For prey these shepherds two he took, Whose metal stiff he knew he could not bend With hearsay pictures, or a window look, With one good dance, or letter finely penned. Sidney. The pens that did his pinions bind, Were like main-yards with flying canvas lined. Spenser. Never durst poet touch a pen to write, Until his ink were tempered with love's sighs. Shakspeare. I would be loath to cast away my speech; for, besides that it is excellently well penned, I have taken great pains to con it. Id. A PEN is usually formed of a goose's quill. Pens are also sometimes made of silver, brass, or iron. Dutch pens are made of quills that have passed through hot ashes, to take off the grosser fat and moisture, and render them more transparent. PEN, OF PENSTOCK. See PENSTOCK. PEN, FOUNTAIN, is a pen made of silver, brass, &c., which has been contrived to contain a considerable quantity of ink, and let it flow out by gentle degrees, so as to supply the writer a long time without being under the necessity of taking fresh ink. PEN, GEOMETRIC, an instrument in which, by a circular motion, a right line, a circle, an ellipse, and other mathematical figures, may be described. It was first invented and explained by John Baptist Suardi, in a work entitled Nouvo Istromenti per la Descrizzione di diverse Curve Antichi e Moderne, &c. Several writers had observed the curves arising from the compound motion of two circles, one moving round the other; but Suardi first realised the principle, and first reduced it to practice. It has been lately introduced with success into the steamengine by Watt and Bolton. PEN, SEA. See PENNATULA. PENEA, in botany, a genus of the monogynia order, and tetrandria class of plants; and in the natural method ranking with those of which the order is doubtful; CAL. diphyllous; COR. campanulated; the style quadrangular; CAPS. tetragonal, quadrilocular, and octospermous. PENAL, adj. Fr. penal, from Lat. pana. PENALTY, n. s. Denouncing, or enacting, or used for, punishment: penalty is the punishment incurred or denounced. Lend this money, not as to thy friend, But lend it rather to thine enemy, Who, if he break, thou mayest with better face Exact the penalty. Shakspeare. Merchant of Venice. Adamantine chains and penal fires. Milton. Many of the ancients denied the Antipodes, and some unto the penalty of contrary affirmations; but the experience of navigations can now assert them beyond all dubitation. Browne. Political power is a right of making laws with penalties of death, and consequently all less penalties, for preserving property, and employing the force of, the community in the execution of laws. Locke. Gratitude plants such generosity in the heart of man as shall more effectually incline him to what is brave and becoming than the terror of any penal law. South. Beneath her footstool science groans in chains, And wit dreads exile, penalties, and pains. PEN'ANCE, or cipline for sin. Dunciad. PENANCE is a punishment, either voluntary or imposed by authority, for the faults a person has committed. Penance is one of the seven sacraments of the Romish church. Besides fasting, alms, abstinence, and the like, which are the general conditions of penance, there are others of a more particular kind; as the repeating a certain number of ave-mary's, paternosters, and credos, wearing a hair shirt, and giving one's self a certain number of stripes. In Italy and Spain it is usual to see Roman Catholics almost naked, loaded with chains and a cross, and lashing themselves at every step. PENATES, in Roman antiquity, a kind of tutelar deities, either of countries or particular houses; in which last sense they differed in nothing from the lares. See LARES. They were properly the tutelar gods of the Trojans, and were adopted by the Romans, who gave them the title of penates. PENCARROW, a cape of Cornwall, on the south coast of the English Channel; two miles east of the mouth of the Fowey. PENCIL, n. s. Lat. penicillum. A small brush of hair which painters dip in their colors : an instrument for writing with black lead. Painting is almost the natural man; For since dishonour trafficks with men's nature,' Shakspeare. The Indians will perfectly represent in feathers whatsoever they see drawn with pencils. Heylyn. Pencils can by one slight touch restore Smiles to that changed face, that wept before. Dryden. For thee the groves green liveries wear, For thee the graces lead the dancing hours, And nature's ready pencil paints the flowers. Id. A sort of pictures there is, wherein the colours, as laid by the pencil on the table, mark out very odd figures. Locke. The faithful pencil has designed Some bright idea of the master's mind, Where a new world leaps out at