Queen Elizabeth, at whose court, it is said, though on | doubtful authority, that he resided for a considerable period. With the sanction of Parliament, he carried on for several years extensive works for the embankment of the Thames, and so reclaimed a large quantity of waste land, part of which was bestowed upon him by way of recompense. His gratitude to Queen Elizabeth was expressed in the dedication to her of his celebrated Collection of the Stratagems of Satan, which has been often translated, and has passed through many editions. Various opinions have been given of this work, which advocated toleration to an extent that many considered indifference. The nature of its doctrine may perhaps be best gathered from the fact that it gained for the author the praise of Arminius, and the strong condemnation of the Calvinists. Acontius also wrote a treatise, De Methodo, which was published at Basel in 1558. He died in London about the year 1566.

ACORUS, a genus of monocotyledonous plants belonging to the natural order Aroidea, and the sub-order Orontiaceæ. Acorus Calamus, sweet-sedge or sweet-flag, is a native of Britain. It has an agreeable odour, and has been used as a strengthening remedy, as well as to allay spasms. The starchy matter contained in its running stem or rhizome is associated with a fragrant oil, and it is used as hairpowder. Confectioners form a candy from the rhizomes of the plant, and it is also used by perfumers in preparing aromatic vinegar.

ACOSTA, CHRISTOVAL D', a Portuguese naturalist, born at Mozambique in the early part of the 16th century. On a voyage to Asia he was taken captive by pirates, who exacted from him a very large ransom. After spending some years in India, chiefly at Goa, a Portuguese colony, he returned home, and settled as a surgeon at Burgos. Here he published his Tratado de las drogas y medecinas de las Indias orientales (1578). This work was translated| into Latin, Italian, and French, became well known throughout Europe, and is still consulted as an authority. Acosta also wrote an account of his travels, a book in praise of women, and other works. He died in 1580.

ACOSTA, JOSEPH D', a celebrated Spanish author, was born at Medina del Campo about the year 1539. In 1571 he went to Peru as a provincial of the Jesuits; and, after remaining there for seventeen years, he returned to his native country, where he became in succession visitor for his order of Aragon and Andalusia, superior of Valladolid, and rector of the university of Salamanca, in which city he died in February 1600. About ten years before his death he published at Seville his valuable Historia Natural y Moral de las Indias, part of which had previously appeared in Latin, with the title De Natura Novi Orbis, libri duo. This work, which has been translated into all the principal languages of Europe, gives exceedingly valuable information regarding the condition of South America at the time. On the subject of climate Acosta was the first to propound the theory, afterwards advocated by Buffon, which attributed the different degrees of heat in the old and new continents to the agency of the winds. He also contradicted, from his own experience, the statement of Aristotle, that the middle zone of the earth was so scorched by the sun as to be destitute of moisture, and totally uninhabitable. Even after the discovery of America this Aristotelian dogma was an article of faith, and its denial was one ground of the charge of scepticism and atheism brought against Sir Walter Raleigh. Acosta, however, boldly declared that what he had seen was so different from what he had expected, that he could not but "laugh at Aristotle's meteors and his philosophy." In speaking of the conduct of his countrymen, and the means they employed for the propagation of their faith, Acosta is in no respect superior to the other prejudiced writers of his country and age. Though he

acknowledges that the career of Spanish conquest was marked by the most savage cruelty and oppression, he yet represents this people as chosen by God to spread the gospel among the nations of America, and recounts a variety of miracles as a proof of the constant interposition of Heaven in favour of the merciless and rapacious invaders. Besides his History, Acosta wrote the following works:-1. De Promulgatione Evangelii apud Barbaros; 2. De Christo Revelato; 3. De Temporibus Novissimis, lib. vi.; 4. Concionum tomi iii.

