PENDULUM

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PENDULUM, in dynamics, is a simple ponderous body, so suspended by a flexible cord from an axis of suspension, that it is at liberty to vibrate by the action of its own gravity alone, when it is once raised, by any external force, to the right or left of its quiescent position; and, in demonstrating the theory of its motion, mathematicians are obliged to assume, that there is no rigidity in the cord, no friction at the axis of suspension, no resistance to motion made by the air, and no variation in the total length of the cord, arising from the variable temperature or moisture of the atmosphere; and if these assumptions were strictly correct, a pendulum, once put in motion, would continue to move, ad infinitum, without a further accession of any external force; but, when the pendulum is applied as the regulator of a clock, for which purpose it is admirably adapted, the assumptions which we have stated, require an equal number of mechanical corrections, of which the theoiy, simply considered, takes no notice. In horology, therefore, the pendulum must be considered not simply as a selfmoving pendulous body, without any tendency to come to a state of rest, but as a body whose motion is perpetuated by repeated accessions of force in aid of its own gravity, and whose vibrations are rendered isochronal by a nice adaptation of mechanical contrivances, that prevent or remedy the influence of all natural impediments to uniform and uninterrupted motion. The first kind of pendulum (the theoretical) is called a mathematical or simple pendulum, the other the physical or compound pendulum. In the mathematical pendulum, the matter of the pendulous ball or bob is supposed to be collected into one point, so that the centres of gravity and of oscillation coincide. The doctrine of the pendulum is of the highest importance, but, as it cannot be fully developed without the aid of mathematics, nor rendered clear without diagrams, we can state only some of the most obvious properties and circumstances connected with it. A pendulum, once put in motion, would never cease to oscillate in arcs, were it not for the friction at the point of suspension, and the resistance of the air. Neither of these circumstances can ever be avoided entirely, but their effect may be rendered comparatively slight by giving to the weight a lenticular shape, and suspending the rod on a sharp edge9 on which it plays with very little friction. The times of the vibrations of a pendulum depend, 1. on the magnitude of the angle of elongation, viz. that angle by which the heavy body of the pendulum is removed from the vertical line; 2. upon the length of the pendulum; and 3. upon the accelerating power of gravity. If all these circumstances are perfectly equal in the case of two PENDULUMs, they will perform an equal number of oscillations in the same time ; but if there is a difference in either of the circumstances, the oscillations will differ immediately. Thus, if one pendulum is shorter than the other, and all the other circumstances equal, the shorter pendulum will move quicker than the longer. The law which has been found to exist is, that the lengths of the pendulums are in an inverse proportion to the squares of their oscillations; hence the times of the oscillations are inversely as the square roots of the lengths of the pendulums. Hence a pendulum which is four times as long as another, will vibrate with but half the rapidity, or the shorter pendulum will perform two oscillations whilst the larger performs but one. The pendulum does not perform its oscillations in equal times in all parts of the earth. This is owing to the third of the circumstances enumerated above, upon which the oscillations depend. The gravity, or, what is the same thing, the power of attraction in the earth, does not operate every where with equal force on the pendulum, which, therefore, in some parts of the earth, oscillates more slowly than in others. The cause of this lies in the centrifugal force (q. v.), or in the diminution of the power of gravity caused by it. This becomes more perceptible the nearer the place where the pendulum is observed is to the equator. (See Earth.) At the equator, therefore, a pendulum vibrating seconds must be somewhat shorter than at a distance from it. The length of a seconds pendulum at the equator is, according to Biot, 39.011684 inches: in latitude 45°, 39.116820, in 90°, 39.221956. If the globe were a perfect spheroid, the meridians would be perfect ellipses, and in such case the length of seconds pendulums would immediately afford a 1* basis for a calculation of the length of the degrees in the various latitudes; but actual measurements have shown that the meridians contain some irregularities, from which it has been justly concluded, that the earth has not a perfectly regular form, but deviates more or less from the shape of a sphere. We can, therefore, properly draw conclusions from the oscillations of the pendulum respecting the power of gravity only, and not respecting the form of the earth. Besides the friction of the rod, &c, and the resistance of the air, there are also other circumstances which influence the oscillations of the pendulum, These are the changes of heat and cold. Heat lengthens the rod of the pendulum, cold contracts it; hence common pendulum clocks go much quicker in winter; and the change of temperature in rooms which are heated during the day influences them considerably. Many contrivances have been devised for overcoming this mconvenience. One is, by making pendulums of the form of a gridiron, consisting of several parallel bars of different metals, so connected that the effect of one set of them counteracts that of the others. These have been very successful. Rods are sometimes made of certain kinds of wood, well seasoned, which are little influenced by