his command, And ready nature waits upon his hand. Pope. Mark with a pen or pencil the most considerable things in the books you desire to remember. Watts. Pulse of all kinds diffused their od'rous powers, Where nature pencils butterflies on flowers. Harte. One spirit-His Who wore the platted thorns with bleeding brows, Rules universal nature. Not a flower But shows some touch, in freckle, streak, or stain, Of his unrivalled pencil. Couper. PENCILS are of various kinds, and made of boars' bristles, the thick ends of which are bound various materials; the largest sorts are made of to a stick, bigger or less according to the uses they are designed for: these, when large, are called brushes. The finer sorts of pencils are made of camels, badgers, and squirrels' hair, and of the down of swans; these are tied at the upper end with a piece of strong thread, and enclosed in the barrel of a quill. All good pencils, on being drawn between the lips, come to a fine point. PENCILS, for drawing, are made of long pieces of black-lead or red chalk, placed in a groove cut in a slip of cedar; on which other pieces of cedar being glued, the whole is planed round, and, one of the ends being cut to a point, it is fit for use. PENCKUM, a town of Germany, in Anterior Pomerania; thirteen miles south-west of Old Stettin, and forty-four N. N. W. of Custrin. Long. 31° 59′ E. Ferro, lat. 53° 15′ N. PENDA, the first king of Mercia, founded that kingdom, A. D. 626. He was killed by Oswy, king of Northumberland, A. D. 655. See MERCIA. PENDA. See PEMBA. A Fr. pendant of Lat. pendens, pendeo. jewel or any thing suspended; a pendulum; a small flag: pendence, pendency, or pendulosity and pendulousness all mcan suspension; the state of being pendent or hanging: pending is depending; hence undecided: pendulous, synonymous with pendent. Quaint in green she shall be loose enrobed With ribbons pendent, flaring about her head. Shakspeare. A pendent rock, A forked mountain, or blue promontory With trees upon't, that nod unto the world, And mock her eyes with air. Id. All the plagues, that in the pendulous air Hang fated o'er men's faults, light on thy daughters. ld. The Italians give the cover a graceful pendence or slopeness, dividing the whole breadth into nine parts, whereof two shall serve for the elevation of the highest top or ridge from the lowest. Wotton. To make the same pendant go twice as fast as it did, or make every undulation of it in half the time it did, make the line, at which it hangs, double in geometrical proportion to the line at which it hanged before. Digby on the Soul. They brought by wond'rous art Milton's Paradise Lost. His slender legs he increased by riding, that is, the humours descended upon their pendulosity, having no support or suppedaneous stability. Browne's Vulgar Errours. The grinders are furnished with three roots, and in the upper jaw often four, because these are pendulous. I sometimes mournful verse indite, and sing Ray. Philips. A person pending suit with the diocesan, shall be defended in the possession. Ayliffe. The judge shall pronounce in the principal cause, nor can the appellant alledge pendency of suit. Id. The spirits Some thrid the mazy ringlets of her hair, Some hang upon the pendents of her car. Pope. PENDANTS are often composed of diamonds, pearls, and other jewels. PENDANTS, in heraldry, parts hanging down from the label, to the number of three, four, five, or six, at most, resembling the drops in the Doric freeze. When they are more than three, they must be specified in blazoning. PENDANTS OF A SHIP are those streamers, or long colors, which are split and divided into two parts, ending in points, and hung at the head of masts, or at the yard-arm ends. PENDENNIS, a peninsula of Cornwall, at the mouth of Falmouth haven, a mile and a half in compass. On this Henry VIII. erected a castle, opposite to that of St. Maw's, which he likewise built. It was fortified by queen Elizabeth, and served them for the governor's house. It is one of the largest castles in Britain, and is built on a high rock. It is stronger by land than St. Maw's, being regularly fortified, and having good outworks. PENDULUM, n. s. Fr. pendule; Lat pendulus. Any weight hung so that it may easily swing backwards and forwards. See below. Upon the bench I will so handle 'em, That the vibration of this pendulum Shall make all taylors yards of one Unanimous opinion. Hudibras. A PENDULUM is a vibrating body suspended from a fixed point. For the history of this invention, see CLOCK. The theory of the pendulum depends on that of the inclined plane. Hence, to understand the nature of the pendulum, it will be necessary to premise some of the properties of this