ACOSTA, URIEL D', a Portuguese of noble family, was born at Oporto towards the close of the 16th century. His father being a Jewish convert to Christianity, he was brought up in the Roman Catholic faith, and strictly observed the rites of the church till the course of his inquiries led him, after much painful doubt, to abandon the religion of his youth for Judaism. Passing over to Amsterdam, he was received into the synagogue, having his name changed from Gabriel to Uriel. He soon discovered, however, that those who sat in Moses' seat were shameful perverters of the law; and his bold protests served only to exasperate the rabbis, who finally punished his contumacy with the greater excommunication. Persecution seemed only to stimulate his temerity, and he soon after published a defence, Examen das tradiçoens Phariseas, &c., in which he not merely exposed the departures of the Jewish teachers from the law, but combated the doctrine of a future life, holding himself supported in this position by the silence of the Mosaic Books. For this he was imprisoned and fined, besides incurring public odium as a blasphemer and atheist. Nothing deterred, he pursued his speculations, which ended in his repudiating the divine authority of the law of Moses. Wearied, however, by his melancholy isolation, and longing for the benefits of society, he was driven, in the inconsistency of despairing scepticism, to seek a return to the Jewish communion. Having recanted his heresies, he was readmitted after an excommunication of fifteen years, but was soon excommunicated a second time. After seven years of miserable exclusion, he once more sought admission, and, on passing through a humiliating penance, was again received. These notices of his singular and unhappy life are taken from his autobiography, Exemplar Humana Vita, published, with a "refutation," by Limborch, and republished in 1847. It has been said that he died by his own hand, but this is, to say the least, doubtful. eventful history forms the subject of a tale and of a tragedy by Gutzkow.

His

ACOTYLEDONES, the name given to one of the Classes of the Natural System of Botany, embracing flowerless plants, such as ferns, lycopods, horse-tails, mosses, liverworts, lichens, sea-weeds, and mushrooms. The name is derived from the character of the embryo, which has no cotyledon. Flowering plants have usually one or two cotyledons, that is, seed-leaves or seed-lobes connected with their embryo; while in flowerless plants the body representing the embryo consists of a cell, called a spore, without any leaves. The plants have no flowers, and their organs of reproduction are inconspicuous, hence they are called by Linnæus cryptogamous. Some flowering plants, such as dodders, have no cotyledons; and some have the cotyledons divided into more than two, as in conifers. Some acotyledonous spores, when sprouting, produce a leaf-like expansion called a prothallus, on which the organs of reproduction, consisting of antheridia and archegonia, are produced. This is well seen in the case of ferns. In the interior of the antheri dian cells, moving filamentous bodies, called spermatozcids, have been observed. These fertilise the archegonial cells, whence new plants are produced. In the article BOTANY these plants will be noticed under Class III. of the Naturd System.

Definition. 1.

Sound is due to

COUSTICS (from άkouw, to hear) is that branch of Natural Philosophy which treats of the nature of sound, and the laws of its production and propagation, in so far as these depend on physical principles. The description of the mechanism of the organ of voice and of the ear, and the difficult questions connected with the processes by which, when sound reaches the drum of the ear, it is transmitted to the brain, must be dealt with in separate articles of this work. It is to the physical part of the science of acoustics that the present article is restricted.

PART I.

General notions as to Vibrations, Waves, &c.

2. We may easily satisfy ourselves that, in every instance in which the sensation of sound is excited, the body, vibrations. whence the sound proceeds, must have been thrown, by a blow or other means, into a state of agitation or tremor, implying the existence of a vibratory motion, or motion to and fro, of the particles of which it consists.

Sound is

Thus, if a common glass-jar be struck so as to yield an audible sound, the existence of a motion of this kind may be felt by the finger lightly applied to the edge of the glass; and, on increasing the pressure so as to destroy this motion, the sound forthwith ceases. Small pieces of cork put in the jar will be found to dance about during the continuance of the sound; water or spirits of wine poured into the glass will, under the same circumstances, exhibit a ruffled surface. The experiment is usually performed, in a more striking manner, with a bell-jar and a number of small light wooden balls suspended by silk strings to a fixed frame above the jar, so as to be just in contact with the widest part of the glass. On drawing a violin bow across the edge, the pendulums are thrown off to a considerable distance, and falling back are again repelled, &c.

It is also in many cases possible to follow with the eye the motions of the particles of the sounding body, as, for instance, in the case of a violin string or any string fixed at both ends, when the string will appear, by a law of optics, to occupy at once all the positions which it successively assumes during its vibratory motion.

3. It is, moreover, essential, in order that the ear may propagated be affected by a sounding body, that there be interposed to the ear between it and the ear one or more intermediate bodies by vibra(media), themselves capable of molecular vibration, which tions of air, shall receive such motion from the source of sound, and &c. transmit it to the external parts of the ear, and especially to the membrana tympani or drum of the ear. This statement is confirmed by the well-known effect of stopping the ear with soft cotton, or other substance possessing little elasticity.

