peaceful. They want nothing that does not honestly belong to them. All they wish is that the Treaty of Prague should be rigorously observed. By this treaty Prussia is bound to allow the States of South Germany to form themselves into an independent Confederation, and she is also bound to refer the question of the nationality of North Schleswig to the decision of the North Schleswigers themselves. All that France and Austria ask is that Prussia will do what she has engaged to do, and will be kind and friendly to the Danes, and will not interfere directly or indirectly in the affairs of South Germany. This is all that is asked, and very moderate it seems. Prussia is only to do what she is bound to do. But no one who knows the circumstances believes that the case is quite so simple as this statemeut of the facts might lead us to suppose. How far does North Schleswig extend? The Danes had a dim notion that it must be large enough to include Alsen and Duppel; but Prussia laughed at the notion that she could be called on to give up positions that she had spent much and endured much to win. And at last the Danes, who had taken to very grand ways and seemed like heroes on the eve of a gigantic conflict, have had orders to be tamer and more sensible; and the probabilities are that the North Schleswig business will not henceforth give much trouble. The Danes will be told by their big friends at Vienna and Paris to keep quiet, and they are sure to obey. But this only makes the crisis more dangerous as regards South Germany. In the matter of Schleswig, it is very hard to prove Prussia in the wrong. No attempt, therefore, is to be made to cast odium on Prussia for what she has done to Denmark; and the attention of men is concentrated on that which is to be made the main grievance, the relations of Prussia to Southern Germany. If the Treaty of Prague is to be observed to the letter. the Northern States are to be kept apart from those States which form what was meant to be the Southern Confederation. The Treaty of Prague contemplates these Southern States as independent of Prussia, and recognises Germany as divided into three sections. To aim at the unity of Germany is, therefore, to violate the Treaty of Prague, and to uphold the Treaty of Prague is to oppose the unity of Germany. The Prussian papers naturally talk much less pacifica ly than the EMPERORS do. Toey sy very plainly that a sort of challenge his been given to Prussia and to Germany, and they are quite ready to accept it. Out of this state of things war might grow so easily that it would be much more probable than not that a few months will see the beginning of a campaign, were it not that there is no overt act of defiance which either party can feel its If impelled to take. If France is pacific, Prussia in her turn may be passive. She is not called on, in her own defence or for her own honour, to violate any article of the Treaty of Prague. She does not wish that the States of the South should change their position at present. She much prefers that they should remain outside the Confederation of the North, which already contains many adverse and unreliable, and perhaps even some dangerous, members. Meanwhile the effect in the South of the league between France and Austria can scarcely fail to be favourable to Prussia. The South Germans see clearly before them the choice of being the vassals of France or the allies of Prussia. An alliance with Prussia is not exactly the alliance they would wish for. They do not like Prussian officials, or the Prussian conscription, or the Prussian system of high-handed government. But to Germans anything is better than not being German. The necessities of daily life, the interchange of commodities and material interests in every shape, will add continually to the practical union which will subsist between the North and the South. The Prussians cannot avoid seeing that time is working in their favour, and that they can afford to wait, and need not wish to violate the Treaty of Prague in any flagrant manner. In this lies the real hope of peace. Why should any one begin to take a step that must lead to war? Prussia, in letting things remain as they are, is getting what she wants, and France and Austria are pledged not to interfere if Prussia lets things go on as they are. The only thing is that the Emperor of the FRENCH speaks of his recent policy as a decisive one. France, he says, has resumed her proper place in Europe; but how has she done this? If France is to wait and do nothing as long as Prussia keeps quiet, and if this keeping quiet is obviously and avowedly preparing the way for Prussia to exercise a supremacy, in one shape or other, over the whole of Germany, how can it be said that France has resumed her proper place, or got any advantage whatever? Prussia has lost nothing and France gained nothing by the meeting at Salzburg; and if this is so, the effect which that meeting was intended to produce is at an end. Prussia has not yielded anything, nor has France done any thing on which she can