plane. I. Let AC, fig. 1, Plate PENDULUM, be an inclined plane, A B its perpendicular height, and D any heavy body: then the force which impels the body D to descend along the inclined plane A C is to the absolute force of gravity as the height of the plane AB is to its length AC; and the motion of the body will be uniformly accelerated. II. The velocity acquired in any given time by a body descending on an inclined plane, AC, is to the velocity acquired in the same time, by a body falling freely and perpendicularly, as the height of the plane A B to its length A C. The final velocities will be the same; the spaces described will be in the same ratio; and the times of description are as the spaces described. III. If a body descend along several contiguous planes, AB, BC, CD (fig. 2), the final velocity, namely, that at the point D, will be equal to the final velocity in descending through the perpendicular A E, the perpendicular heights being equal. Hence, if these planes be supposed indefinitely short and numerous, they may be conceived to form a curve; and therefore the final velocity acquired by a body in descending through any curve AF, will be equal to the final velocity acquired in descending through the planes AB, BC, CD, or to that in descending through A E, the perpendicular heights being equal. IV. If, from the upper or lower extremity of the vertical diameter of a circle, a cord be drawn, the time of descent along this cord will be equal to the time of descent through the vertical diameter; and therefore the times of descent through all cords in the same circle, drawn from the extremity of the vertical diameter, will be equal. V. The times of descent of two bodies through two planes equally elevated will be in the subduplicate ratio of the lengths of the planes. If, instead of one plane, each be composed of several contiguous planes similarly placed, the times of descent along these planes will be in the same ratio. Hence, also, the times of describing similar arches of circles similarly placed will be in the subduplicate ratio of the lengths of the arches. VI. The same things hold good with regard to bodies projected upward, whether they ascend upon inclined planes or along the arches of circles. The point or axis of suspension of a pendulum is that point about which it performs its vibrations, or from which it is suspended. The centre of oscillation is a point in which, if all the matter in a pendulum were collected, any force applied at this centre would generate the same angular velocity in a given time as the same force when applied at the centre of gravity. The length of a pendulum is equal to the distance between the axis of suspension and centre of oscillation. Let PN (fig. 3) represent a pendulum suspended from the point P; if the lower part N of the pendulum be raised to A, and let fall, it will by its own gravity descend through the circular arch AN, and will have acquired the same velocity at the point N that a body would acquire in falling perpendicularly from C to N, and will endeavour to go off with that velocity in the tangent ND; but, being prevented by the rod or cord, will move through the arch Ñ B to B, where, losing all its velocity, it will by its gravity descend through the arch BN, and, having acquired the same velocity as before, will ascend to A. In this manner it will continue its motion forward and backward along the arch AN B, which is called an oscillatory or vibratory motion; and each swing is called a vibration. Prop. I. If a pendulum vibrates in very small circular arches, the times of vibration may be considered as equal, whatever be the proportion of the arches. Let PN (fig. 4) be a pendulum; the time of describing the arch AB will be equal to the time of describing CD; these arches being supposed very small. Join AN, CN; then since the times of descents along all cords in the same circles, drawn from one extremity of the vertical diameter, are equal; therefore, the cords AN, CN, and consequently their doubles, will be described in the same time; but the arches AN, CN, being supposed very small, will therefore be nearly equal to their cords: hence the times of vibrations in these arches will be nearly equal. PROP. II.-Pendulums which are of the same length vibrate in the same time, whatever be the proportion of their weights. This follows from the property of gravity, which is always proportional to the quantity of matter, or to its inertia. When the vibrations of pendulums are compared, it is always understood that they describe either similar finite arcs, or arcs of evanescent magnitude, unless the contrary is mentioned. PROP. III.