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in hydrodynamics-it is, in fact, the motion of an aeriform fluid, in consequence of an impulse applied at one point of its mass. To render the question more susceptible of analytic treatment, mathematicians imagine a cylindrical column of the fluid, and inquire when one branch is put in motion what will take place. in the adjoining one, under the supposition that the particles are destitute of gravity, and that the column is enclosed in a canal, where it may advance or recede without friction, and where the sides prevent any lateral motion.

This case is analytically investigated by Mr. Peirce. The general problem would involve an examination of the motion in every direction; but the analysis here is highly incomplete, while experience has confirmed its results in the special case which, simple as it may appear, leads to a partial differential equation, to integrate which, recourse has been had to particular hypotheses, which are fortunately not wide of the truth. Its complete solution in a dynamical point of view, would force us to treat indifferently the case in which the particles describe large oscillations, and those where their motion is all but insensible; but with this generality, it is unsusceptible of a solution. If, on the contrary, we only consider the case where the motion of each transversal section of the column is extremely small, as is nearly the case in the propagation of sound, the differential equation obtained becomes simplified, and admits of a general integral, the interpretation of which conducts to various acoustical laws, which experience confirms to a certain point, if we take into account the increment of temperature of the layers in consequence of the compressions they undergo. It is in this last mode that Laplace treated the question; basing bis investigation upon Gay Lussac's and Welter's experiments, he found for the velocity of the propagation of sound in the air, a result differing but little from the one furnished by experiment.

Mr. Peirce considers the question only as it was treated before Laplace, and enters into every desirable development. As we cannot here follow him through the resolution of differential equations, we shall confine ourselves to an expression of our pleasure on seeing the chapter which, without making the work an analytical treatise, at least affords the student an opportunity of seeing how the calculus is applied to physics, and may be employed in the discovery of facts which seem essentially the province of experiment.

In the third chapter are applied the formulæ obtained in the preceding. Results are immediately deduced for the velocity

etc.

of the propagation of sound in various gases, which experience, in most cases, nearly verifies. The law is, that these velocities are directly as the densities of the gases at the same temperature. To produce a sound, a substance need not possess any especial characteristic. The generation of sound depends, as we have already seen, upon the physical or molecular constitution of substances; and this also seems under other circumstances to play a conspicuous part in the phenomena of heat, of electricity, At a certain period, a body receives an impulse which is gradually diffused through all its parts in consequence of this physical constitution or of the resulting elasticity. Hence there ensues, in the whole mass, an oscillatory motion which is communicated to the air without change- that is, without loss of velocity-and is propagated in this medium which conveys it to the ear, when the latter, if the vibrations are performed with. sufficient quickness, perceives a peculiar sensation. This will, with slight modifications, be a cry, a sound, or a noise. A cry when it ceases instantly, a sound when the cry is continued, and a noise when consisting of cries or sounds in dissonance.

We regret Mr. Peirce has not awarded to the term acoustics the generality ascribed to it by men of science in the present day, who, expanding the meaning implied in the Greek, from which it is derived, view it as the science of vibrations. This enlarged frame would have been the more desirable since the discoveries of M. Savart, who, by studying the mute vibrations of liquid veins, has partially ascertained what occurs in wind instruments when sounded. It was in prosecuting these inquiries, also, that he had occasion to remark the strange influence exercised by a violin, or violoncello, note upon a vein or sheet of water.

The second part treats of musical sounds of the number of vibrations requisite for their respective production, of the relations between the various notes and intervals, of the means whereby they are produced in different instruments, of the ancillary circumstances, and of the determination of laws to aid in constructing and improving musical instruments. Any one who has seen a harp, will recollect that as the strings decrease in length the sounds increase in intensity, and this inverse ratio forms the basis of the researches made in this branch of acoustics. It is a curious fact, that in instruments whose length, like the trumpet's, is not altered by lateral apertures, the tube only serves to strengthen the sound produced by the lips at the embouchure. There are three classes of musical instruments. In the first the sound is produced by the vibrations of a solid body;

in the second it is generated by those of a fluid; and these two elements are combined in the third class. The wooden instruments of the Indians; the harmonica with glass plates or tubes; the violin in its various forms, and the piano-forte, appertain to the first group; the flute, trumpet, trombone, and sirène, to the second; and the clarinet, the hautbois, the accordion, the German harmonica, the jews-harp, perhaps the hunting-horn, and more especially the organ, to the third.

The organ pipe is formed of two very distinct parts; the reed that produces the sound, and the pipe destined to augment its intensity without changing the pitch. The former is a tube of prismatic or cylindrical shape, open at both ends, and on one side presenting a rectangular opening, where a metallic tongue coincident in form is so fixed by one of its edges as to move in the aperture without touching the other three. A blast of air forced through the tube sets this tongue in vibration, and is, at the same time, alternately intercepted and suffered to escape through the rectangular opening. The air and metallic body thus perform iso-synchronous vibrations, and sound in unison.

