TABLE V-ALTERNATING CURRENT METERS APPROVED TABLE VI.-MAXIMUM DEMAND INDICATORS APPROVED CHAPTER II. GENERAL PRINCIPLES OF CONTINUOUS CURRENT METERS. General Equations-Law of the Chemical Meter-Electro-magnetic Action-Laws of the Motor Meter with Brake-Law of the Motor Meter without Brake-Law of the Clock Meter-Thermal Effect-Behaviour of Continuous Current Three-wire Energy Motor Meters. General Equations.—The electrical energy delivered to a circuit during any given interval of time is expressed by the general equation where cand v are respectively the instantaneous values of the current flowing in the circuit and the potential difference applied to its terminals, T1 and T2 denoting the commencement and termination of the period under consideration, and dt is the short interval during which the power, c.v is supposed to remain constant. If c be the value of the current in amperes, v be the pressure expressed in volts, and the hour be taken as the unit of time, then the electrical energy is expressed in watt-hours. The function of an electricity meter is to register the electrical energy consumed in a given period, and a meter that performs the operation expressed on the right-hand side of equation (1) is called an energy meter, or more usually a watt-hour meter. In some instances these instruments are still erroneously termed recording wattmeters. A recording wattmeter does not measure energy, i.e. does not integrate the values of c.v.dt, but measures power, and traces out on record paper, mounted on a continuously revolving drum, a curve, the ordinates of which represent the values of the power supplied to the circuit. In electricity supply systems in which the supply pressure is kept practically constant, v is a constant, and the general equation may be written An electricity meter in this case does not integrate the different values of the energy, but simply the quantities of electricity in ampere-hours; in other T2 words, it performs the operation fe.dt, and is then called a quantity or an T, ampere-hour meter. A quantity meter is sometimes designated a coulomb meter. The term 'coulomb meter' should, however, not be used in this sense, as the coulomb represents one ampere-second, whereas in quantity meters the unit of quantity is the ampere-hour. Quantity meters are usually calibrated so that their indications are in watt-hours, hectowatt-hours, or kilowatt-hours at the voltage of the circuit to which they are connected. If both c and v be constant, that is, the power taken be always the same, then W being the power in watts. For this purpose hour-meters are used, which consist of clocks electrically controlled, whose function is to register the time in hours during which current has been flowing in the circuit. If the current c remain constant, then equation (1) becomes A meter which measures the quantity expressed under the integral is termed a volt-hour meter. The above equations hold for both continuous and alternating current, provided that c and v represent the instantaneous values of the current and pressure. In a continuous current system the instantaneous values are identical with the effective values, as measured by an ammeter and voltmeter. This is, however, not the case with alternating currents, as both the current and the voltage are periodic functions, and in general sine functions of the time, varying in a cyclic manner both in sense and magnitude, and are also not necessarily in phase with one another. If in an alternating current system cand v' denote the effective or virtual values (the virtual value is the square root of the mean of the squares of the values during half a period) of the current and pressure as given by an alternating current ammeter and voltmeter, and be the phase displacement between c' and ', then the power is c'.v'. cos p, cos & being the power factor of the circuit. Equation (1) then becomes and the other equations are modified in a similar manner. An Law of the Chemical Meter. Either the chemical, electro-magnetic, or thermal action of a current is utilised in the construction of meters. electrolytic meter depends on the chemical action of a current of electricity, and is essentially a quantity meter. It follows, from the nature of electrolytic action, that such a meter can only be used for direct currents. current of electricity passes through certain liquids, such as dilute acids and solutions of metallic salts, chemical decomposition takes place. When a The current enters the electrolytic cell by the one conductor, the anode, and leaves it by the other conductor, the cathode, the electro-positive elements of the electrolyte being deposited at the cathode and the electro-negative elements at the anode. The amount of electrolytic decomposition, i.e. the amount of metal deposited or of gas evolved, depends on three factors, i.e. the strength of the current, the time-interval during which the current flow lasts, and the nature of the electrolyte, or the electro-chemical equivalent of the substance liberated. where M denotes in grammes the amount of metal or gas set