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vibrations

vibrations Sentence Examples

  • She feels the vibrations and understands what is said to her.

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  • We find that this dissipation, although undoubtedly going on, proceeds with extreme slowness, so that the vibrations pass their energy on to the ether as rapidly as they acquire it, and the " normal state " is never established.

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  • If the fork makes exactly 32 vibrations and the wheel 8 revolutions in one pendulum beat, then the positions will be fixed, and every two seconds, the time of a complete pendulum vibration, he will see the two positions looked at flash out in succession at an interval of a second.

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  • Vibrations increase in rapidity as a note rises and decrease as it falls.

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  • a surface at which the primary vibrations are in one phase.

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  • His most extensive single work is a book on Sound, which, in the second edition, has become a treatise on vibrations in general.

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  • This, therefore, is the number of vibrations corresponding to the note A3.

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  • The condenser method of making oscillations is analogous to the production of air vibrations by twanging a harp string at short intervals.

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  • Considering the time at which he wrote, Reis seems to have understood very well the nature of the vibrations he had to reproduce, but he failed to comprehend how they could be reproduced by electricity.

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  • Considering the time at which he wrote, Reis seems to have understood very well the nature of the vibrations he had to reproduce, but he failed to comprehend how they could be reproduced by electricity.

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  • The result, was in Helmholtz's words, to establish beyond doubt that ordinary light consists of electrical vibrations in an all-pervading ether which possesses the properties of an insulator and of a magnetic medium.

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  • He proposed to make the armature partake of the vibrations of the atmosphere either by converting it into a suitable vibrator or by controlling its vibrations by a stretched membrane of parchment armature had the form of a hinged lever one end, which pressed against the centre.

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  • In reading my teacher's lips I was wholly dependent on my fingers: I had to use the sense of touch in catching the vibrations of the throat, the movements of the mouth and the expression of the face; and often this sense was at fault.

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  • She is able not only to distinguish with great accuracy the different undulations of the air and the vibrations of the floor made by various sounds and motions, and to recognize her friends and acquaintances the instant she touches their hands or clothing, but she also perceives the state of mind of those around her.

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  • Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).

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  • Japan also experiences a vast number of petty vibrations not perceptible without the aid of delicate instruments.

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  • This alteration of charge caused a corresponding change in the mutual attraction of the plates of the condenser; hence the flexible plate was made to copy the vibrations of the diaphragm of the transmitter.

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  • Both Bell and Gray proposed to do this by introducing a column of liquid into the circuit, the length or the resistance of which could be varied by causing the vibrations of the diaphragm to vary the depth of immersion of a light rod fixed to it and dipping into the liquid.

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  • 5 He proposed to introduce into the circuit a cell containing carbon powder, the pressure on which could be varied by the micro- vibrations of a diaphragm.

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  • In the capital (Tokyo) the average yearly number of shocks throughout the 26 years ending in 1906 was 96, exclusive of minor vibrations, hut during the 50 years then ending there were only two severe shocks (i8S4 and 1894), and they were not directly responsible for any damage to life or limb.

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  • Such vibrations may be damped out to a considerable extent by the use of a dash-pot, or may be practically prevented by using a relatively stiff spring.

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  • Such vibrations may be damped out to a considerable extent by the use of a dash-pot, or may be practically prevented by using a relatively stiff spring.

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  • Soc.), regards the property as occasioned by internal vibrations within the molecule conditioned by a symmetrical double tautomerism, light of one wave-length being absorbed by one form, and emitted with a different wave-length by the other.

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  • The weighing is conducted in the usual way by vibrations, except when the weight be small; it is then advisable to bring the pointer to zero, an operation rendered necessary by the damping due to the adhesion of water to the fibre.

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  • I stood in the middle of the church, where the vibrations from the great organ were strongest, and I felt the mighty waves of sound beat against me, as the great billows beat against a little ship at sea.

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  • the total number of vibrations of the fork in any time may be accurately determined.

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  • By means of vibrations or shocks transmitted through the - Sub water, or by displacements in the balance or position of the animal, the otoliths are caused to impinge against the bristles of the sensory cells, now on one side, now on the other, causing shocks or stimuli which are transmitted by the basal nerve-fibre to the central nervous system.

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  • The relation between the pitch of a note and the frequency of the corresponding vibrations has also been studied by graphic methods.

