duced; above that limiting velocity of vibration, sound is produced; and experience shows that the pitch of the sound becomes more and more acute as the vibrations are more rapid, until a second limit of velocity is attained, beyond which the human ear is affected with no sensation of sound. To prove this experimentally, let a strip of tempered steel have one of its ends firmly fixed in a vice, and let the other end be drawn aside from the position of rest. As soon as the force by which the strip is bent is removed, the steel commences a series of vibrations, which become smaller and smaller until the position of rest is again attained. But the vibrations are all performed in equal times, and if sufficient length is given to the strip, they take place so slowly as to admit of being accurately counted. On shortening the strip, they become more rapid; and at a certain length a low sound is emitted. If the strip be still further shortened, a fiddle-bow drawn over its upper edge will be necessary to throw it into vibration, and a higher note will now be heard. By continuing to reduce the length of the strip, the pitch of the note will correspondingly rise; for the excursion of the steel to and fro is augmented in rapidity, and the pitch of a note depends on the rate of vibration. It might perhaps be possible so far to shorten the strip, and still to throw it into vibration, that its last shrill note shall be followed by no audible sound.

Long before the vibrations of the strip attain that degree of rapidity which is necessary for the production of sound, it becomes impossible to count them directly. But it is demonstrable that when a strip of metal of equal thickness throughout is made to vibrate in the manner now supposed, the time of a vibration is directly proportional to the square of the length of the strip, and consequently the number of vibrations in a given time is inversely as this square; so that if the number in a second corresponding to any length of the strip has been counted, the number corresponding to any other given length can be readily computed. In this manner it has been found that a metallic strip or plate begins to sound when the number of complete vibrations in a second is 16; and at this velocity of vibration, the sound which it gives is of the same pitch as that of an organ pipe 32 feet in length, open at both ends.

This appears to be the minimum velocity of vibration capable of producing sound. The other limit, or maximum velocity at which sound ceases to be appreciable, has also been determined. Until recently it has been usual to fix it at 8,200 vibrations in a second; but Savart has discovered that by increasing the amplitude of the vibrations, acute sounds may be distinguished at a velocity of 24,000 whole vibrations in a second; and more recently Despretz has fixed the upper limit of audible sounds at 36,800 whole vibrations per second. The number of vibrations producing a sound of any given pitch can be determined with great

ease and exactness in various ways. Savart employed for this purpose a cog wheel which was made to revolve, and in doing so the teeth were caused to strike a piece of card. A musical sound of any pitch could thus be produced by regulating the velocity of the wheel. The number of revolutions being indicated by machinery, the number of vibrations made by the card could be at once found by multiplying the revolutions of the wheel by the number of teeth it contained. Still more perfectly may the rate of vibration be determined by means of an ingenious instrument, invented by Cagniard Latour, called the syren. [SYREN.]

Some of the most acute sounds, or highest tones which the ear can distinguish, are given by the wings of insects; and they correspond to the astonishing rapidity of 12,000 or 15,000 vibrations in a second. When we reflect how extremely probable it is that the tympanum of the ear vibrates in unison with the sounds that affect it, we cannot fail to be struck with the wonderfully delicate organisation of a substance which possesses the power of adapting itself to all velocities of vibration, from 16 times in a second up to 30,000, or even higher. The limits, however, at which very acute sounds cease to be audible appear to vary considerably in different individuals, some being altogether insensible to sounds which painfully affect others. For example, the piercing chirp of the grasshopper is quite unheard by some persons. (See a very interesting paper on sounds inaudible to certain ears by Dr. Wollaston in the Phil. Trans. for 1820.)

Propagation of Sound.-In order to convey an idea of the manner in which the vibratory motions of a sonorous body are communicated to the atmosphere or other elastic medium, let us conceive a tube, T T, of an indefinite length, Fig. 1.

