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The electrometers first used were a modified form of Coulomb's torsion instrument by Mr. Latimer Clark, which was replaced by a more sensitive arrangement of Peltier's electrometer which I had constructed. This in turn gave way to Sir William Thomson's quadrant electrometer, which under skilful manipulation is the most certain and convenient instrument, especially for demonstration, as a few yards of core will suffice for the experiment.

In practice an ordinary reflecting astatic galvanometer is generally used, in which case, instead of being guided by the deflections, we note the rush of current into the core when each drum alternately is connected to earth after a few moments' previous insulation.

I will first describe the method employed when an electrometer is used.

The length of wire to be operated on is immaterial, provided that the whole or a portion of it can be coiled on an insulated drum, and that between the parts coiled the surface of the core for a length of 6 or 8 inches can be cleaned and dried so as to prevent conduction.

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In the first case (when the whole can be coiled on a drum), one half is coiled off on a second drum, and the two drums A and B afterwards carefully insulated. The surface of the core CD between the drums is well cleaned and dried. The conductor is attached to an electrometer, and the two drums are connected to earth by an attendant at each drum, when by connecting the battery to the electrometer and core the whole will become charged; the battery is then disconnected from the electrometer, and the earth-wires simultaneously taken off the drums. It is best to leave the battery on until the earth-wires are removed from the drums.

The insulation of the drums A and B and the electrometer E should be such that no loss can be perceived after a few minutes, when, if the earth-wire be applied first to one drum and then to the other, the fault will be found on that drum which causes the greatest fall in the electrometer. The wire is coiled from the faulty side to the other, and the test repeated as often as is required. A mile of core with a small fault in it can by a little Phil. Mag. S. 4. Vol. 47. No. 314. June 1874. 2 E

practice be put right in an hour or two, involving no more waste than the insulator, which can be held between the fingers, and without even cutting the conductor. The position of the fault can be reduced into a length represented by CD by cleaning and drying the surfaces on each side of it.

It is obvious if C D represent a joint, it may be tested by this method with great ease. In fact so delicate is this test when used for joints in this way, that if A and B each be 2 or 3 miles in length, and C D, a length of 10 inches, be slightly heated above the portions on A and B, the difference in insulation will be readily perceptible on the electrometer when this portion is connected to earth. The limits to the delicacy of the test are only reached when A and B are absolutely insulated.

A very interesting lecture-experiment may be formed from these circumstances.

Let A F represent a length of insulated wire (a series of insulated Leyden jars would answer as well). Clean the outer surface at B,C,D, and E; charge the core on an electrometer, connecting the portions A B, BC, CD, DE, and EF to earth. Remove

A

B

C

D

E

the earth-wires and finally the battery wire. We can if we wish remove the whole of the charge from any of these sections without affecting the charge in any of the other sections.

Suppose we wish to remove the charge from the section DE; we first connect the earth-wire to the surface between D and E, and touch A or the electrometer if still left on, when the needle will instantly fall to zero; we remove the earth-wire and afterwards test the other sections, when we shall find that their charges have been unaltered; and if the spaces have been well cleaned and dried, we shall find that, although the conductor is continuous, no charge will flow into DE; the charge in E F can be noted on the electrometer; and although a section DE between it and the electrometer be empty, it will not communicate a particle of its charge to it.

In the second case, where the bulk would prevent the whole from being insulated, we should continue to coil the core upon an insulated drum until the fault disappeared-that is, until it was coiled on the drum. This is a useful method when dealing with "served core" at a cable factory.

When a galvanometer is used, the corrections are as for ordinary insulation-tests. The galvanometer is short-circuited; and A and B, whilst connected to earth, are charged as before. The earth-wires are removed and the short-circuit key opened. The drums are after a few moments connected to earth alternately,

when the loss of charge is soon rendered visible on both sides; but as the lengths on A and B may be very unequal, the rush

D

-EARTH

of current alone will not enable us to say on which side the fault may be; but by carefully watching the electrification for an equal time on each side, no difficulty will be found in fixing upon the drum containing the fault.

Two or more faults existing together form no embarrassment to the test. All to be done is, if the faults are of unequal magnitude, to remove the more extensive first, or to keep one side right by removing the faults as they are coiled over to it. In any case the battery-power required will vary with the magnitude of the fault and the sensitiveness of the instrument. Tamworth House,

Mitcham Common.