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  • In remembrance of these victims of popular wrath Jalal-uddin founded the order of the Maulawi (in Turkish Mevlevi) dervishes, famous for their piety as well as for their peculiar garb of mourning, their music and their mystic dance (sama), which is the outward representation of the circling movement of the spheres, and the inward symbol of the circling movement of the soul caused by the vibrations of a Sufi's fervent love to God.

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  • The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.

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  • The frequency of these phenomena is in some degree a source of security, for the minor vibrations are believed to exercise a binding effect by removing weak cleavages.

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  • When a wave of sound travelling through one medium meets a second medium of a different kind, the vibrations of its own particles are communicated to the particles of the new medium, so that a wave is excited in the latter, and is propagated through it with a velocity dependent on the density and elasticity of the second medium, and therefore differing in general from the previous velocity.

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  • Or, if the same plate be moved in contact with two tuning-forks, we shall, by comparing the number of sinuosities in the one trace with that in the other, be enabled to assign the ratio of the corresponding numbers of vibrations per second.

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  • If, at the same time, a tuning-fork of known number of vibrations per second be made to trace its own line close to the other, a comparison of the two lines gives the number corresponding to the sound under consideration.

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  • The utility of the curve depends upon the fact that the elements of arc represent, in amplitude and phase, the component vibrations due to the corresponding portions of the primary wave-front.

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  • The vibrations corresponding to the two parts are precisely antagonistic, since if both were operative the resultant would be zero.

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  • The vibrations corresponding to the two parts are precisely antagonistic, since if both were operative the resultant would be zero.

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  • If we consider a number of particles which all lie upon a primary ray, we see that the phases of the secondary vibrations which issue along this line are all the same.

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  • When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot.

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  • According to the best determinations the value of elm does not exceed 1.8X Io', and T is of the order of Io 15 second, the period of luminous vibrations; hence OM/M must always be less than 109 H, and therefore the strongest fields yet reached experimentally, which fall considerably short of Io %, could not change the magnetic moment M by as much as a ten-thousandth part.

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  • What is understood by a" tone " in this language is distinguished in reality, not by the number of sonorous vibrations which belong to it, but rather by a use of the vocal apparatus special to each.

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  • In acoustics he invented, about 1819, the improved siren which is known by his name, using it for ascertaining the number of vibrations corresponding to a sound of any particular pitch, and he also made experiments on the mechanism of voice-production.

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  • As a verb, the word means to stifle or check; hence damped vibrations or oscillations are those which have been reduced or stopped, instead of being allowed to die out naturally; the "dampers" of the piano are small pieces of feltcovered wood which fall upon the strings and stop their vibrations as the keys are allowed to rise; and the "damper" of a chimney or flue, by restricting the draught, lessens the rate of combustion.

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  • If we divide this by 2 3 or 8, we obtain 440 as the number of vibrations answering to the note A.

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  • If, then, we can determine the number m of revolutions performed by the plate in every second, we shall at once have the number of vibrations per second corresponding to the audible note by multiplying m by n.

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  • Thus may be obtained, either separately or in various combinations, the four notes whose vibrations are in the ratios of the above numbers, and which therefore form the fundamental chord (Cegc 1).

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  • They agree very well with experiment, and require us to suppose that the vibrations are perpendicular to the plane of polarization.

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  • The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

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  • This corresponds to the electrical discharge of the antenna, and the subsequent string vibrations to the electrical vibrations.

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  • 6); and it has been suggested that the association of these two is analogous to the association of the rods and cones of the animal eye with their pigment layer, the light absorbed by the red pigment-spot setting up changes which react upon the refractive granule and being transmitted to the flagellum bring about those modifications in its vibrations by which the direction of movement of the organism is regulated.

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  • The first group, named the " luminophore," is such that when excited by suitable aetherial vibrations emits radiant energy; the other, named the " fluorogen," acts with the luminophore in some way or other to cause the fluorescence.

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  • Any obscurity that may hang over Huygens's principle is due mainly to the indefiniteness of thought and expression which we must be content to put up with if we wish to avoid pledging ourselves as to the character of the vibrations.

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  • In fact the proved tendency for the gas to pass into the " normal state " in which there is equipartition of energy, represents in this case nothing but the tendency for the translational energy to become dissipated into the energy of innumerable small vibrations.

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  • Until the vibrations of a source have a frequency in the neighbourhood of 30 per second the ear can hear the separate impulses, if strong enough, but does not hear a note.