and open at both ends, to be filled with air of a uniform temperature and density throughout. Let us also suppose a piston, P Q, which closely fits the tube, and is movable within it along the direction of the axis, to be propelled suddenly from the position P Q to RS; and to simplify the consideration, let the distance P R be supposed one foot, and the time in which the piston moves from P Q to R S to be one second. Now, assuming the air within the tube to have been in a state of rest before the piston began to move, let us consider what will be its state at the instant when the piston arrives at RS. If the air in the tube were acted upon as a perfectly hard body, any motion communicated to the particles at one extremity would be instantaneously conveyed to the other; and when the piston arrived at R S a quantity of air, equal to that which was contained between P Q and R S, would be expelled at T', and all the particles within the tube would come to rest at the same time with the piston. But in

consequence of the compressibility of the air the motion is not communicated to the distant particles instantaneously, but only after a sensible interval of time; and we may conceive the tube to be so long that when the piston has arrived at RS no air has yet been propelled from the tube at T. In fact, the disturbance or compression of the particles, which takes place at the instant the piston begins to move, is propagated along the tube with a certain determinate volocity, depending on the elasticity of the air, and when the piston reaches R S will only have reached to a certain determinate

distance. Let A B be the section of the tube which the first compression has reached at the instant the piston comes to RS; then, at the instant of time on which we have to fix our attention, the column of air between R S and AB will be in a state of compression, and betwen A B and the end of the tube at T it will still remain in its natural state. The column of air between R S and A B, which is thus modified by the stroke of the piston, is called a condensed wave.

On attending to the state of the molecules in the column Ř A, it will readily be seen that they are not subjected to the same degree of compression through its whole length. Conceive the wave to be divided into a very great number of thin layers by sections parallel to RS or AB, and that the piston, in passing from the position PQ to RS, has produced the effect, not instantaneously, but by a great number of successive small impulses. At the instant the piston comes to R S the disturbance has by hypothesis been propagated only to A B, and consequently the particles in the infinitely thin layer next to A B have suffered only the slightest degree of compression, or that caused by the first impulse of the piston. In the second layer next to A B the molecules of air are in a state of greater compression; inasmuch as they have sustained not only the compression due to the first impulse of the piston, but also that which is due to the second, the effect of which is propagated to them at the same instant at which the effect of the first is propagated to A B. In like manner, the compression in the third layer preceding A B is greater than in the second; and so on to the middle of the If we now attend to the state of the molecules at the other extremity R S of the wave, a similar effect will be manifest. The instant after the piston stops, the layer next to Fig. 2.

wave.

ing out this mode of reasoning it will readily appear that the particles in the state of greatest compression are those towards the middle of the wave; and that if upon S B, as an axis (fig. 2), we raise a great number of perpendiculars, a a, b b, c c, &c., each proportional to the compression at the corresponding point of the column, the curve drawn through the summits of these perpendiculars will represent the law of compression, and hence is of the form represented in the annexed diagram, the parts on each side of the middle ordinate b b being perfectly symmetrical.

If we now attend to the motions developed on the other side of the piston, it will be easily seen that similar phenomena must take place; but in a reverse order, inasmuch as the air within the tube on that side must be rarefied instead of being compressed by the motion of the piston from P Q to R S. Let C D (fig. 1) be a section of the tube, so that the column C R is equal to R A; then, as the velocity of propagation depends only on the nature of the medium, it is obvious that at the instant in which the piston arrives at R S the disturbance of the molecules will have extended only to CD. The whole column between CD and RS will be rarefied by the withdrawal of the piston of air between PQ and RS; but the rarefaction will be greatest at the middle of the column, for the

If, now, as in fig. 3, we represent the rarefaction by negative ordinates, a' a', 'b', c'e', and the condensation, as before, by the positive or dinates a a, b b, c c, the state of the column of air between A B and CD (fig. 1) and this is all which is modified by the passage of the piston from P Q to R S-will be represented by the double curve DSb B (fig. 3), the small part between P Q and R S being neglected as insensible. The first part of this curve, from D to S, constitutes a rarefied wave; and the second part, from S to B, a condensed wave. Now, as both the rarefied and condensed waves have been produced simultaneously by one motion of the piston, the whole curve from D to B constitutes a single wave or undulation. The length of a wave is, therefore, the distance between the points D and B, or the distance between the centre of one condensation or rarefaction to the centre of the next.