THE

LIII. A Contribution to the Theory of Resonators.
By LORD RAYLEIGH, M.A., F.R.S.*

HE following paper is an extract from a work on Acoustics on which I have been for some time engaged; on this account it is not quite self-contained, but will, I hope, be found sufficiently intelligible. Most of the materials have already been in my possession upwards of a year; and the interest of the subject seemed to render further delay in publication unadvisable. Unfortunately the rapid completion of my book has been much interfered with by various causes of a private character.

The operation of a resonator when under the influence of a source of sound in tune with itself, has been the subject of much misapprehension, from which even Helmholtz does not appear to have been free. In a dictionary of science we read:-"The loudness of the sound produced by a sounding body is augmented by bringing the body into the neighbourhood of a column of air which is capable of vibrating in unison with itself"+. Now this statement, though true in certain cases, as, for example, when a tuning-fork is held over a resonator, requires, to say the least, serious limitation. The exceptions, if not more frequent, are, * Communicated by the Author.

+ Dictionary of Science. Rodwell. Art. Resonance.

from a theoretical point of view, more important than the cases in which the rule holds good. Indeed I should prefer to reverse the statement, and say that the neighbourhood of a resonator in unison with a sounding body diminishes the loudness thereof.

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As the subject is rather a delicate one, we will begin by simplifying the conditions as much as possible. Let us suppose that the source of sound is a piston, A, imbedded in an infinite rigid plate. In the neighbourhood of A is another piston, B, backed by a spring, whose natural period is exactly the same as that of the vibration imposed upon A. ED is a rigid surface, enclosing A and B, and only allowing the communication of motion to the external atmosphere by means of a movable piston, C. The space enclosed by this surface is supposed to be occupied by gas devoid of inertia. It is easy to see that under these circumstances the piston C, though free to move, would yet remain at rest. For if the pressure within the vessel DE were in truth variable, the piston B would be acted upon by a force whose period was in exact agreement with that natural to itself, and its amplitude of vibration would increase without limit. The actual motion of B must be such as to leave the capacity of the vessel and the pressure constant; and then there is no force tending to move C, or rather to keep up the motion of C in the face of the dissipation which would be the necessary consequence of such motion. We may express this effect by saying that the condensations and rarefactions emitted by A are absorbed by B; and since if B were fixed, C would certainly move on account of the variation of pressure behind it, we see that the effect of the resonator is not to augment the sound, but, on the contrary, absolutely to stop it.

D

This conclusion does not depend on the rather artificial circumstances that we have here imagined. If the rigid walls represented by D E be removed, the same argument still shows that the pressure in the space surrounding A B must be invariable; and even if the inertia of the gas be restored, the general result will not be disturbed, provided that the distance A B is only a very small fraction of the wave-length, and that allowance is made for the inertia of the air in the neighbourhood of B in estimating the natural pitch of the resonator.

An instructive view of this question may also be obtained by means of the general principle of reciprocity established in

Chapter IV. Let A be a simple source of sound at a distance from the mouth of the pipe. We know that at a point B (not too near the mouth) whose distance from the closed end is ex

λ

actly there is no variation of density. From this it follows,

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end) instead of concentrated in one point. Here again the resonator may be said to absorb sound that would otherwise diffuse itself in surrounding space; or, if the non-emission of energy be thought incompatible with the existence of sound, we may say that the effect of the resonator is to dry up the source. For the present purpose it will be most convenient to use the expression "source of sound" in the sense of Chapter VIII., implying a given periodic production or abstraction of fluid, or something equivalent in its effect thereto, whether there be or be not emission of energy. The latter case will occur when there is on the whole no variation of pressure at the source itself.

We see then that, as far as external space is concerned, the neighbourhood of a resonator, far from augmenting the effect of a source, annuls it altogether, by absorbing the condensations and rarefactions into itself. The resonator acts, in fact, in the same way as would an equal and opposite source in the same position.

The principle here laid down, paradoxical as it will seem to many, is illustrated by the action of very simple apparatus, such as that employed by Quincke and others to stop sound of a particular pitch. Two varieties (figs. 1 and 2) are represented in

* See a paper by the author, "On some General Theorems relating to Vibrations," Proceedings of the Mathematical Society, June 1873.

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