the weather. Astronomical clocks of the present day do not err to the amount of one beat or oscillation of the pendulum in a year. A common clock is merely a pendulum with wheelwork attached to it, to record the number of vibrations, and with a weight or spring to counteract the retarding effects of friction and the resistance of the air. Huygens, who developed the doctrine of the pendulum, which had been treated already by Galileo, first applied it to clocks, and thus became the inventor of the pendulum clock (in 1656). (See Clock.)For the application of pendulums to horology, see Berthoud's Essai sur VHorlogene (Paris, 1763, 2 vols., 4to.).See, also, Biot's treatise Sur la Longueur du Pendule a Secondes, in the third volume of his Traite d'Astronomie Physique (second edition, Paris, 1810). See, also, Bode's Anlcitung zur Kenntniss der Erdkugel (second edition, Berlin, 1803). PENELOPE. (See Ulysses.) PENGUIN. (See Pinguin.) PENITENTIARIES. (See Prisons.) PENN, William, was born in London, in 1644. He was the only son of William Penn, of the county of Wilts, viceadmiral of England in the time of Cromwell, and afterwards knighted by king Charles II, for his successful services against the Dutch. He appears to have been seriously inclined from his youth, having imbibed religious impressions as early as his twelfth year, which were soon afterwards confirmed by the ministry of Thomas Loe, an eminent preacher among the people called Quakers, then newly associated in religious fellowship. In his fifteenth year, he was, notwithstanding, entered as a gentleman commoner of Christchurch, Oxford, where, meeting with some other students who were devoutly inclined, they ventured to hold private meetings among themselves, wherein they both preached and prayed. This gave great offence to the heads of the college, by whom these zealous tyros were at first only confined for nonconformity ; but persisting in their religious exercises, they were finally expelled the university. On his return home, his father endeavored in vain to divert him from his religious pursuits, as being likely to stand in the way of his promotion in the world; and at length, finding him inflexible in what he now conceived to be his religious duty, beat him severely, and turned him out of doors. Relenting, however, at the intercession of his mother, and hoping to gain his point by other means, he sent his son to Paris, in company with some persons of quality; whence he returned so well skilled in the French language, and other polite accomplishments, that he was again joyfully received at home. After his return from France, he was admitted of Lincoln's Inn, with a view of studying the law, and continued there till his twentysecond year, when his father committed to him the management of a considerable estate in Ireland a circumstance which unexpectedly proved the occasion of his finally adhering to the despised cause of the Quakers, and devoting himself to a religious life. At Cork, he met again with Thomas Loe, the person whose preaching had affected him so early in life. At a meeting in that city, Loe began his declaration 1 with these penetrating words, ¦" There is a faith that overcomes the world, and there is a faith that is overcome by the world;" which so affected Penn, that from that time he constantly attended the meetings of the Quakers, though in a time of hot persecution. He was soon afterwards, with many others, taken at a meeting in Cork, and carried before the mayor, by whom they were committed to prison; but young Penn was soon released, on application to the earl of Orrery, then lord president ofMunster. His father, being informed of his conduct, remanded him home; and, finding him unalterably determined to abide by his own convictions of duty, in respect to plainness of speech and deportment, he would have compounded with him, if he would only have consented to remain uncovered before the king, the duke (afterwards James II), and himself. Being disappointed in this, he could no longer endure the sight of his son, and a second time drove him from his family. Yet after a while, becoming convinced of his integrity, he permitted him to return ; and though he never openly countenanced him, he would use bis interest to get him released, when imprisoned for his attendance at religious meetings. In the year 1668, in the twentyfourth year of his age, Penn first appeared as a minister and an author; and it was on account of his second essay, entitled the Sandy Foundation Shaken, that he was imprisoned in the Tower, where he remained seven months, during which time he wrote his most celebrated work, No Cross no Crown, and finally obtained his release from confinement by an exculpatory vindication, under the title of Innocency with her open Face. In 1670, the meetings of dissenters were forbidden, under severe penalties. The Quakers,however, believing it their religious duty, continued to meet as usual; and when forcibly kept out of their meetinghouses, they assembled as near to them as they could in the street. At one of these meetings, William Penn preached to the people thus assembled for divine worship; for which pious action he was committed to Newgate, and, at the next session at the Old Bailey, was indicted for " being present at, and preaching to, an unlawful, seditious, and riotous assembly." He pleaded his own cause, though menaced by the recorder and was finally acquitted by the jury but he was, nevertheless, detained in Newgate, and the jury fined. Sir William died this year, fully reconciled to his son, to whom he left a plentiful estate, taking leave of him in these memorable words: "Son William, let nothing in this world tempt you to wrong your conscience. So will you keep peace at home, which will be a feast to you in a day of trouble." Shortly after this event, Penn travelled, in the exercise of his ministry, into Holland and Germany. In