversely as the square root of the intensity of gravity. See METRIC SYSTEM ; WEIGHTS AND MEASURES. Consult, also, Everett, and Physical Constants.'