This same principle has been recently applied to the construction of a new and exquisitely toned instrument aptly entitled the orgue expressive. It consists of a chord so vibrating in the tube as to produce the same sound with the vibrations of the surrounding air. This, unlike other keyed instruments, is susceptible of temperament, and will doubtless be much used when brought to perfection. Imagine a string stretched between two laminæ of metal or wood, like the tongues of the anches libres. At one end, a blast of air sets it in vibration, while it may be shortened at the other by the fingers, as in the violin, or by stops. It is in other words a violin where a blast of air is substituted for a bow, and is to the fiddle, what to the common harp is the Æolian, that favorite and beautiful illustration of Jean Paul Richter's, sounding under atmospheric vibrations in lieu of fingers.

For many other important facts, we must refer our readers to the volume in which they are so copiously enumerated; if, indeed, any further incitement be necessary to direct their attention to so inviting a topic. Of all human accomplishments, music seems the most unrivalled. We are bound to it by taste and by feeling, by sympathy and by association. In every ear, in every bosom, its universal language finds an echo, an inter

*This instrument was known to the Chinese some centuries before its invention in Europe.

+ Comptes Rendus de l'Académie des Sciences, 1835, 2de Semestre, p. 367.

pretation. On its melodious wings, we float back to the past, its sonorous joy gladdens the present, and in its stirring harmonies we see the future mirrored. The colors of the painter's masterpiece obey no mortal law; for them are neither seasons nor death; the leaf falls not, and the bloom is unfading. The creation of the chisel seems a mockery of human life and beauty. The statue, greater than its author, obscures the name of him it outlives, while the monumental edifice testifies to the reality of the universal doom. These all live; but the rainbow hues of melody, the majesty of harmonic inspiration, share the destinies of the artist, the audience, and the composer. The uttered note is diffused through endless time, but imperceptibly. The music of an age is its voice, and the tone yields to time. Therefore should we regard music as dwelling in our hearts, to cease with their pulsations, and love the note which a coming generation may receive with as little favor as many a philosophical doctrine has found, upon the demise of its author, in his successor's minds.

Far is our philosophy from prescribing that, whilst the soulmoving symphony or aerial waltz are reacting upon the very orchestra which lends life and brilliancy to the thought of Beethoven, or the smile of Strauss, one should restlessly inquire how this harmony is produced, or seek to know by what miraculous. organization the inanimate string, or faint breath, stir up the soul. But there are moments when we may ask such questions, and wish for so responsive an oracle as Mr. Peirce. And if the spirit joys in the influence of music, not inferior will be our mental satisfaction when we come to understand the mechanism of sound, and to appreciate the simplicity of the means employed by the Almighty to accomplish phenomena, apparently so complicated.

In addition to the numerous and interesting details which are appropriately embodied in this portion of his work, Mr. Peirce has here described and illustrated by drawings, those magical harmonic features assumed by sand strewed over vibrating plates, and to which we marvel that the term visible music should not have been assigned. These fanciful shapes of sound being little known to a majority of readers, will doubtless excite interest and admiration. The laborious process of copying them with a pencil, which Chladni employed in obtaining the sixty or seventy figures he has bequeathed us, has been simplified by M. Savart, who strews the discs with lithmus in place of sand, and, when the figures are formed, carefully superposes a sheet

of white paper, rendered adhesive by gum water. To this the blue particles adhere, and form these fantastic shapes; and the labor of days becomes the operation of a few minutes. The parts where an accumulation of sand takes place, are called nodal lines. When the plate vibrates, these are at rest, and the particles are heaped up from the places of agitation. The sounds called harmonics which a skilful player draws from the violin, are formed by placing the finger on some one of the nodal points of the vibrating string. A slip of paper, cut in the shape of a reversed V, and made to ride upon a musical cord in vibration, will find the nearest node and there sit at rest. The same is true of a rod or bar, and a plate may be regarded as composed of a quantity of parallel rods. The discs employed in these experiments should be perfectly homogeneous, and M. Savart has given the preference to brass, as the substance most susceptible of uniform density and polish. Plates of this metal are preferable to glass discs the latter being brittle. Various forms are employed, and certain laws and properties have been ascertained, with much patience and ingenuity. Whether the plate be square, or round, or oval, or triangular, the lines composing the figures have been found never to intersect. They bend, and assume in the circle, for instance, the appearance of radii, while in reality they are curved at the centre, which, like the asymptote, they approach but never touch. The experiments of Wheatstone and Chladni have been continued of late years, and the philosophical transactions are full of rich and varied specimens of these acoustical figures. Since certain principles have been discovered respecting their formation, are we to despair of seeing a symphony or concerto one day delineated in these magical outlines? A note or an accord revealed by every graceful curve in nature, were fresh sources of inspiration to the composer.

In this captivating science, each day reveals some new phenomenon, as beautiful as inexplicable, and its delighted yet puzzled votaries grope in the dark amongst innumerable sounds and vibrations. Is it not singular, in this age, a science, philosophically speaking, in its infancy? And stranger yet seems the infatuation of those who consecrate their lives to a branch of knowledge centuries may not be able to systematize. There must be in the pursuits of science a fascination superior to the intensest allurements of pleasure. The maddest disciple of Epicurus would forswear enjoyment, did its Hierophants exact one half the devotion the naturalist and the student voluntarily pay

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