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  • ix.) used a string loaded at the middle point so that the higher tones were several octaves above the fundamental, and so not likely to be mistaken for it; he found that with 37 vibrations per second a very weak sensation of tone was heard, but with 34 there was scarcely anything audible left.

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  • A determinate musical pitch is not perceived, he says, till about 40 vibrations per second.

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  • Then, as we shall prove later, the vibrations of the string may be represented by the travelling of two trains in opposite directions each with velocity /tension=mass per unit length each half the height of the train represented in fig.

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  • V i brat i ons thus excited are termed forced vibrations, and their amplitude is greater the more nearly the period of the applied force approaches that of the system when vibrating freely.

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  • The mathematical investigation of forced vibrations (Rayleigh,Sound, i.

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  • Suppose that a mass M is controlled by some sort of spring, so that moving freely it executes harmonic vibrations given by -µx, where µx is the restoring force to the centre of vibration.

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  • (22) Let us assume that the body makes vibrations in the new period 27rp, and let us put x = B sin pt; substituting in (22) we have p 2 B +n 2 B +P/M =0, whence P r B - M p2 _ n2 and the " forced " oscillation due to -P sin pt is x = P

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  • The direct and reflected systems are practically equal, and by suitably timing the vibrations of the hand for each case the rope may be made to vibrate as a whole, as two halves, as three-thirds and so on.

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  • The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.

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  • The open end is therefore a loop. It is to be noted that the exciter of the vibrations is in general at the open end, and that the two trains forming the stationary system consist of the direct waves from the exciter travelling into the tube, and the waves reflected back from the closed end.

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  • When the wire was heated by an electric current a fine line of vapour descended from each drop. The pipe was closed at the centre by a membrane which prevented a through draught, yet permitted the vibrations, as it was at a node.

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  • The vibrations of the larger mass are communicated to the thread, which by proper adjustment of its length and tension vibrates in unison and divides itself into one or more loops or ventral segments easily discernible by a spectator.

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  • Longitudinal Vibrations of Wires and Rods.

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  • Transverse Vibrations of Bars or Rods.

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  • We cannot investigate the vibrations in an elementary manner.

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  • When a cart wheel is ungreased it produces a very high note, probably due to torsional vibrations of the axle.

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  • The torsional vibrations of a wire are excited when it is bowed.

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  • If small paper rings are put on a monochord wire they rotate through these vibrations when the wire is bowed.

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  • 39, middle and rubbing it lengthwise FIG with a bit of cloth powdered with resin, till the rod gives a distinct note; the vibrations are communicated to the plate, which consequently vibrates transversely, and causes the sand to heap itself into one or more concentric rings.

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  • The membrana tympani or drum of the ear, has, in like manner and on the same principles, the property of repeating the vibrations of the external air which it communicates to the internal parts of the ear.

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  • The jet tube, for a reason which will be given when we consider the maintenance of vibrations, must be less than c a9 half the length of the sounding tube.

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  • Suppose the two notes to correspond to 200 and 203 vibrations per second; at some instant of time, the air particles, through which the waves are passing, will be similarly displaced by both, and consequently the joint effect will be a sound of some intensity.

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  • This will be followed by an increase of intensity until the lapse of another sixth of a second, when the less rapidly vibrating note will have lost another half-vibration relatively to the other, or one vibration reckoning from the original period of time, and the two component vibrations will again conspire and reproduce a maximum effect.

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  • By similar reasoning it may be shown that the number of beats per second is always equal to the difference between the numbers of vibrations in the same time corresponding to the two interfering notes.

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  • If both forks are in vibration, and are prefectly in tune, this line may either be increased or diminished permanently in length according to the difference of phase between the two sets of vibrations.

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  • Thus, two low notes of 32 and 30 vibrations respectively, whose interval is therefore la or 12-, i.e.

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  • a semitone, give two beats per second, while the same number of beats are given by notes of 32 X 16 (four octaves higher than the first of the preceding) or 512, and 514 vibrations, which are only slightly out of tune.

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  • This want of proportionality will have a periodicity, that of the impinging waves, and so will produce vibrations just as does the variation of pressure in the case last investigated.

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  • But if a load is so applied that the deflection increases with speed, the stress is greater than that due to a very gradually applied load, and vibrations about a mean position are set up. The rails not being absolutely straight and smooth, centrifugal and lurching actions occur which alter the distribution of the loading.