SOUTH SEA COMPANY South Sea Company. In 1711, the proprietors of certain government debts were formed into a joint-stock company, which, in consideration of certain exclusive privileges of trading to the South Seas, offered the government easier terms for the advance or negotiation of loans than could be obtained from the general public. The charter dated from the first of August. The financial expedient of a system by which public debts should be firmed by a company was frequent and to some extent advantageous, and the doctrine that parliament could or should give monopolies of foreign trade was generally accepted. In the present case, it seems that the scheme was intended to rival that of the bank of England. It was favoured by Harley and the Tories, and it was stipulated in the charter that no person should be at once a director of this company and that of the Bank or the East India Company. It was provided that even if the public debt were redeemed, the monopoly of trade should be perpetual. At the time when the company was formed, its stock stood at 77 per cent., East India being 124, Bank 1111; and for some time the price of the stock did not rise materially; nor did the company regularly enter on its trading schemes till 1717, when its first annual ship was sent to Vera Cruz.

The origin of the famous bubble of 1720 was the proposal on the part of the directors of the South Sea Company to negotiate all the public debts, at certain rates, and the rivalry which this excited on the part of the bank of England. So keen was this rivalry, that the general public anticipated enormous advantages from the plan, and the stock rose rapidly. It was 126 in Dec. 1719, and reached 319 in the spring of 1720. By the 1st of May it was 400; by June 2, 890. On June 3, it ranged between 640 and 770. On the 6th it was 820, on the 14th 710. By Midsummer it reached 1,000, and other stocks, as that of the East India Company and the bank of England, were similarly exalted. It was said that the advanced prices of all three stocks were computed at 500 millions sterling, and that this sum represented five times all the cash in Europe, and double the value of the lands and houses in England. In order to keep up the price of the security, the South Sea Company, now high in favour with the government, procured a scire facias against the numerous schemes then afloat.

The infatuation, however, was universal. The newspapers were crowded with advertisements of new companies, subscriptions were eagerly paid, and the projectors decamped with the spoils. So great was the wild confusion in 'Change Alley, that the same project or bubble was known to be sold at the same instant of time ten per cent. higher at one end of the alley than it was at the other.' One projector actually advertised for a subscription of two millions on a certain promising and profitable design, which would hereafter be promulgated. Pieces of playing-card, called globe

SOUTHCOTTIANS

permits, because they had the impression of a globe in wax, which purported to be a security that the possessor would hereafter be entitled to subscribe into a new sail-cloth manufactory, were sold for sixty and seventy guineas. A list of bubbles is given in Macpherson's History of Commerce, some of them being hardly less absurd than the satirical suggestion of a company, with a subscription of two millions, for the invention of melting down sawdust and chips, and casting them into clean deal boards without cracks or knots.

The South Sea Company discovered its error in suing out a suit of scire facias against some of these bubbles, and foresaw that, unless they adopted some expedient, their own ruin was involved in that of their competitors. To defer it, they issued a notice on August 30 that the half-year's dividend should be at the rate of 60 per cent. and that for the next twelve years it should be 50. But these magnificent promises were discredited. The stock sank from 810 on the 1st of September to 410 on the 20th, and to 130 by the last day of the month.

The fraudulent directors of the company, among whom was Mr. Aislabie, the chancellor of the exchequer, were prosecuted and fined, and some small assistance was given out of their estates to a few persons who had been swindled by these officials. But of course a vast mass of misery and ruin remained pitied but unassisted, and long afterwards the most prominent among the great speculations of the year 1720 was known as the Bubble.

For thirty years afterwards the South Sea Company continued their trade, though with very imperfect success, and up to almost the present time the capital subscribed to government, which was the plea of their exclusive privileges, was treated as a separate debt, under the name of South Sea Stock.

Southcottians. In Religious History, the followers of Joanna Southcott, who was born at Gittisham, in Devonshire, in 1750, and seems to have first persuaded herself of her miraculous calling in 1792. From that time she traversed the west of England, preaching and prophesying, with a select body of followers, and gradually collected about her a considerable number of disciples. She came to London about 1803, when she announced a meeting for the purpose of satisfying the world of the reality of her mission. Several such meetings took place, the last in 1804; and many persons, including several clergymen, attested their belief in her pretensions. At last, in 1814, she announced her supernatural pregnancy; and this strange announcement took great hold on the public imagination, Dr. Reeve and other medical men having declared their belief that she was actually pregnant in her sixty-fifth year. Her death, in December of that year, did not undeceive her disciples: even when her body was opened, and no trace discovered to verify her assertions, many of them continued to proclaim their