The air around us forms the most important medium of communication of sound to our organs of hearing; in fact, were air devoid of this property, we should practically be without the sense of hearing. In illustration of the part thus assigned to the atmosphere in acoustics, an apparatus has been constructed, consisting of a glass receiver, in which is a bell and a hammer connected with clock-work, by which it can be made to strike the bell when required. The receiver is closed air-tight by a metal plate, through which passes, also air-tight, into the interior, a brass rod. By properly moving this rod with the hand, a detent is released, which checks the motion of the wheel-work, and the hammer strikes the bell continuously, till the detent is pushed into its original position. As long as the air in

the receiver is of the usual atmospheric density, the sound is perfectly audible. But on rarefying the air by means of an air-pump (the clock-work apparatus having been separated from the plate of the pump by means of a padding of soft cotton), the sound grows gradually fainter, and at last becomes inaudible when the rarefaction of the air has reached a very low point. If, however, at this stage of the experiment, the metal rod be brought into contact with the bell, the sound will again be heard clearly, because now there is the necessary communication with the ear. On readmitting the air, the sound recovers its original intensity. This experiment was first performed by Hawksbee in 1705.

motion.

4. Inasmuch, then, as sound necessarily implies the Laws of existence in the sounding body, in the air, &c., and (we vibratory may add) in the ear itself, of vibratory motion of the particles of the various media concerned in the phenomenon, a general reference to the laws of such motion is essential to a right understanding of the principles of acoustics.

The most familiar instance of this kind of motion is afforded by the pendulum, a small heavy ball, for instance, attached to a fine string, which is fixed at its other end. There is but one position in which the ball will remain at rest, viz., when the string is vertical, there being then equilibrium between the two forces acting on the body, the tension of the string and the earth's attractive force or gravity. Thus, in the adjoining fig., if C is the point of suspension, and CA the vertical through that point of length 1, equal to the string, A is the equilibrium position of the particle.

A

Fig. 1.

m

Let now the ball be removed from A to P, the string being kept tight, so that P describes the arc AP of a circle of radius equal to 1, and let the ball be there dropped. The tension of the string not being now directly opposite in direction to gravity (g), motion will ensue, and the body will retrace the arc PA. In doing so, it will continually increase its velocity until it reaches the point A, where its velocity will be a maximum, and will consequently pass to the other side of A towards Q. But now gravity tends to draw it back towards A, and hence the motion becomes a retarded one; the velocity continually diminishes, and is ultimately destroyed at some point Q, which would be at a distance from A equal to that of P, but for the existence of friction, resistance of the air, &c., which make that distance less. From Q it will next move down with accelerated motion towards A, where it will have its greatest velocity in the direction from left to right, and whence it will pass onwards towards P, and so on. Thus the body will vibrate to and fro on either side of A, its amplitude of vibration or distance between its extreme positions gradually diminishing in consequence of the resistances before mentioned, and at last being sensibly reduced to nothing, the body then resuming its equilibrium-position A.

If the amplitude of vibration is restricted within inconsiderable limits, it is easy to prove that the motion takes place just as if the string were removed, the ball deprived altogether of weight and urged by a force directed to the point A, and proportional to the distance from that point. For then, if m be any position of the ball, the chord mA may be regarded as coincident with the tangent to the

Acoustic

direction.

abc..

Confining our attention to propagation in the direction we have next to remark that each particle in that line will be affected by the disturbance always later than the particle immediately preceding it, so as to be found in

Am

Cm

or

On this supposition of indefinitely small vibrations, the pendulum is isochronous; that is, the time occupied in passing from one extreme position to the other is the same, for a given length 7 of the pendulum, whatever the extent of vibration.

We conclude from this that, whatever may be the nature of the forces by which a particle is urged, if the resultant of those forces is directed towards a fixed point, and is proportional to the distance from that point, the particle will oscillate to and fro about that point in times which are independent of the amplitudes of the vibrations, provided these are very small.

5. The particle, whose vibratory motion we have been considering, is a solitary particle acted on by external vibrations. forces. But, in acoustics, we have to do with the motion of particles forming a connected system or medium, in which the forces to be considered arise from the mutual actions of the particles. These forces are in equilibrium with each other when the particles occupy certain relative positions. But, if any new or disturbing force act for a short time on any one or more of the particles, so as to cause a mutual approach or a mutual recession, on the removal of the disturbing force, the disturbed particles will, if the body be elastic, forthwith move towards their respective positions of equilibrium. Hence arises a vibratory motion to and fro of each about a given point, analogous to that of a pendulum, the velocity at that point being always a maximum, alternately in opposite directions. Thus, for example, if to one extremity of a pipe containing air were applied a piston, of section equal to that of the pipe, by pushing in the piston slightly and then removing it, we should cause particles of air, forming a thin section at the extremity of the pipe, to vibrate in directions parallel to its axis.