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  • (5) Speed of train produces no effect on the mean deflection, but only on the magnitude of the vibrations.

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  • Maxwell had himself, at an early stage of his theory, tested the absorbing power of gold-leaf for light, and found that the effective conductivity for luminous vibrations must be very much greater than its steady ohmic value; it is, in fact, there a case of incipient conductivity, which is continually being undone on account of the rapid alternation of force before it is fully established.

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  • In 1764 Leonhard Euler employed the functions of both zero and integral orders in an analysis into the vibrations of a stretched membrane; an investigation which has been considerably developed by Lord Rayleigh, who has also shown (1878) that Bessel's functions are particular cases of Laplace's functions.

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  • which does not consist of simple vibrations of a definite wave-length, undergoes refraction at the surface of any transparent medium, the different colours corre sponding to the different wave-lengths become separated or .dispersed.

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  • When the instrument was played, the vibrations were transmitted silently, and became audible in the lyre, which thus appeared to play of itself.

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  • - The spectroscope is an instrument which allows us to examine the vibrations sent out by a radiating source: it separates the component parts if they are homogeneous, i.e.

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  • The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power."

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  • 3 Although the vibrations in the infra-red have a considerably greater intensity, they are more difficult to register than those in the ultra-violet.

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  • It is only recently that owing to the introduction of carbon tubes heated electrically the excitement of the luminous vibrations of molecules by temperature alone has become an effective method for the study of their spectra even in the case of metals.

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  • Especially when large gratings are employed do we find that the electric arc alone seems sufficient to give vibrations of the requisite power.

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  • Thus if a molecule were set into vibration at a specified time and oscillated according to the above equation during a finite period, it would not send out homogeneous vibrations.

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  • - It is natural to consider the frequencies of vibrations of radiating molecules as analogous to the different notes sent out by an acoustical vibrator.

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  • Each band, as has been stated, is made up of lines indicating highly homogeneous vibrations.

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  • It is in the case of the absorption spectra of liquids that we can most often discover some connexion between vibrations of a complex system and that of the simpler systems which form the complex.

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  • Secondly, his theory of inference contains the admission that we infer beyond sensations: he remarks that the space of the geometer is beyond space-sensations, and the time of the physicist does not coincide with time-sensations, because it uses measurements such as the rotation of the earth and the vibrations of the pendulum.

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  • We know, from the concomitant variations between its vibrations and our perceptions, that its vibrations are not mere conditions but real causes of our perceptions; and that those vibrations are not our perceptions, because we cannot perceive them, but are real attributes of the bell.

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  • Great steadiness of card under severe shocks and vibrations, combined with a minimum of friction in the cap and pivot, is obtained with this compass.

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  • In creased length necessitated an increase in the diameter of the main tube to limit the amplitude of the vibrations caused by being pushed through the water.

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  • Nevertheless the press uses much less power than the hammer, because much of the force of the latter is dissipated in setting up useless - indeed harmful, and at times destructive - vibrations in the foundations and the surrounding earth and buildings.

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  • Popularly it is supposed that earthquake recorders are instruments so sensitive to slight vibrations that great care is necessary in selecting a site for their installation.

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  • Although this supposition is correct for a certain class of apparatus, as for example that which will record rapid elastic vibrations produced by the movement of a train a mile distant, it is far from being so for the ordinary apparatus employed by the seismologist.

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  • Generally speaking, the instruments used for these purposes are not disturbed by the vibrations resulting from ordinary traffic. In almost every household something may be found which will respond to a gentle shaking of the ground.

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  • If a style projecting from this pendulum rests upon say the smoked surface of a glass plate fixed to the ground, the vibratory motion of the ground will be recorded on the glass plate as a set of superimposed vibrations.

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  • There is also an extension from the upper surface of the pendulum, in contact with a system of levers and rods attached to the case; an air-dampkig cylinder is fitted to annul the free vibrations of the pendulum.

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  • In 1754 Euler communicated to the Berlin Academy a further memoir, in - which, starting from the hypothesis that light consists of vibrations excited in an elastic fluid by luminous bodies, and that the difference of colour of light is due to the greater or less frequency of these vibrations in a given time, he deduced his previous results.

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  • The size and shape, the complicated spinning motion which it is seen to execute, the internal strains and vibrations which doubtless take place, are all sacrificed in the mental picture in order that attention may be concentrated on those features of the phenomenon which are in the first place most interesting to us.

