way between these, at the point where the two opposite and correlative motions meet and neutralize one another, will be a node or point of rest. In this instance the pipe will give its lowest or fundamental note. If the force of the current be increased, a shorter wave may be set in action, a node being established at one-fourth of the whole length from the embouchure, and another at the same distance from the top. The pipe then speaks its first harmonic, the octave of the fundamental. By a further wind-pressure three nodes may form, the first of which is one-sixth from the embouchure, the third at a similar distance from the top, and the second halfway between the other two; the pipe giving its second harmonic a twelfth above the foundation. As the lengths of the waves are in the proportion,,, it is obvious the times of vibration will be 3, 2, 1, or corresponding to the series of natural numbers.

Midway between each consecutive pair of nodes there is a loop, or place of no pressure-variation. At any of these loops a communication may be established with the external air, without causing any disturbance of the motion. The loops are places of maxinium velocity, and the nodes those of maximum pressure-variation,

In stopped pipes a different law obtains; for the waves have clearly to traverse twice instead of once the length of the tube, being returned by the closed extremity. This fact also influences the position of the nodes. When the fundamental note is struck the column is unbroken, the only node being at the stopped end. In sounding the first harmonic another node is set up at one-third of length from the open end. With the second harmonic, a node forms at one-fifth of length from the open end, the second dividing the lower four-fifths into two equal parts. In any case, the stopped end must be a node, so that the second form of vibration of the open pipe, and all others which would render it the centre of a ventral segment, are excluded. Hence the harmonics of a stopped pipe follow the series of the odd numbers 1, 3, 5, &c. These relations between the fundamental note of a tube and its overtones were discovered by Daniel Bernoulli and are generally known as the Laws of Bernoulli. When the length of a tube exceeds its diameter considerably, the note is independent of the latter, and varies with the length alone. In both stopped and open pipes, the distance from an open end to the nearest node is a quarter-wave length of the note emitted. In the open pipe there is no further limitation; but in the case of the stopped pipe, the nearest node to the mouth

piece must also be distant an even number of quarter wavelengths from the stopped end, which is itself a node.

These distinctions hold good with pipes of which the bore is cylindrical or prismatic with parallel sides. It was, however, shown by Wheatstone that a pipe of conical bore, while giving out a similar fundamental note to one of the same length of cylindrical shape, differs as regards the position of the nodes when emitting one of its harmonies. The first node, for instance, in an open conical pipe is not in the middle, but some way towards the smaller end. In conical stopped pipes, therefore, or in instruments which resemble them, such as the oboe and bassoon, the even harmonics are not necessarily excluded. In the clarinet alone, of which the bore is truly cylindrical, they are not to be detected.

It appears from more modern observations that the Laws of Bernoulli require a correction which will be given in a later chapter.

Vibrations from Heat.

Trevelyan's Rocker.

A heated brass or copper bar so shaped as to rock readily from one point of support to another, is laid upon a cold

block of lead. The communication of heat through the point of support expands the lead lying immediately below in such a manner that the rocker receives a small impulse. During the interruption of the contact, the communicated heat has time to disperse itself in some degree into the mass of lead,

and it is not difficult to see that the impulse is of a kind to encourage the motion, and to produce sound.

Fig. 23.-Trevelyan's instrument. Cause of vibratory movements.

Sondhauss's Experiment.

When a bulb about of an inch in diameter is blown at the end of a narrow tube 5 or 6 inches in length, a sound is sometimes heard proceeding from the heated glass. It was proved by Sondhauss that vibration of the glass is no essential part of the phenomenon. An explanation of the production of sound has been given by Lord Rayleigh, which will be fully detailed in Chapter VIII.

Singing Flames. Although the series of small explosions by which the combustion of gas is marked have contributed some brilliant experiments to physicists, they can hardly as yet be said to be a practical source of musical sound. The flame of hydrogen has long been known as a means of originating a note; and of late a second form of the experiment has utilized the ordinary flame of coal-gas as a very delicate consonator and test for sounds produced extraneously in its neighbourhood. The former are termed singing, the latter sensitive, flames. The sensitive flames may best be considered elsewhere; but a short account of the singing-flame is required to complete the series of sound-producers.

It is easy, whenever a jet of hydrogen is inflamed, or even when coal-gas issues from a burner with some force, to hear an unmusical hissing or roaring accompanying the process. Even in this case, the noise often puts on a more or less definite form of vibration, and an impure note of coarse quality makes itself manifest. But if the jet be surrounded by a resonating tube, this has the power of reducing the irregular vibrations to a greater uniformity, and of selecting those which synchronise with its own vibration-period. The note in this case is often very pure and powerful. The general type of the process may be studied in the ordinary Bunsen burner. In this very convenient laboratory appliance, ordinary coal-gas is allowed to issue by a small orifice into a larger tube, perforated at its lower extremity with several

holes admitting more or less atmospheric air, the admission of which is regulated by a slide. An explosive mixture of gas and air is thus made, which is prevented from communicating with the source of gas by the cooling effect of the surrounding tube, just as occurs in the wire-gauze envelope of a Davy safety-lamp. If only a small amount of

Fig. 24.-Philosophical lamp or chemical harmonicon.

air is admitted the mixture burns with a semi-luminous flame and silently. But as the proportion of air is allowed to increase by opening the slider, the flame loses its luminosity and at length begins to roar. The combustion gradually becomes discontinuous, and is indeed composed of a series of short successive explosions. At length the mixture becomes too explosive even for this, it lights throughout its whole

length with emission of a single report, and carries the combustion down the tube to the small gas-jet itself. If the Bunsen burner, freely supplied with air, be introduced into a tall vertical tube, the roaring is toned to consonance and gives a pure note instead of an irregular roar. It is not always easy with quietly burning coal-gas in a tube to obtain any sound at all. But if the flame be reduced in size, and moved up and down the consonating tube, it may be observed to become tremulous at certain spots, and if left there, suddenly, by increase of the pulsations, bursts into sound. This action may be determined by the method first named as a means of exciting musical oscillation in a pipe, namely, by striking a slight blow with the palm of the hand on the upper orifice of the tube. The wave thus sent downwards is instantly taken up by the flame, and the note starts out, sometimes with such vehemence as to extinguish it altogether. it can also be set going by the voice. Many of the older works on chemistry and physics give the simple experiment with a hydrogen flame and a glass tube. Dr. Higgins names it in 1777; but Wheatstone was the first who attempted successfully to produce a definite scale of notes by this method. His instrument is now preserved in the Museum of King's College, and was recently shown at the Loan Exhibition at South Kensington. A series of glass tubes, with metal sliders for the purpose of tuning, are arranged in a row like the pipes of an organ. Within each of these is a fine conical tube pierced above with a capillary orifice. The lower end slides air-tight in a second tube connected with a supply of gas. In front is a short keyboard like that of a piano. Each key, on being depressed, lifts the small gas-jet from its position at the bottom of the tube to about the junction of the lower and two upper thirds, which, being a sensitive point, immediately originates the fundamental note of the tube.

The Pyrophone.-M. Kastner has endeavoured to utilize this principle in a musical instrument, but on a slightly different system. He says, "If two flames of a certain size be introduced into a tube made of glass, and if they be so disposed that they reach the third part of the tube's height, measured from the bottom, the flames will vibrate in unison. The phenomenon continues as long as the flames remain apart, but as soon as they are united, the sound ceases." By means of finger-keys the flames are united and separated so that a melody can be played. There is some uncertainty about the instrument, depending on the pressure of gas; so