In order that a medium may be capable of molecular vibrations, it must, as we have mentioned, possess elasticity, that is, a tendency always to return to its original condition when slightly disturbed out of it.

6. We now proceed to show how the disturbance whereTransmis by certain particles of an elastic medium are displaced from their equilibrium-positions, is successively transmitted to vibrations. the remaining particles of the medium, so as to cause these also to vibrate to and fro.

sion of

Let us consider a line of such particles y, x, a, b, &c.

y xa a a b c d e f g h i k l m n ор

equidistant from each other, as above; and suppose one of them, say a, to be displaced, by any means, to a. As we have seen, this particle will swing from a, to a, and back again, occupying a certain time T, to complete its double vibration. But it is obvious that, the distance between a and the next particle b to the right being diminished by the displacement of the former to a,, a tendency is generated in to move towards a,, the mutual forces being no longer in equilibrium, but having a resultant in the direction ba The particle b will therefore also suffer displacement, and be compelled to swing to and fro about the point b. For similar reasons the particles c, d . . . will all likewise be thrown into vibration. Thus it is, then, that the disturbance propagates itself in the direction under consideration. There is evidently also, in the case sup

the preceding particle.

7. Two particles which are in the same stage of vibra- Phasetion, that is, are equally displaced from their equilibriumpositions, and are moving in the same direction and with equal velocities, are said to be in the same phase. Hence we may express the preceding statement more briefly thus: Two particles of a disturbed medium at different distances from the centre of disturbance, are in the same phase at different times, the one whose distance from that centre is the greater being later than the other.

8. Let us in the meantime assume that, the intervals ab, bc, cd. . . . being equal, the intervals of time which elapse between the like phases of b and a, of c and b . . . . are also equal to each other, and let us consider what at any given instant are the appearances presented by the different particles in the row.

T

Ρ

T

T being the time of a complete vibration of each particle, let be the interval of time requisite for any phase of a to pass on to b. If then at a certain instant a is displaced to its greatest extent to the right, b will be somewhat short of, but moving towards, its corresponding position, c still further short, and so on. Proceeding in this way, we shall come at length to a particle p, for which the distance ap=p. ab, which therefore lags in its vibrations behind a by a time =px T, and is consequently precisely in the same phase as a. And between these two particles a, p, we shall evidently have particles in all the possible phases of the vibratory motion. At h, which is at distance from a lap, the difference of phase, compared with a, will be T, that is, h will, at the given instant, be displaced to the greatest extent on the opposite side of its equilibrium-position from that in which a is displaced; in other words, h is in the exactly opposite phase to a.

Ρ

=

10. Now the reasoning employed in the preceding case Wave of will evidently admit of general application, and will, in transversal displaceparticular, hold for transversal vibrations. Hence if we ments. mark (as is done in fig. 2) the positions a, b, c, . . ., occupied by the various particles, when swinging transversely, at the instant at which a has its maximum displacement above its equilibrium-position, and trace a continuous line running through the points so found, that line will by its ordinates indicate to the eye the state of motion at the given instant. ai bici

t

1

1

1 1

Fig. 2.

C

Thus a and p are in the same phase, as are also b and q, c and r', &c. a and h are in opposite phases, as are also and i, c and k, &c.

Distances ap, bq, &c., separating particles in the same phase, and each of which, as we have seen, is passed over by the disturbance in the time T of a complete vibration, include within them all the possible phases of the motion.

Beyond this distance, the curve repeats itself exactly, that is, the phases recur in the same order as before.

Now the figure so traced offers an obvious resemblance to the undulating surface of a lake or other body of water, after it has been disturbed by wind, exhibiting a wave with its trough A,B, and its crest Bp,C. Hence have been introduced into Acoustics, as also into Optics, the terms wave and undulation. The distance ap, or bq... or A C, which separates two particles in same phase, or which includes both a wave-crest and a wave-trough, is termed the length of the wave, and is usually denoted by λ.

