Pendulum

“ The pendulum is indeed an extraordinary instrument, and has been a useful handmaid to science. We are familiar with it as the time-regulator of our clocks, and the ease with which they may be made to go faster or slower by adjusting its length. ”

“ The vibrations of a pendulum, resemble the descent of a body on an inclined plane, and are produced by the same cause; now you must recollect, that the greater the perpendicular height of such a plane, in proportion to its length, the more rapid will be the descent of the body; a short pendulum ascends to a greater height than a larger one, in vibrating a given distance, and of course its descent must be more rapid. ”

“ In The Pendulum, the children follow each other in a circle, moving one arm before them, like a pendulum, in time to the music, and with a strongly marked motion, while they all sing the song. When one arm is tired, the other can be used for the pendulum. ”

“ Let a pendulum be constructed, whose length between the point of suspension and the centre of oscillation is equal to the breadth of the waves; and in the time that the pendulum will perform one single oscillation, the waves will advance forward nearly a space equal to their breadth. ”

“ Everybody knows what is meant by a pendulum in its simplest form, a weight hanging by a thread to a fixed point. Such was the pendulum experimented upon long ago by Galileo, who discovered the well-known law of isochronous vibrations, applicable to the same. ”

“ The fancy was that if I could keep that pendulum wagging long enough, it would set all those trees going too; and if I still kept it swinging, we should have such a storm of wind as no living man had ever felt or heard of. That I more than half believed it, will be evident from the fact that, although I frequently carried the pendulum, as I shall call it, to the window sill, and set it in motion by way of experiment, I had not, up to the time of a certain incident which I shall very soon have to relate, had the courage to keep up the oscillation beyond ten or a dozen strokes ”

“ However there is here a mistake; for the whole time of the swing, when the pendulum moves through small arches, bears to the time required for a body to fall down through half the length of the pendulum very nearly the same proportion, as the circumference of a circle bears to its diameter ”

“ Compound pendulum, every ordinary pendulum is compound, as differing from a Simple pendulum, which is a material point suspended by an ideal line; Invariable pendulum, a pendulum for carrying from station to station to be oscillated at each so as to fix the relative acceleration of gravity; Long and short pendulum, a pendulum for determining the absolute force of gravity by means of a bob suspended by a wire of varying length. [L., neut. of pendulus, hanging—pendēre, to hang.] ”

“ Büchner. “The pendulum of every clock shows the conversion of gravitation into motion” (p. 21) .
Reader. Indeed? What do you mean by gravitation? The attractive power of the earth, or its action, or the weight of the pendulum? Surely the attractive power of the earth is not converted into movement; for it remains in the earth, and it continues its work. Neither is the weight of the pendulum converted into movement; for the pendulum does not cease, while moving, to have weight, nor does it weigh more when, at rest ”

“ A gyroscopic pendulum is made by the addition to it of a fly-wheel, balanced and mounted, as in Gilbert’s barogyroscope, in a ring movable about an axis fixed in the pendulum, in the vertical plane of motion. ”

“ The two pendulums will guide the motion of the lever, which then partakes of the power of a351 pendulum, giving fresh impulse at every vibration of the pendulum, and every half revolution of the revolving pendulum; for, as each extremity of the lever rises, the weight within falls to the opposite extremity, and gives fresh impulse to the whole: thus (if my idea is correct) will be produced motion perpetual—that is to say, perpetual so long as the materials of which it is made will hold together. ”

“ But if, on moving the clock gently so as to set the pendulum in motion, we hear it wobbling about irregularly, and at the same time observe that there is no ticking of any kind, we come to the conclusion that the pendulum has somehow or other escaped the little catch that connects it with the mechanism, we have been really thinking. From the fact that the pendulum wobbles irregularly, we infer that it has lost its proper catch. ”

“ A vibrating pendulum in motion describes a segment of a circle, and returns on the same segment, and at every vibration its described segment decreases.
A revolving pendulum is composed of two or more pendulums, united at their lighter extremities, there revolving on an axis, the heavier extremities being placed at equal distances in the outer circle: this, I believe, is what is termed a fly-wheel when affixed to hand-mills, etc.
The tubular lever is the chief instigator of the whole, and must contain a weight apportioned to the weights of the two pendulums. ”