pride herself. And in this lies the great danger of war- that France is thus in a manner defeated by peace. But this is, we may hope, a somewhat remote danger; it is not like the danger, or rather the certainty, of war that would exist if there were some distinct act which Prussia was known to be desirous to do, and which France distinctly forbad her to do. Things may remain quiet until the general feelings of Frenchmen and Germans are a little altered, until internal changes take place in one country or the other, until France can do something in some other quarter to make it evident that she has resumed her proper position. Still the state of things is exceedingly critical, and we must not allow ourselves to be too readily cheered by the pacific speeches of the EMPEROR. PROFESSOR TYNDALL ON SOUND.* We cannot say that these lectures strike us as equally interesting with the previous series on Heat. Not that they exhibit by comparison any defect in the lecturer's treatment of the subject, in the fluency of his language, or the clearness of his experiments. The falling off, if any, is due to the subject itself. In dealing with the phenomena of sound we find ourselves shut up at once in a comparatively restricted area. The medium within which we move is more limited, and affords less scope for widespread and glowing speculations. The phenomena of light and heat connect us immediately with the furthest range of cosmical forces, and carry us on the wings of imagination to the extremes of infinite space. But the facts relating to sound lie essentially within the narrow bounds of our atmosphere. They are not cosmical, but terrestrial. Imagination itself is distanced the moment we try to pass beyond the limited aerial envelope which swathes our planet, and which conveys to us all we are capable of knowing of the nature of sound. ObserFrom the Saturday Review. vation gives us direct evidence of the agencies of light and heat affecting worlds of untold remoteness from our own, and theory PROFESSOR TYNDALL deservedly holds can roam at will over realms of space witha place among the foremost of our lec-out any misgiving that the analogies of turers on science. His style is clear, connected, and animated. He has the art of seizing at once the most essential and prominent features of his subject, while at the same time throwing himself into the mental position of his auditors, so as to appear a fellow-learner with them. It is thus that he seems to make himself a link of intelligence between them and the body of facts under illustration, and to enable them, so to say, to see through the medium of his own mind. His experiments are unsurpassed in neatness, and never miscarry. The lecturer's voice and manner join with the habitual perspicuity of his language in engaging the attention and kindling the intelligence of his hearers. A certain glow of enthusiasm acting upon a fine imagination and a happy command of language gives an air of poetry to what in common hands is often bald, prosaic, and uninviting in the extreme, and throws an artistic finish over the hard substratum of fact. We are glad to have the opportunity of studying in print the series of lectures on Sound which during the last season drew full and attentive audiences to the lecture room of the Royal Institution. Sound. A Course of Lectures delivered at the Roval Institution of Great Britain. By John Tyndall, LL.D., F.R.S., &c. London: Longmans & Co. 1867. physics as taught us by experience here will fail us wheresoever the eye can extend its range. But what of the nature of sound, when fancy ventures to branch out beyond the few hundred miles within which we seem compelled to limit the acoustic medium, or ocean of air, in whose lower depths we live? Take, as the nearest instance, the moon. Who shall say what are the relations of sound to a planet in which the indications of an atmosphere, if appreciable at all, are so slight and indeterminate? In the presence of vast cosmical convulsions such as the telescope seems to certify as even now in progress in the moon, are we to divest our thoughts of all that class of effects which to us forms perhaps the most emphatic evidence of physical change? Is the crash of worlds before our eyes going on in vacuo? Is the moon's rigid metallic crust upheaved and broken, or does the titanic crater sink down into the abyss of central fire, without awaking a vibration in the eternal silence? We can only come back baffled from the feeblest flight into space to make the most that we can of the narrower and more commonplace facts actually within our ken. Even here, too, we soon encounter a further cause of limitation. The widest range of acoustics can be, as we have said, but conterminous with the atmosphere whose vibra tions give rise to the property of sound. heard by some persons who possess a sensiBut there are limits, too, to the powers of tive ear for lower sounds. The ascent of a the ear or the brain to receive or to appre- single note is sometimes sufficient to produce ciate the vibrations of that