the year 1672, he married Gulielma Maria Springett, whose father (sir William) having been killed at the siege of Bamber, in the civil wars, her mother had married Isaac Penington, of Chalfont, in Bucks, an eminent minister Barclay, the celebrated apologist, he again set sail on a religious visit to Holland and Germany, where he and his friends were received by many pious persons as the ministers of Christ, particularly at Herwerden, by the princess Elizabeth of the Rhine, daughter of the king of Bohemia, and granddaughter of James I of England. The persecutions of dissenters continuing to rage, notwithstanding their repeated applications to parliament for sufferance and protection, William Penn now turned his thoughts towards a settlement in the new world, as a place where himself and his friends might enjoy their religious opinions without molestation, and where an example might be set to the nations of a just and righteous government. "There may be room there," said he, "though not here, for such a holy experiment." He therefore, in 1681, solicited a patent from Charles II, for a province in North America, which the king readily granted, in consideration of his father's services, aad of a debt still due to him from the crown. Penn soon after published a description of the province, proposing easy terms of settlement to such as might be disposed to go thither. He also wrote to the Indian natives, informing them of his desire to hold his possession with their consent and goodwill. He then drew up the Fundamental Constitution of Pennsylvania, and the following year he published the Frame of Government, a law of which code held out a greater degree of religious liberty than had at that time been allowed in the world. " All persons living in this province, who confess and acknowledge the One Almighty and Eternal God to be the Creator, Upholder, and Ruler of the world, and that hold themselves obliged in conscience to live peaceably and justly in civil society, shall in no wise be molested or prejudiced for their religious persuasion or practice, in matters of faith and worship; nor shall they be compelled at any time to frequent or maintain any religious worship, place or ministry whatsoever." Upon the publication of these proposals, many respectable families removed to the new province; the city of Philadelphia was laid out, upon the banks of the Delaware; and in 1682, the proprietor visited his newlyacquired territory, where he remained about two years, adjusting its concerns, and establishing a friendly intercourse with his colonial neighbors; during which period no less Germany. Soon after Penn returned to England, king Charles died ; and the respect which James II bore to the late admiral, who had recommended his son to his favor, procured to him free access at court. He made use of this advantage to solicit the discharge of his persecuted brethren, fifteen hundred of whom remained in prison at the decease of the late king. In 1686, having taken lodgings at Kensington, to be near the court, he published a Persuasive to Moderation towards Dissenting Christians, &c, humbly submitted to the King and his great Council, which is thought to have hastened, if it did not occasion, the king's proclamation for a general pardon, which was followed the next year by his suspension of the penal laws. At the revolution, in 1688, Penn's intimacy with the abdicated monarch created suspicions, of which he repeatedly cleared himself before authority, until he was accused by a profligate wretch, whom the parliament afterwards declared to be a cheat and an impostor. Not caring to expose himself to the oaths of such a man, he withdrew from public notice, till 1693. In that year, through the mediation of his friends at court, he was once more admitted to plead his own cause before the king and council, and was again acquitted of all suspicion of guilt. The most generally known production of his temporary seclusion bears the title of Fruits of Solitude, in Reflections and Maxims relating to the Conduct of Human Life. Not long after his restoration to society, he lost his wife, Gulielma, to which he said all his other troubles were as nothing in comparison. He travelled, however, the same year, in the west of England, and in the next prosecuted an application to par liament for the relief of his friends, the Quakers, in the case of oaths. In the year 1696, he married a second wife, Hannah, the daughter of Thomas Callowhill, an eminent merchant of Bristol, and soon after buried his eldest son, Springett, a remarkably pious and promising youth. In 1698, he travelled in Ireland, and resided the following year at Bristol. In 1699, he again sailed for Pennsylvania, with his second wife and family, intending to make his province the place of their future residence; but advantage was taken of his absence to undermine proprietary governments, under color of the king's prerogative, and he thought it necessary to return to England again in 1701. After his arrival, the measure was laid aside, and Penn became once more welcome at court, on the accession of queen Anne. In 1710, finding the air near the city to disagree with his declining health, he took a handsome seat in Buckinghamshire, at which he continued to reside during the remainder of his life. In the year 1712, he had three distinct fits of the apoplectic kind. The last of these so impaired his memory and understanding as to render him ever after unfit for public action ; but he continued to deliver, in the meeting at Reading, short, but sound and sensible expressions. In 1717, he scarcely knew his old acquaintance, or could walk without leading. He died in 1718. The writings of Penn (first published in two volumes folio) bespeak his character as a Christian and a philanthropist. Of his ability as a politician and legislator, the prosperity of Pennsylvania is a lasting monument.