mail FREQUENCY AND HIGH POTENTIAL CURRENTS. 387

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the resistance is —, and with the same current density the cur-n

rent would be n 2 G ; hence the heating effect is n 3 times greater,while the surface is only n 2 times as great. For this reason verylarge arcs would not emit any rhythmical sound even with a verylow frequency. It must be observed, however, that the soundemitted depends to some extent also on the composition of thecarbon. If the carbon contain highly refractory material, this,when heated, tends to maintain the temperature of the arc uni-form and the sound is lessened ; for this reason it would seemthat an alternating arc requires such carbons.

With currents of such high frequencies it is possible to obtainnoiseless arcs, but the regulation of the lamp is rendered ex-tremely difficult on account of the excessively small attractionsor repulsions between conductors conveying these currents.

An interesting feature of the arc produced by these rapidlyalternating currents is its persistency. There are two causes forit, one of which is always present, the other sometimes only.One is due to the character of the current and the other to aproperty of the machine. The first cause is the more importantone, and is due directly to the rapidity of the alternations.When an arc is formed by a periodically undulating current,there is a corresponding undulation in the temperature of thegaseous column, and, therefore, a corresponding undulation inthe resistance of the arc. But the resistance of the arc variesenormously with the temperature of the gaseous column, beingpractically infinite when the gas between the electrodes is cold.The persistence of the arc, therefore, depends on the inability ofthe column to cool. It is for this reason impossible to maintainan arc with the current alternating only a few times a second.On the other hand, with a practically continuous current, the arcis easily maintained, the column being constantly kept at a hightemperature and low resistance. The higher the frequency thesmaller the time interval during which the arc may cool and in-crease considerably in resistance. With a frequency of 10,000per second or more in an arc of equal size excessively small varia-tions of temperature are superimposed upon a steady temperature,like ripples on the surface of a deep sea. The heating effect ispractically continuous and the arc behaves like one produced bya continuous current, with the exception, however, that it maynot be quite as easily started, and that the electrodes are equally