the diagram, which, though somewhat different in appearance, are substantially identical.

In both cases the sound enters, or rather is free to enter, at A; and at B finds itself at the mouth of a resonator BC, whose natural pitch agrees with its own. Under these circumstances the sound is absorbed, and there is no vibration propagated along BD. It is clear that the cylindrical tube may be replaced by any other resonator of the same pitch (fig. 3) without prejudice to the action of the apparatus. The ordinary explanation by the interference (so called) of direct and reflected waves would then not apply, at any rate not without extensive modification.

The nature of the influence of a resonator on a simple source of sound in the immediate neighbourhood of its mouth will now be tolerably clear; the difficulty is rather to explain why the result

Fig. 3.

is so different in the common experiment with the tuningfork. Yet it is evident that a vibrating tuning-fork is something very different from a simple source of sound. The advancing face of either prong may be treated as a diffused source tending to produce a condensation; but this is always accompanied by an equal and opposite source due to the retreating face. Even if we confine ourselves to a single vibrating bar, the source cannot be approximately represented as any thing simpler than a double source, composed of two neighbouring equal and

D

opposite sources; the representation of the complete tuningfork will require at least four simple sources. The fact is that the simple source of theory, or even a reasonable approximation thereto, is rarely met with in practice. When a solid body, such as a string, bar, or bell, vibrates, there is usually but little change of volume; and thus the algebraic sum of the sources is approximately zero, the effect depending mainly on the different situation of the positive and negative parts. It is true that the resonance-board of a musical instrument may be regarded as more nearly a simple source, in the sense that the principal component parts have the same sign; but the diffusion would generally be great enough to separate it considerably from the ideal simple source concentrated in one point.

In order to see how materially the action of a resonator depends upon the character of the source, we need only take the case of a double source, whose components are sufficiently far apart to be dealt with separately, but not so far that the interval amounts to a sensible fraction of the wave-length. In consequence of the last supposition, the joint effect at a moderate distance is but a very small part of what would be due to either component separately; the fluid emitted by the one is instantly sucked up by the other, and vice versa. Now suppose that a resonator of the same pitch is presented to one of the component sources. Its effect, we have seen, will be to neutralize the source in question, and thus to leave the other free. The result is a considerable augmentation of loudness, which, however, to the eye of theory still appears as the absorption rather than as the production of sound.

In general, whenever a resonator is so situated that there would be at its mouth, supposed to be closed, a sensible variation of pressure due to external sources, the opening of the mouth will entail a great alteration in the mechanical conditions. There will be developed such a transfer of air backwards and forwards through the mouth as would, if it existed alone, produce a variation of pressure at the mouth equal and opposite to that above spoken of. Until this condition of things is attained (that is, until the total pressure at the mouth is constant) the vibration of the resonator must increase. Now the characteristic of a resonator is that vibrations escape from it slowly, that a large vibration within it corresponds to but a small variation of pressure at the mouth. Hence it follows that, under the supposed circumstances, there will be a large flow of air through the mouth, or, in other words, that the resonator will behave as a simple source of considerable power. If the system of external sources be of such a character as to produce by itself little effect, the operation of the resonator is attended by an augmentation of

loudness; otherwise it may happen that a part or the whole of the previously existing sound is extinguished.

The first case is that of the tuning-fork. In consequence of the comparative thinness of the prongs, the positive and negative sources nearly neutralize each other at a little distance, the air displaced by the advancing faces readily taking advantage of the room afforded by those retreating. Although the fluid moves nearly as though it were incompressible, there is in consequence of the inertia a certain variation of pressure, of which a resonator whose mouth is suitably placed can take advantage.

One of the best examples of this use of a resonator is afforded by a vibrating bar of glass or metal held at the nodes. A strip of plate glass about a foot long and an inch broad, of medium thickness (say inch), supported at about 3 inches from the ends by means of string twisted round it, answers the purpose very well. When struck with a hammer it gives but little sound except overtones; and even these may be nearly got rid of by choosing a hammer of suitable softness. This is a consequence of the small dimensions of the bar in comparison with the wavelength, which allows of the easy transfer of air from one side to the other. If now the mouth of a resonator of the right pitch* be held over one of the free ends, a sound of considerable force and purity is obtained by a well-managed blow. In this way may be constructed an improved harmonicon, with tones much graver than would be possible without resonators. In the ordinary instrument the wave-lengths are sufficiently short for the bar to communicate vibrations to the air independently.

