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Rh WATTIGNIES, a village of France 5½ m. S.S.E. of Maubeuge, the scene of a battle in the (q.v.), fought on the 15th–16th October 1793. The Allied army, chiefly Austrians, under Coburg, was besieging Maubeuge, and the Revolutionary army, preparing to relieve it, gathered behind Avesnes. Coburg disposed a covering force of 21,000 astride the Avesnes-Maubeuge road, 5000 on the right with their flank on the Sambre, 9000 in the centre, on a ridge in an amphitheatre of woods, and 6000 on the left, chiefly on the plateau of Wattignies. A long line of woods enabled the Republican commander, Jourdan, to deploy unseen; 14,000 men were to attack the right, 16,000 were sent towards Wattignies, and 13,000 were to demonstrate in the centre till the others had succeeded and then to attack. Meantime (though this part of the programme miscarried) the Maubeuge garrison, which was almost as strong as its besiegers, was to sally out. Even without the Maubeuge garrison Jourdan had a two-to-one superiority. But the French were still the undisciplined enthusiasts of Hondschoote. Their left attack progressed so long as it could use “dead ground” in the valleys, but when the Republicans reached the gentler slopes above, the volleys of the Austrian regulars crushed their swarms, and the Austrian cavalry, striking them in flank, rode over them. The centre attack, ordered by Carnot on the assumption that all was well on the flanks, was premature; like the left, it progressed while the slopes were sharp, but when the Republicans arrived on the crest they found a gentle reverse slope before them, at the foot of which were Coburg's best troops. Again the disciplined volleys and a well-timed cavalry charge swept back the assailants. The French right reached, but could not hold, Wattignies. But these reverses were, in the eyes of Carnot and Jourdan, mere mishaps. Jourdan wished to renew the left attack, but Carnot, the engineer, considered the Wattignies plateau the key of the position and his opinion prevailed. In the night the nearly equal partition of force, which was largely responsible for the failure, was modified, and the strength of the attack massed opposite Wattignies. Coburg meanwhile strengthened his wings. He heard that Jourdan had been reinforced up to 100,000. But he called up few fresh battalions, and put into line only 23,000 men. In reality Jourdan had not received reinforcements, and the effects of the first failure almost neutralized the superiority of numbers and enthusiasm over discipline and confidence. But at last, after a long fight had eliminated the faint-hearted, enough brave men remained in the excited crowds held together by Carnot and Jourdan to win the plateau. Coburg then drew off. His losses were 2500 out of 23,000, Jourdan's 3000 out of 43,000.  WATTLE AND DAB, a term in architecture (Lat. cratitius) applied to a wall made with upright stakes with withes twisted between them and then plastered over. It is probably one of the oldest systems of construction; the Egyptians employed the stems of maize for the upright stakes; these were secured together with withes and covered over with mud, the upper portions of the maize stems being left uncut at the top, to increase the height of the enclosure; and these are thought by Professor Petrie to have given the origin for the cavetto cornice of the temples, the torus moulding representing the heavier coil of withes at the top of the fence wall. Vitruvius (ii. 8) refers to it as being employed in Rome. In the middle ages in England it was employed as a framework for clay chimneys.  WATTMETER, an instrument for the measurement of electric power, or the rate of supply of electric energy to any circuit. The term is generally applied to describe a particular form of electrodynamometer, consisting of a fixed coil of wire and an embracing or neighbouring coil of wire suspended so as to be movable. In general construction the instrument resembles a Siemens electrodynamometer (see ). The fixed coil is called the current coil, and the movable coil is called the potential coil, and each of these coils has its ends brought to separate terminals on the base of the instrument. The principle on which the instrument works is as follows: Suppose any circuit, such as an electric motor, lamp or transformer, is receiving electric current; then the power given to that circuit reckoned

in watts is measured by the product of the current flowing through the circuit in amperes and the potential difference of the ends of that circuit in volts, multiplied by a certain factor called the power factor in those cases in which the circuit is inductive and the current alternating.