=

=

As the curve repeats itself at intervals each λ, it follows that particles are in the same phase at any given moment, when the distances between them in the direction of transmission of the disturbance A, 2A, 3A... and generally nλ, where n is any whole number. Particles such as a and h, b and i, &c., which are at distances being in opposite phases, so will also be

=

particles separated by distance, A+λ=3, or, in general,

by

2'

-+mλ = (2m+1)1⁄2, that is, by any odd multiple of 11. A like construction to the one just adopted for the displacements of the particles at any given instant, may be also applied for exhibiting graphically their velocities at the same instant. Erect at the various points a, b, c, &c., perpendiculars to the line joining them, of lengths proportional to and in the direction of their velocities, and draw a line through the extreme points of these perpendiculars; this line will answer the purpose required. It is indicated by dots in the previous figure, and manifestly forms a wave of the same length as the wave of displacements, but the highest and lowest points of the one wave correspond to the points in which the other wave crosses the line of equilibrium.

12. In order to a graphic representation of the displacements and velocities of particles vibrating longitudinally, it is convenient to draw the lines which represent those quantities, not in the actual direction in which the motion takes place and which coincides with the line abc..., but at right angles to it, ordinates drawn upwards indicating displacements or velocities to the right (i.e., in the direction of transmission of the disturbance), and ordinates drawn downwards indicating displacements or velocities in the opposite direction. When this is done, waves of displacement and velocity are figured identically with those for transversal vibrations, and are therefore subject to the same resulting laws.

13. But not only will the above waves enable us to see at a glance the circumstances of the vibratory motion at the instant of time for which it has been constructed, but also for any subsequent moment. Thus, if we desire to T consider what is going on after an interval we have " p simply to conceive the whole wave (whether of displacement or velocity) to be moved to the right through a distance ab. Then the state of motion in which a was before will have been transferred to b, that of b will have been transferred to c, and so on. At the end of another such interval, the state of the particles will in like manner be represented by the wave, if pushed onward through another equal space. In short, the whole circumstances may be pictur d to the eye by two waves (of displacement

=

14. There is one very important distinction between the Variations two cases of longitudinal and of transversal vibrations which of density due to lon now claims our attention, viz., that whereas vibrations of gitudinal the latter kind, when propagated from particle to particle vibrations. in an elastic medium, do not alter the relative distances of the particles, or, in other words, cause no change of density throughout the medium; longitudinal vibrations, on the other hand, by bringing the particles nearer to or further from one another than they are when undisturbed, are necessarily accompanied by alternate condensations and

rarefactions.

fig. refers, the displacements of the particles immediately

Thus, in fig. 2, we see that at the instant to which that

adjoining a are equal and in the same direction; hence at that moment the density of the medium at a is equal to that of the undisturbed medium. The same applies to the points h, p, &c., in which the displacements are at their maxima and the velocities of vibration 0.

=

At any point, such as c, between a and A, the displacements of the two adjoining particles on either side are both to the right, but that of the preceding particle is now the greater of the two, and hence the density of the medium throughout aA exceeds the undisturbed density. So at any point, such as ƒ, between A and h, the same result holds good, because now the displacements are to the left, but are in excess on the right side of the point f. From a to h, therefore, the medium is condensed.

From h to B, as at k, the displacements of the two particles on either side are both to the left, that of the preceding particle being, however, the greater. The medium, therefore, is here in a state of rarefaction. And in like manner it may be shown that there is rarefaction from B to p; so that the medium is rarefied from h to p.

At A the condensation is a maximum, because the displacements on the two sides of that point are equal and both directed towards A. At B, on the other hand, it is the rarefaction which is a maximum, the displacements on the right and left of that point being again equal, but directed outwards from B.

It clearly follows from all this that, if we trace a curve of which any ordinate shall be proportional to the difference between the density of the corresponding point of the disturbed medium and the density of the undisturbed medium-ordinates drawn upwards indicating condensation, and ordinates drawn downwards rarefaction-that curve will cross the line of rest of the particles abc... in the same points as does the curve of velocities, and will therefore be of the same length A, and will also rise above that line and dip below it at the same parts. But the connection between the wave of condensation and rarefaction and the wave of velocity, is still more intimate, when the extent to which the particles are displaced is very small, as is always the case in acoustics. For it may be shown that then the degree of condensation or rarefaction at any point of the medium is proportional to the velocity of vibration at that point. The same ordinates, therefore, will repre