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  • Theory of vibrations.

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  • The type of motion represented by (6) is of fundamental importance in the theory of vibrations (~ 23); it is ~- called a simple-harmonic or (shortly) a simple vibration.

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  • In the case of very rapid vibrations it is usual to specify, not the period (21r/o), but its reciprocal the frequency, i.e.

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  • the number of complete, vibrations per unit time.

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  • This appears to be the case very approximately with steel or glass balls; generally, however, there is some appreciable loss of apparent energy; this is accounted for by vibrations produced in the balls and imperfect elasticity of the materials.

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  • The motion is therefore the resultant of two simple vibrations in perpendicular directions, of periods 22r ./ (pug), 2ir ~I (pf/g).

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  • The motion of G then consists of two superposed circular vibrations of the type x=a cos (ai+s), ya sin (at+~), (36)

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  • become to some extent indeterminate, and elliptic vibrations of the individual particles are possible.

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  • We proceed to the forced vibrations of the system.

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  • Free vibrations must of course be superposed on the forced vibrations given by (29) in order to obtain the complete solution of the dynamical equations.

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  • In practice the vibrations of a system are more or less affected by dissipative forces.

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  • The most important applications of the theory of vibrations are to the case of continuous systems such as strings, bars, membranes, plates, columns of air, where the number of degrees of freedom is infinite.

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  • In a paper by Dr C. Chree, The Whirling and Transverse Vibrations of Rotating Shafts, Proc. Phys.

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  • The phenomena attendant on the passage of electricity through solids, through liquids and through gases, are described in the article Electric conduction, and also Electrolysis, and the propagation of electrical vibrations in Electric Waves.

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  • The vibrations of this medium constitute the agency called light.

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  • These violent shocks are usually limited to comparatively small districts, though the vibrations may be felt at long distances from the centre of disturbance.

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  • Disturbances of the former kind lead to vibrations of harmonic type, whose amplitudes always remain small; but disturbances, whose wave-length exceeds the circumference, result in a greater and greater departure from the cylindrical figure.

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  • The detached masses into which a jet is resolved do not at once assume and retain a spherical form, but execute a series of vibrations, being alternately compressed and elongated in the direction of the axis of symmetry.

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  • The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

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  • Even when the resolution is regularized by the action of external vibrations of suitable frequency, as in the beautiful experiments of Savart and Plateau, the drops must still come into contact before they reach the summit of their parabolic path.

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  • A calculation analogous to that of Lord Kelvin may be applied to find the frequency of small transverse vibrations of a cylinder of liquid under the action of the capillary force.

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  • Vibrations of this kind are observed whenever liquid issues from an elliptical or other non-circular hole, or even when it is poured from the lip of an ordinary jug; and they are superposed upon the general progressive motion.

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  • In so far as the vibrations may be regarded as isochronous, the distance between consecutive corresponding points of the recurrent figure, or, as it may be called, the wavelength of the figure, is directly proportional to the velocity of the jet, i.e.

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  • But as the head increases, so do the lateral velocities which go to form the transverse vibrations.

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  • The transverse vibrations of non-circular jets allow us to solve a problem which at first sight would appear to be of great difficulty.

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  • When feathered or provided with secondary barbs the setae will respond to movements or vibrations in the surrounding water, and have been supposed to have an auditory function.

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  • The wing, during its vibrations, rotates upon two separate centres, the tip rotating round the root of the wing as an axis (short axis of wing), the posterior margin rotating around FIG.

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  • Quick as are the vibrations of natural wings, the speed of certain parts of the wing is amazingly increased.

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  • 13, where the effect of a single absorbing system upon vibrations of all wave-lengths is shown.

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  • In order to deaden the vibrations of the index arm when weighing goods a vertical rod is attached to the lever from the lever machine near its left-hand end, and this rod carries on its lower end a plunger which works in a closed cylindrical dash-pot containing oil or glycerin.

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  • At the bottom of the vertical leg from the goods-pan there is also a projecting piece which is attached to the top of a vertical piston rod, the piston of which plays in a dash-pot of glycerin as the beam sways, and deadens the vibrations of the index arm.

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  • By means of suitable and simple mechanism this vertical movement of the cylinders works plunger pistons in a pair of cylinders which contain glycerin, and these deaden the vibrations of the machinery while weighing is going on.