medium. The the change from sound to silence. Two range of hearing is no doubt infinitely vari- persons, neither of them deaf, may be found, ous among different classes of sentient life. the one complaining of the penetrating It differs, we find by experience, among in- shrillness of a sound, the other maintaining dividuals in the case of mankind. But the that no sound exists. In the Glaciers of the human ear itself at its best is limited in Alps, Professor Tyndall has referred to a both directions of the scale in its perception case of short auditory range of this kind. of sounds, whether grave or acute. The While crossing the Wengern Alp his ear was most satisfactory test of this fact lies in the rent with the shrill chirruping of the insects sensibility of the ear to sounds so sustained which swarmed in the grass on either side as to have a definite or musical pitch. The of the path, while a friend by his side heard experiments of men of science have result- not a sound of all this insect music. The ed in an arithmetical scale for the normal pitch of sounds has something closely analopower of the organ of hearing :gous to the various hues of light, which are excited by different rates of vibration. Both alike arise out of the pulses or waves of their respective media. But in its width of perception the ear greatly transcends the eye. The chromatic scale over which the eye ranges consists but of little more than a single octave, while upwards of eleven octaves lie within the compass of the ear. The quickest vibrations or shortest waves of light, which correspond to the extreme violet, strike the eye with only about twice the rapidity of the slowest or extreme red of the spectrum; whereas the quickest vibrations that strike the ear as a musical sound have, as Professor Tyndall remarks, more than two thousand times the rapidity of the Savart fixed the lower limit of the human ear at eight complete vibrations a second; and to cause these slowly recurring vibrations to link themselves together, he was obliged to employ shocks of great power. By means of a toothed wheel and an associated counter, he fixed the upper limit of hearing at 24,000 vibrations a second. Helmholtz has recently fixed the lower limit at 16 vibrations, and the higher at 38,000 vibrations, a second. By employing very small tuning-forks, the late M. Depretz showed that a sound corresponding to 38,000 vibrations a second is audible. Starting from the note 16 and multiplying continually by 2; or more compendiously raising 2 to the 11th power, and multiplying this by 16, we should find that at 11 octaves above the fundamental note the number of vibrations would be 32,778. Taking, therefore, the limits assigned by Helmholtz, the entire range of the human ear embraces about 11 octaves. But all the notes comprised within these limits cannot be employed in music. The practical range of musical sounds is comprised between 40 and 4,000 vibrations a second, which amounts, in round numbers, to 7 octaves. slowest. An admirable adjunct to our instrumental means of measuring the lengths of velocities of sonorous waves lies in the syren, the invention of M. Cagniard de la Tour, improved by Dove and Helmholtz. This ingenious little contrivance, of which instructive and amusing use was made by the lecturer at almost every period of his course, is explained at length with the aid of very Dr. Wollaston was the first to take note clear illustrations. A brass disc pierced of the difference that exists in the power of with four series of holes, 8, 10, 12, and 16 hearing between different persons. While in number, disposed along four concentric ciremployed in estimating the pitch of certain cles, is arranged so as to revolve upon a sharp sounds, he was struck with the total steel axis which passes through a fixed cylinsensibility of a friend to the sound of a inder of brass pierced with a corresponding small organ-pipe which, in respect to acute- series of holes. These perforations being made ness, was far within the ordinary limits of oblique to the surface of the cylinder in one hearing. The acoustic sense in this case direction, and to that of the disc in the other, extended no higher than four octaves above a stream of air forced through both series by the middle E of the pianoforte, while other means of bellows causes the disc to rotate persons have a distinct perception of sounds more or less rapidly according to the force of two octaves higher. Professor Tyndall has the current. A simple device for registering accumulated various instances of the limits the number of revolutions enables us to at which the power of hearing ceases in determine the number of vibrations or different individuals. The squeak of the waves of sound corresponding to the pitch bat, the sound of the cricket, even the chir- of the notes given out by the syren when rup of the common house-sparrow, are un-in motion. When turned slowly, a succes sion of beats or puffs of sound is heard, the velocity of sound in atmospheric air. following each other so slowly that