free in T2 - T1 hours, Z is the electro-chemical equivalent expressed in grammes per amperehour, and c is the current in amperes, supposed constant during the small interval of time dt. or, the ampere-hours are proportional to the amount in grammes of the electrolytic deposit. The electro-chemical equivalent in grammes per amperehour of water is 3356, of mercury from a mercurous salt 7·466, of zinc 1·213, and of copper from a cupric solution 1.178. Thus 3.36 grammes of water are decomposed per Board of Trade unit at 100 volts, and in a water-decomposing meter the whole current to be measured flows in general through the electrolytic cell. In the case of chemical meters in which the electrolyte consists of a solution of a metallic salt, only a small fraction of the total current is used to effect the decomposition, as the amount of deposit would otherwise be excessively large, amounting per Board of Trade unit at 100 volts to 74-7 grammes for mercury and 12-13 grammes for zinc. In a mercury electrolytic meter, the fluidity of the metal is made use of for its measurement by volume instead of by weight. Electro-magnetic Action.-The electro-magnetic effect of a current flowing in a conductor is the external action which it produces, and is due to the creation of a magnetic field in the medium surrounding the conductor. A circuit conveying a current is acted upon by a magnet, or by an adjacent circuit traversed either by the same or a different current. This electrodynamic action between currents, or between a current and a magnet, is utilised in meters to produce a rotational or oscillatory motion, and to influence an already moving system, such as a pendulum. In motor meters the motion is one of rotation, and results from the interaction of two magnetic fields, generated either by two current systems, the one stationary and the other movable, or by one movable current system and a fixed permanent magnet. In oscillatory and pendulum meters the same electro-dynamic principle is involved, but in the former the moving system oscillates, and in the latter the periodic time of the pendulum is either increased or decreased. Such meters are at the present day used almost exclusively for direct currents, although, provided that they contain no iron, they are applicable to alternating current measurements. Alternating current meters are, however, based on the principle of induction, which is explained in Chapter VII. Laws of the Motor Meter with Brake. In watt-hour motor meters, the speed of rotation of which should be proportional to the power, the one magnetic field is due to the main current flowing in the circuit, and the other magnetic field is created by a current proportional to the supply pressure. The main current, which is the variable current to be measured, flows in one or two stationary coils, and the pressure current, which is approximately constant, traverses the revolving armature, having a commutator and brushes, the motor constituting an electro-dynamometer with a continuously revolving coil. In ampere-hour motor meters, the speed of rotation of which should be a measure of the current, the one field is variable, and is produced by the whole or a fractional part of the main current in the armature, and the other field is either fixed, and due to a permanent magnet, or it is variable with the current, and is created by a series electro-magnet. The turning moment, or driving torque, exerted on the armature is proportional to the product of the two magnetic fields. These two magnetic fields in a watt-hour motor meter are made dependent, the one on the main current, and the other on the pressure current, the latter being proportional to the supply voltage. In an ampere-hour motor meter, however, either the two magnetic fields are produced by the main current, or this current only gives rise to one magnetic field, and the other is then a fixed field, due to a permanent magnet. If C denote the main current in amperes and V the applied P.D. in volts, then for a watt-hour motor meter D= K1.C.V, for an ampere-hour motor meter with a permanent magnet D= K2.C, and for an ampere-hour motor meter with a series electro-magnet D= Kg.C", (7), (8), (9). The speed of rotation must always be proportional to the power or the current, and each value of the electrical magnitude must correspond to a perfectly definite speed, which must not vary, provided the particular electrical quantity remains the same. This condition of no acceleration is satisfied when the armature is at rest, and for it to be fulfilled when motion ensues, or, in other words, to obtain steady motion, an opposing torque must be provided which will equilibrate the torque exerted by the electrical system producing motion. If T denote the resisting torque, then the condition for steady motion is D-T=0. The retarding torque of the brake system employed in the meter must be an exactly similar function of the speed, as the driving torque is of the electrical magnitude. When steady motion has been established, if n denote the revolutions per minute of the armature when |