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  • The magnitude of the unbalanced force, for a mass of w pounds at a radius of r feet and a velocity of v feet per second, is expressed by wv 2 /gr lb; and, since the force varies as the square of the velocity, it is necessary carefully to balance a pulley running at a high speed to prevent injurious vibrations.

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  • His theory assumes the correspondence of mind and body, and is applied pari passu to the formation of ideas from sensations, and of " compound vibratiuncules in the medullary substance " from the original vibrations that arise in the organ of sense.2 The same general view was afterwards developed with much vigour and clearness on the psychical side alone by James Mill in his Analysis of the Human Mind.

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  • Earthquakes are frequent, especially in the districts which are peculiarly volcanic. Historical evidence goes to show that they are closely associated with three naturally defined regions: (I) the region between Skjalfandi and Axarfjdrllr in the north, where violent earth tremblings are extremely common; (2) at Faxafloi, where minor vibrations are frequent; (3) the southern lowlands, between Reykjanes and Myrdalsj6kull, have frequently been devastated by violent earthquake shocks, with great loss of property and life, e.g.

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  • Eisenlohr and others, with the view of determining the direction of the vibrations in polarized light (vide infra), but the results have not been consistent, and H.

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  • That this is actually the case is proved by experiments on the interference of polarized light, from which it may be deduced that the polarization-vector of a train of plane waves of plane polarized light executes rectilinear vibrations in the plane of the waves.

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  • In the particular case in which a= b and a -, (3 = (2n + 1) 7r/2, the vibrations are circular and the light is said to be circularly polarized.

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  • The intensities of the incident, reflected and refracted streams are then measured in the same way, and we have merely to express that the square of the amplitude of the incident vibrations is equal to the sum of the squares of the amplitudes of the reflected and refracted vibrations.

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  • Fresnel obtained his formulae by assuming that the optical difference of media is due to a change in the effective density of the ether, the elasticity being the same - an assumption inconsistent with his theory of double refraction - and was led to the result that the vibrations are perpendicular to the plane of polarization.

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  • Franz Neumann and James MacCullagh, starting from the opposite assumption of constant density and different elasticities, arrived at the same formulae for the intensities of the reflected light polarized in the principal azimuths, but in this case the vibrations must be regarded as parallel to the plane of polarization.

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  • 104) has, however, shown that the polarization of the light from the sky can only be explained on the elastic solid theory by Fresnel's hypothesis of a different density, and from the study of Hertzian oscillations, in which the direction of the electric vibrations can be a priori assigned, we learn that when these are in the plane of incidence there is no reflection at a certain angle, so that the electric force is perpendicular to the plane of polarization.

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  • Now Fresnel's formulae were obtained by assuming that the incident, reflected and refracted vibrations are in the same or opposite phases at the interface of the media, and since there is no real factor that converts cos T into cos (T+p), he inferred that the occurrence of imaginary expressions for the coefficients of vibration denotes a change of phase other than 7r, this being represented by a change of sign.

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  • A subsequent determination of the plane of polarization gives the ratio of the amplitudes of the vibrations in the component streams.

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  • According to the phase of the vibrations at this common point, the waves mutually strengthen or weaken their action, and there arises greater clearness or obscurity.

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  • Both heat and light are regarded as vibrations of this diffused ether.

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  • accelerometers fitted on skis to identify the most important vibrations.

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  • balancer shaft to reduce vibrations even further.

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  • As the vibrations from the bones in the middle ear enter the cochlea, they cause the fluid to move.

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  • Those people actually were not cognizant in any way of many of the higher vibrations that now come to you.

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  • The theory behind pedestrian induced lateral vibrations on bridges is that of synchronous lateral excitation.

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  • gyro sensors detect unwanted vibrations, triggering the corresponding movement of a correcting lens group perpendicular to the optical axis.

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  • The harmonics of the string vibrations were supposed to correspond to the observed hadrons.

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  • traffic humps Traffic humps on Ashford Road would increase traffic noise and vibrations, so would not be an acceptable solution.

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  • Movement of body energies and sound (chanting om, chanting triple gem etc) send powerful vibrations through the mind and body.

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  • Use the pump to create a vacuum that holds the cup in place, then turn up the vibrations and experience thrilling orgasms...

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  • At higher temperatures the increased thermal vibrations cause the permittivity to drop again.

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  • Fetal monitoring using phonography involves the transcription and analysis of vibrations originating in the fetus.

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  • self-excited vibrations of mechanical systems using parametric excitation in two degrees of freedom.