they An entirely different scale of vibratory may be counted. But as the motion increases, the puffs succeed each other with increasing rapidity, till they blend into a deep continuous musical note. With the increased velocity of rotation the note rises in pitch, till it becomes so shrill as to be painful to the ear, and, if urged beyond a certain point, becomes even inaudible to human ears. Not that this last result would prove the absence of vibratory motion in the air. It would but show the incompetence of our auditory apparatus to take up vibrations whose rapidity exceeds a certain limit, or that of our brain to translate them into sound. The eye, as Professor Tyndall proceeds to show, is in this respect precisely similar to the ear. motion comes in when we consider the transmission of sound through media of various kinds. The researches of Dulong have given us an experimental table of the velocities of sound through different gases at an uniform temperature. It thus appears that the velocity of sound in oxygen is 1,040 feet in a second, in carbonic acid 858, in carbonic oxide 1,107, and in bydrogen no less than 4,164, the velocity in common air being 1,092. According to theory, the velocities of sound in oxygen and bydrogen should be inversely proportional to the square roots of the densities of the two gases. Oxygen being sixteen times heavier than hydrogen, the velocity of sound in the latter gas ought to be four times its velocity By means of the syren, the rapidity of vi- in the former. Experiment shows it to be bration of any sonorous body can be deter so very nearly. The velocity of sound in mined with extreme accuracy. The body liquids may be determined experimentally may be a vibrating string, an organ-pipe, as well as by theory, and a table with this a reed, or the human voice. We might view has been drawn up by the late M. even determine from the hum of an insect Wertheim. Hence we learn that sound the number of times it flaps its wings in a travels with very different velocity through second. A tuning-fork to a certain note is different liquids. A salt dissolved in water sounded for one minute, and the number of augments the velocity, and the salt that revolutions of the disc, when kept in unison produces the greatest augmentation is chlowith it, is found registered as 1,440. Multi- ride of calcium. Seawater transmits sound plying this figure by 16, the number of holes more rapidly than fresh. In water as in open during the experiment, we get 23,040 air, the velocity increases with the temperas the number of puffs of air or waves of ature. Thus at 15°C. the velocity in Seine sound passing through the syren in a min- water was 4,714 feet, at 30° it was 5,013 ute, corresponding to the number of vibra- feet, and at 60° 5,657 feet, a second. The tions executed by the tuning-fork. Divid- less the compressibility, the greater the ing this total by 60, we find the number of elasticity; and the greater in consequence vibrations in a second to be 384. We can the velocity of sound through the liquid. now ascertain with the same facility the In solids, as a rule, the elasticity as comlength of the corresponding sonorous wave. pared with the density is greater than in The velocity of a sound wave in free air at liquids, and consequently the propagation the freezing-point has been found to be 1,- of sound more rapid. In Wertheim's table 090 feet in a second. In air of the ordina- the velocity of sound through lead at 20°C. ry temperature of a room the distance may is but 4,030 feet a second, that through gold be taken at 1,120 feet. Dividing 1,120 by 5,717, through silver 8,553, through copper 384, the number of sonorous waves em- 11,666, through cast-steel 16,357, and through braced in this distance, we find the length iron 6,822. As a rule, here too, velocity is augof each wave to be nearly 8 feet. Taking mented by temperature. But in the case of the rates of four different tuning-forks we iron a remarkable exception exists. While in find them to be 256, 320, 384, and 512, cor- copper a rise from 20° to 100°C. causes the responding to wave lengths of 4 feet 4 inch-velocity to fall from 11,666 to 10,802, the es, 3 feet 6 inches, 2 feet 11 inches, and 2 feet 2 inches respectively. "The waves generated by a man's organs of voice in common conversation are from 8 to 12 feet, those of a woman are from 2 to 4 feet in length. Hence a woman's ordinary pitch in the lower sounds of conversation is more than an octave above a man's; in the higher sounds it is two octaves." These experiments refer exclusively to same rise produces in the case of iron an increase of velocity from 16,882 to 17,386. Between 100°, however, and 200°, iron falls from the last figure to 15,483. In iron, that is, up to a certain point, the elasticity is augmented by heat; beyond that point it is lowered. Silver, we learn, is an example of the same kind. The rate of transmission through a solid body depends further upon the manner in which the molecules of the the first great novelty in acoustic observa tions was