The reinforcement of the sound of a bell by a resonator in a well-known lecture-experiment is an example of the same mode of action.

The other part of the theory (the neutralization of a simple source) is not so easily illustrated experimentally, for reasons already referred to. It usually requires more elaborate appliances to produce a simple than a compound source; and then there is a certain incongruity in the use of the word simple. The following experiment, however, deserves mention. Suppose that, in the manner just explained, we have obtained a pure sound by the combination of a resonator with a vibrating bar. In this arrangement the mouth of the resonator is the effective source; and according to theory we should expect that the sound would be again extinguished by the presentation to the first of a second resonator, held in such a position that the bar does not act upon

*To get the best effect the mouth of the resonator ought to be pretty close to the bar; and then the pitch is often decidedly lower than it would be in the open. The final adjustment may be made by varying the amount of obstruction.

it directly. This experiment succeeds perfectly: however strongly the bar be excited, there is but little sound heard. If about a second after the stroke the resonator be suddenly withdrawn, the swelling out of the sound is very striking, and proves conclusively that the presence of a resonator does not always augment the loudness of a sound. The second resonator may be held in such a position that it would by itself have little effect. The experiment may also be made with a tuning-fork held in the hand, or by some soft support.

The reader may perhaps be inclined to suppose, as I did at first, that the theory might be tested in the case of a simple tone produced in one room and heard in the next through a hole in the intervening wall. But a little consideration will show that the requirements of theory are not properly satisfied by this arrangement, in fact that the intensity of the source (at the hole) is itself largely dependent on the presence or absence of the resonator. Thus, if we suppose that the hole is small and the original source distant, the pressure in the neighbourhood of the hole on the first side of the wall will be nearly the same as if the hole were stopped; so that if the inertia of the air near the hole can be neglected, we have on the second side a given pressure, and not, as the theory assumes, a given flow. With a tuning-fork mounted on a resonance-box and held rather close to the hole, I have, however, succeeded in proving that the sound coming through the wall may sometimes be diminished by the neighbourhood of a resonator.

In order to obtain more exact ideas of the operation of a resonator, let us take one whose mouth is furnished with an infinite flange, and which vibrates in response to a source of any kind at a distance. The whole potential outside the resonator may be divided into two parts-one of which is the same as if the mouth of the resonator were closed, and the other the same as if there were no external source, but the motion at the mouth were maintained according to the same law as actually obtains. Over the area of the mouth, which is supposed small, the potential of the former part will be nearly constant, and may be denoted by yo. For the second part, o, we have already had occasion to form the expression

if X represent the total current.

X,

Of these two terms the first

depends upon the inertia of air outside the mouth, whose effect is equivalent to an addition to the mass of the vibrating parts

of the resonator. We here suppose that the natural pitch of the resonator, agreeing with that of the external source, is estimated after allowance for this correction, and may then leave this term out of account. Otherwise, of course, the condition of synchronism is not properly satisfied. In order that the force tending to increase the vibration without limit may vanish, we must have

When the pitch is given, the total current through the mouth of a resonator in synchronism with the source is independent of the form of the resonator, provided that the mouth is furnished with the flange. In the absence of a flange, the relation between X and would be sensibly altered. The effect of the resonator in external space depends only on X, and is therefore always the same, but inside the reservoir will be inversely proportional to the capacity S. Hence, in order to get a great internal effect, the reservoir should be made small, and the pitch kept down to the required point by elongating the neck.

It is proper to state that the preceding theory is at variance with that given by Helmholtz*, who treats the potential o as vanishingly small in comparison with that due to the resonator Po. Helmholtz is thus led to the conclusion that a simple source would be intensified by the neighbourhood of a resonator. If it be thought strange that the very powerful motion within the resonator should produce no more effect than the external source, it must be remembered the small tendency to escape is the very reason of the accumulation.

LIV. On Telegraphic Signalling with Condensers.
By OLIVER HEAVISIDE, Esq.†

GIVEN

IVEN an insulated conductor called the line connecting two places, there may be said to be in present use two distinct methods by which signals made at one end of the line are observed at the other. The first, which is that in most general use, is to connect the line with one end of the coils of an instrument affected by electric currents, and the other end of the coils with earth. The battery at the sending-end being also placed between the line and the earth, a circuit is established, through which a current will flow so long as the battery and instrument remain undisturbed. This current will in a short time after the first mo*Tonempfindungen, Beilage ix.

+ Communicated by the Author.