—If a pendulum vibrates in the small arc of a circle, the time of one vibration is to the time of a body's falling perpendicularly through half the length of the pendulum as the circumference of a circle is to its diameter. Let PE (fig. 5) be the pendulum which describes the arch A N C in the time of one vibration; let PN be perpendicular to the horizon, and draw the cords AC, AN; take the arc Ee infinitely small, and draw EFG, efg, perpendicular to PN, or parallel to A C; describe the semicircle BG N, and draw er, gs, perpendicular to EG; now lett time of descending through the diameter 2 PN, or through the cord AN; then the velocities gained by falling through 2 PN, and by the pendulum's descending through the arch A E, will be as√2PN and BF; and the space described in the time t, after the fall through 2 PN, is 4 PN. But the times are as the spaces divided by the velocities. 4PN √2PN tx Ee time of describing Ee= 2√2PN X BF' But in the similar triangles PE F, Eer, and KGF, Ggs, As PE PN: EF:: Ee:er EF PN Gs= EF PN × Ee; And KG = KD : FG :: Gg × Ee= × Gg. Hence Ee= : : in its mean quantity for all the arches Gg, is 2 BN x 2 PN-NK × BGN; and the 2 BN X2 PN-NK time of describing the whole arch ABC, or the time of one vibration, is = = tx √2 PN x 2 BGN. But, when x 2 BGN = tx BN. 2 BN x2 BN-N K the arch ANC is very small, NK vanishes, and then the time of vibration in a very small arc is tx √2PN 2 BGN 2 BN x 2 PN Now, if t be the time of descent through 2 PN; then, since the spaces described are as the squares of the times, will be the time of descent through PN: therefore the diameter B N is to the circumference, 2 BG N, as the time of falling through half the length of the pendulum is to the time of one vibration. PROP. IV. The length of a pendulum vibrating seconds is to twice the space through which a body falls in one second as the square of the diameter of a circle is to the square of its circumference. Let d diameter of a circle =1, c circumference 3.14159, &c., t to d с the time of one vibration, and p the length of the corresponding pendulum; then by last proposition c d 1′′ : time of falling through Lets space half the length of the pendulum. described by a body falling perpendicularly in the first second: then, since the spaces described are in the subduplicate ratio of the times of ded scription, therefore 1": :: √ √ p. Hence c2 d2: 28: p. It has been found by experiment that in latitude 51° a body falls about 16.11 feet in the first second: hence the length of a pendulum vibrating seconds in that latitude 23 feet 3-174 inches. PROP. V.-The times of the vibrations of town pendulums in similar arcs of circles are in a lums. Let PN, PO (fig. 6), be two pendusubduplicate ratio of the lengths of the pendulums vibrating in the similar arcs A B, CD; the time of a vibration of the pendulum PN is to the time of a vibration of the pendulum P O in subduplicate ratio of PN to PO. Since the arcs AN, CO, are similar and similarly placed, the time of descent through A N will be to the time of descent through CO in the subduplicate ratio of AN to CO: but the times of descent through the arcs AN and CO are equal to half the times of vibration of the pendulums PN, PO, respectively. Hence the time of vibration of the pendulum PN, in the arch A B, is to the time of vibration of the pendulum PO in, the similar arc C D in the subduplicate ratio of A N to CO and since the radii PN, PO, are proportional to the similar ares AN, CO, therefore the time of vibration of the pendulum PN will be to the time of vibration of the pendulum PO in a subduplicate ratio of PN to PO. If the length of a pendulum vibrating seconds be 39-174 inches, then the length of a pendulum vibrating half seconds will be 9-793 inches. For 1":" :: √ 39·174: √✅ a; and 1 : † :: 39.174 39.174 = 9.793. 4 ? : I. Hence r = PROP. VI.-The length of pendulums vibrating in the same time, in different places, will be as the forces of gravity. For the velocity generated in any given time is directly as the force of gravity, and inversely as the quantity of matter. Now, the matter being supposed the same in both pendulums, the velocity is as the force of gravity; and the space passed through in a given time will be as the velocity; that is, as the gravity. Cor. Since the length of pendulums vibrating in the same time in small arcs are as the gravitating forces, and as gravity increases with the latitude on account of the spheroidal figure of the earth and its rotation about its axis; hence the length of a pendulum vibrating in a given time will be variable with the latitude, and the same pendulum will vibrate slower the nearer it is carried to the equator. PROP. VII.