Take first the simplest case of a non-inductive power-absorbing circuit. If an electro-dynamometer, made as above described, has its fixed circuit connected in series with the power-absorbing circuit and its movable coil (wound with fine wire) connected across the terminals of the power-absorbing circuit, then a current will flow through the fixed coil which is the same or nearly the same as that through the power-absorbing circuit, and a current will flow through the high resistance coil of the wattmeter proportional to the potential difference at the terminals of the power-absorbing circuit. The movable coil of the wattmeter is normally suspended so that its axis is at right angles to that of the fixed coil and is constrained by the torsion of a spiral spring. When the currents flow through the two coils, forces are brought into action compelling the coils to set their axes in the same direction, and these forces can be opposed by another torque due to the control of a spiral spring regulated by moving a torsion head on the instrument. The torque required to hold the coils in their normal position is proportional to the mean value of the product of the currents flowing through two coils respectively, or to the mean value of the product of the current in the power-absorbing circuit and the potential difference at its ends, that is, to the power taken up by the circuit. Hence this power can be measured by the torsion which must be applied to the movable coil of the wattmeter to hold it in the normal position against the action of the forces tending to displace it. The wattmeter can therefore be calibrated so as to give direct readings of the power reckoned in watts, taken up in the circuit; hence its name, wattmeter. In those cases in which the power absorbing circuit is inductive, the coil of the wattmeter connected across the terminals of the power-absorbing circuit must have an exceedingly small inductance, else a considerable correction may become necessary. This correcting factor has the following value. If $$\textrm T_S$$ stands for the time-constant of the movable circuit of the wattmeter, commonly called the potential coil, the time constant being defined as the ratio of the inductance to the resistance of that circuit, and if $$\textrm T_R$$ is the time-constant similarly defined of the power-absorbing circuit, and if $$\textrm F$$ is the correcting factor, and $$\textrm p = 2\pi$$ times the frequency n, then,

Hence an electrodynamic wattmeter, applied to measure the electrical power taken up in a circuit when employing alternating currents, gives absolutely correct readings only in two cases—(i.) when the potential circuit of the wattmeter and the power-absorbing circuit have negligible inductances, and (ii.) when the same two circuits have equal time-constants. If these conditions are not fulfilled, the wattmeter readings, assuming the wattmeter to have been calibrated with continuous currents, may be either too high or too low when alternating currents are being used.

In order that a wattmeter shall be suitable for the measurement of power taken up in an inductive circuit certain conditions of construction must be fulfilled. The framework and case of the instrument must be completely non-metallic, else eddy currents induced in the supports will cause disturbing forces to act upon the movable coil. Again the shunt circuit must have practically zero inductance and the series or current coil must be wound or constructed with stranded copper wire, each strand being silk covered, to prevent the production of eddy currents in the mass of the conductor. Wattmeters of this kind have been devised by J. A. Fleming, Lord Kelvin and W. Duddell and Mather. W. E. Sumpner, however, has devised forms of wattmeter of the dynamometer type in which iron cores are employed, and has defined the conditions under which these instruments are available for accurate measurements. See “New Alternate Current Instruments,” ''Jour. Inst. Elec. Eng.'', 41, 227 (1908).

There are methods of measuring electrical power by means of electrostatic voltmeters, or of quadrant electrometers adapted for the purpose, which when so employed may be called electrostatic wattmeters. If the quadrants of an (q.v.) are connected to the ends of a non-inductive circuit in series with the power-absorbing circuit, and if the needle is connected to the end of this last circuit opposite to that at which the induction less resistance is connected, then the reflexion of the electrometer will be proportional to the power taken up in the circuit, since it is proportional to the mean value of (A–B) {C–½ (A+B)}, where A and B are the potentials of the quadrants and C is that of the needle. This expression, however, measures the power taken up in the power-absorbing circuit. In the case of the voltmeter method of measuring power devised by W. E. Ayrton and W. E. Sumpner in 1891, an electrostatic voltmeter is employed to measure the fall of potential V1 down any inductive circuit in which it is desired to