“ From A B to A C energy of motion keeps gaining on energy of position, until when the pendulum reaches C, it has annihilated it. Energy of position has entirely disappeared, and the whole original force expended in raising the pendulum to A B exactly reappears in the force or momentum of the pendulum at its lowest point. ”

“ At the same time, however, that I assert the inefficacy of any experiments with the pendulum as tending to show the earth's rotation, I admit that, provided a pendulum could be made to preserve its plane of oscillation for twenty-four hours, it would oscillate independently of the rotation of the earth, and actually describe a circle round a fixed table in that interval. ”

“ Therefore in pendulums of different lengths, swinging through small arches, the lengths of the pendulums are in a two fold or duplicate proportion of the times, they take in swinging; so that a pendulum of four times the length of another shall take up twice the time in each swing, one of nine times the length will make one swing only for three swings of the shorter, and so on. ”

“ The pendulum can be removed from the influence of the mountain, but it cannot be removed from the influence of the earth: we cannot take away the earth from the pendulum, nor the pendulum from the earth, to ascertain whether it would continue to vibrate if the action which the earth exerts upon it were withdrawn. ”

“ Now, as in the latitude of London a pendulum which is a trifle more than thirty-nine inches in length swings once in a second, it is evident that, by lengthening or shortening the Pendulum, we have the rate of the clock entirely under command. ”

“ Hence a pendulum is a constant representative of space, in its length; and of time, in its oscillation. At any point on the surface of the globe, a rod of a certain given length will invariably, in similar circumstances, beat seconds; and a rod, beating seconds as it swings, will invariably measure a certain fixed length, according to the latitude. ”

“ The pendulum, with a short swing in one direction, has but a short swing in the other; while the long swing to the right invariably means the long swing to the left. An object hurled upward to a certain height has an equal distance to traverse on its return. ”

“ We can pull a pendulum far out from its position of rest, and then when we let it go it makes a big swing: or we can pull it out only a little way and then its swing will be small; but the time of swing will remain the same. This was Galileo's great discovery about the pendulum. In the same way I fancy there are stars with big swings and stars which take only little swings and so never get far from the centre. On the whole the big bright stars will swing out farthest, and the little faint ones will swing quietly ”

“ The second form of pendulum is the compound, or physical, pendulum. It consists of an extended solid body which vibrates about a fixed axis under the action of the weight of the body. A compound pendulum may be constituted to oscillate about one axis only, in which case it is nonreversible and applicable only for relative measurements. Or a compound pendulum may be constituted to oscillate about two axes, in which case it is reversible (or “convertible”) and may be used to determine absolute values of gravity. ”

“ To all appearance, the phenomena exhibited by the pendulum are not to be accounted for by impact: in fact, it is usually assumed that corresponding phenomena would take place if the earth and the pendulum were situated in an absolute vacuum, and at any conceivable distance from, one another. If this be so, it follows that there must be two totally different kinds of causes of motion: the one impact—a vera causa, of which, to all appearance, we have constant experience; the other, attractive or repulsive 'force'—a metaphysical entity which is physically inconceivable. ”

“ A pendulum makes a certain number of swings in a given time, depending on its length. A long pendulum requires more time to complete its swing and will, therefore, make a less number of swings than a short one in the same time. ”

“ Since the creation of classical mechanics in the 17th century, the pendulum has been a basic instrument for the determination of the intensity of gravity, which is expressed as the acceleration of a freely falling body. ”

“ A pendulum, vibrating freely, in small and equal arcs, may be so adjusted in its length, as, by its vibrations, to make this division of the earth's motion into 86,400 equal parts, called seconds of mean time. ”

“ The difficulties of establishing a standard pendulum and of computing the lengths of others vibrating in given times are many and great. In the first place, the experiments are made in air, and the buoyancy of the air lessens the actual weight of the pendulum. Then, since the earth has a diurnal motion on its axis, every object placed on it has a centrifugal tendency which modifies what otherwise would be its gravitation. ”

“ But the pendulum produces its mechanical effect upon the escapement, at the moment of its contact, and each wheel upon the next, at the moment of its contact. As has 192 been said in a Review of this work, ‘The time lost in cases of indirect physical causation is consumed in the movements which take place among the parts of the mechanism in action, by which the active forces so transformed into momentum are transported over intervals of space to new points of action, the motion of matter in such cases being regarded as a mere carrier of force.’ (Quarterly Rev. No. cxxxv. p. 212.) ”