-The time of vibrations of pendulums of the same length, acted upon by different forces of gravity, are reciprocally as the square roots of the forces. For, when the matter is given, the velocity is as the force and time; and the space described by any given force, is as the force and square of the time. Hence the lengths of pendulums are as the forces and the squares of the times of falling through them. But these times are in a given ratio to the times of vibration; whence the lengths of pendulums are as the forces and the squares of the times of vibration. Therefore, when the lengths are given, the forces will be reciprocally as the square of the times, and the times of vibration reciprocally as the square roots of the forces. Cor. Let p ength of pendulum, g force of gravity, and t = time of vibration. Then since = x 12. That Hence 1 £ ; and t = √ px g = px is, the forces in different places are directly as the lengths of the pendulums, and inversely as the square roots of the times of vibration; and the times of vibration are directly as the square roots of the lengths of the pendulums, and inversely as the square roots of the gravitating forces. PROP. VIII-A pendulum which vibrates in the arch of a cycloid describes the greatest and least vibrations in the same time. This property is demonstrated only on a supposition that the whole mass of the pendulum is concentrated in a point but this cannot take place in any really vibrating body; and, when the pendulum is of finite magnitude, there is no point given in posi : tion which determines the length of the pendulum; on the contrary the centre of oscillation will not occupy the same place in the given body, when describing different parts of the tract it moves through, but will continually be moved in respect of the pendulum itself during its vibraThis circumstance has prevented any getion. neral determination of the time of vibration in a cycloidal arc, except in the imaginary case referred to. There are many other obstacles which concur in rendering the application of this curve to the vibration of pendulums designed for the measures of time the source of errors far greater than those which by its peculiar property it is intended to obviate; and it is now wholly disused in practice. Although the times of vibration of a pendulum in different arches be nearly equal, yet, from what has been said, it will appear that, if the ratio of the least of these arches to the greatest be considerable, the vibrations will be performed in different times; and the difference, though small, will become sensible in the course of one or more days. In clocks used for astronomical purposes it will therefore be necessary to observe the arc of vibration; which if different from that described by the pendulum when the clock keeps time, there a correction must be applied to the time shown by the clock. This correction, expressed in seconds of time, will be equal to the half of three times the difference of the square of the given arc, and of that of the arc described by the pendulum when the clock keeps time, these arcs being expressed in degrees; and so much will the clock gain or lose according as the first of these arches is less or greater than the second. Thus, if the clock keeps time when the pendulum vibrates in an arch of 3o, it will lose 10 daily in an arch of 4°. For 4—3a × 3 = 7× = 10}". The length of a pendulum rod increases with heat; and the quantity of expansion answering to any given degree of heat is experimentally found by means of a pyrometer (see PYROMETER); but the degree of heat at any given time is shown by a thermometer: hence that instrument should be placed within the clock-case at a height nearly equal to that of the middle of the pendulum; mined at least once a day. Now, by a table conand its height, for this purpose, should be exastructed to exhibit the daily quantity of accele ration or retardation of the clock, answering to every probable height of the thermometer, the corresponding correction may be obtained. It is also necessary to observe that the mean height of the thermometer during the interval ought to be used. In Six's thermometer this height may be easily obtained; but in the thermometers of the common construction it will be more difficult to find this mean. It has been found, by repeated experiments, that a brass rod equal in length to a second pendulum will expand or contract one 1000th part of an inch by a change of temperature of 1° in Fahrenheit's thermome ter; and, since the times of vibration are in a subduplicate ratio of the lengths of the pendulum, hence an expansion or contraction of one 1000dth part of an inch will answer nearly to 1" daily; therefore a change of 1° in the thermometer will occasion a difference in the rate of the clock |