due to the late Count Schaffgotsch, who showed that a flame in such a tube could A seen body are arranged. Heat is found to be conducted with different facilities through wood according as it passes along the fibre or across it, and again as it follows or cross-be made to quiver in response to a voice es the igneous layers or rings. In like pitched to the note of the tube or to its higher manner, wood possesses three unequal axes octave. Where the note was sufficiently high, of acoustic conduction. For example, in the flame was even extinguished by the acacia wood the velocity along the fibre is voice. Following up this rudimentary idea, 15,467 feet in a second, across the Professor Tyndall was led to take note of a rings 4,840, and along the rings 4,436. series of singular effects with flames and In pine, the corresponding figures are tubes, in which he and the Count seem to 10.900, 4.611, and 2605; in oak 12 622, have been running a race of priority. 5,036, and 4.229. To the extreme elasti- number of these curious and beautiful phecity of woody fibres, especially when in a nomena are described in the sixth lecture. highly dry state, are due the wonderful The cause of this quivering or dancing of effects of sound drawn out of the violin, or the flame is best revealed by an experiment the sounding-board of the piano. There is with the syren. As the pitch of the instrupractically no limit to the distance through ment is raised so as to approach that of the which sound may be transmitted through tube, a quivering of the flame is tubes or rods of wood. The music of in- synchronous with the beats. When perfect struments in a lower room may be made to unison is attained, the beats cease, but bepass to a higher floor, where it is excited gin again when the syren is urged beyond by a proper sounding-board, being all the unison, becoming more rapid as the dissowhile inaudible in the intermediate floors nance is increased. On raising the voice to through which it passes. It would be possi- the proper pitch, the Professor showed that ble to lay on, by means of wooden conduct- a flame which had been burning silently beors, the music of a band to a distance in all gan to sing. The effect was the same, directions, much as we lay on water. Mr. whenever the right note was sounded, at Spurgeon's voice might be turned on from any distance in the room. He turned his a main in the great Tabernacle, or back to the flame. Still the sonorous pulses Mr Beales's eloquence from a platform ran round him, reached the tube, and called in Hyde Park, to the ears of admirers in forth the song. Naked flames uncovered every parlour in the metropolis. by tubes will give forth the same effects if subjected to increased pressure, or suffered to flare. Professor Tyndall ascribes this discovery to Professor Leconte, of the United States, who noticed at a musical party the jets of gas pulsate in synchronism with the audible beats. "A deaf man," he observes, "might have seen the harmony." The tap of a hammer, the shaking a bunch of keys, a bell, whistle, or other sonorous instrument, is answered by the sympathetic tongue of flame. An infinite variety of forms is assumed by the luminous jet, according as the fish-tail, the bat's-wing, or other burner is employed, or a greater or less columu of flame allowed to rise. The most marvellous flame of the series is that from the single orifice of a steatite burner reaching a height of twenty-four inches. So sensitive is this tall and slender column as to sink to seven inches at the slightest tap upon a distant anvil. At the shaking of a bunch of keys it is violently agitated and emits a loud roar. The lecturer could not walk across the floor without agitating it. The creaking of his boots, the ticking of his watch, set it in violent commotion. As he recited a passage from Spenser, the flame picked out certain sounds to which it The fourth and fifth lectures reproduce and illustrate with much force and neatness the beautiful experiments of Chladni, Wheatstone, Faraday, and Strehlke, by which sonorous waves are made visible by means of the vibrations of metal plates strewn with fine sand. The curved lines, nodes, and other modifications of form which sand or the fine seeds of lycopodium exhibit under different degrees of excitement enable the eye to realize the rhythmical relations which belong to the phenomena of sound. The Pythagorean theory of figures, as applied to music, has its counterpart in the geometrical as well as in the arithmetical laws which are shown to govern the movements of sonorous waves. No portion of the present course, however, is more original and striking than that which treats of "soundling flames," or the effects produced by sound upon ignited jets of gas. Some experiments in this direction were made by Chladni and De la Rive towards the beginning of the present century, and Professor Faraday, as early as 1818. showed that certain tones were pro luced by tubes surrounding the flames of a spirit-lamp or a jet of carbonic oxide. After these experiments, |