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  • Effectively dampens vibrations through polymer shock absorbers, allowing active camcorder use.

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  • It consists of a horizontal spindle, carrying at one end the wax cylinder, on which the sonorous vibrations are to be imprinted.

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  • This can be used to establish the need for particles to transmit vibrations.

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  • Skin Artist produces 1.7 million ultrasonic vibrations per second.

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  • Hence approximations of the eigenfrequencies for the longitudinal and torsional vibrations can be found immediately.

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  • The theory behind pedestrian induced lateral vibrations on bridges is that of synchronous lateral excitation.

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  • In non-geek speak that means the sonic signals are transferred into mechanical vibrations to produce 15 watts (RMS) of surprisingly rich sound.

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  • These are effective in reducing phonon conduction, i.e. heat transfer by lattice vibrations.

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  • When the male wolf spider stridulates, he sends the vibrations through a leaf to the chosen female.

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  • These forces have the same period and direction as the undisturbed luminous vibrations themselves.

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  • The disturbance, consisting of transverse vibrations, is propagated outwards in all directions from the centre; and, in consequence of the symmetry, the direction of vibration in any ray lies in the plane containing the ray and the axis of symmetry; that is to say, the direction of vibration in the scattered or diffracted ray makes with the direction of vibration in the incident or primary ray the least possible angle.

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  • In passing from one part of the spectrum to another, A is the only quantity which varies, and we have the important law: - When light is scattered by particles which are very small compared with any of the wave-lengths, the ratio of the amplitudes of the vibrations of the scattered and incident lights varies inversely as the square of the wave-length, and the ratio of intensities as the inverse fourth power.

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  • They agree very well with experiment, and require us to suppose that the vibrations are perpendicular to the plane of polarization.

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  • So far as (7) is concerned the alternative supposition that AD vanishes would answer equally well, if we suppose the vibrations to be executed in the plane of polarization; but let us now revert to (5), which gives w 3 = _ PAN y z - = + PAN xy _ PAN z 2 - x2 8 N r 2 N r2' W 2 + N r2 (8) from 0 along which there is no scattered light, - two along the axis According to these equations there would be, in all, six directions of y normal to the original ray, and four (y z = =x) at angles of 45° with that ray.

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  • So long as the particles are small no such vanishing of light in oblique directions is observed, and we are thus led to the conclusion that the hypothesis of a finite AN and of vibrations in the plane of polarization cannot be reconciled with the facts.

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  • No form of the elastic solid theory is admissible except that in which the vibrations are supposed to be perpendicular to the plane of polarization, and the difference between one medium and another to be a difference of density only (Phil.

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  • Accordingly, if E be the energy of the primary wave, dE 87-2n (D' - D) 2 T2 E dx 3 D2%4 ' whence E = Eoe-hx (II) where h = 8?r 2 n (D' - D)2T2 3 D2 x 4, (12) If we had a sufficiently complete expression for the scattered light, we might investigate (12) somewhat more directly by considering the resultant of the primary vibration and of the secondary vibrations which travel in the same direction.

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  • If we consider a number of particles which all lie upon a primary ray, we see that the phases of the secondary vibrations which issue along this line are all the same.

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  • Moreover, if OP = r, and AO=x, then r 2 =x 2 + p2, and pdp=rdr. The resultant at 0 of all the secondary vibrations which issue from the stratum dx is by (3), with sin ¢ equal to unity, ndx f ?

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  • Vibrations increase in rapidity as a note rises and decrease as it falls.

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  • Table III., showing orchestral pitches obtained in 1899, for the measurements of which the writer is responsible, prove how chimerical it is to hope for greater accuracy than is found between 435 and 440 vibrations a second for a', inasmuch as temperature must always be reckoned with.

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  • His most extensive single work is a book on Sound, which, in the second edition, has become a treatise on vibrations in general.

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  • The result, was in Helmholtz's words, to establish beyond doubt that ordinary light consists of electrical vibrations in an all-pervading ether which possesses the properties of an insulator and of a magnetic medium.

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  • This corresponds to the electrical discharge of the antenna, and the subsequent string vibrations to the electrical vibrations.

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  • The condenser method of making oscillations is analogous to the production of air vibrations by twanging a harp string at short intervals.

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  • circuit at each vibration, thus transmitting as many electric pulses through the circuit as there were vibrations in the sound.

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  • His first idea seems to have been to employ the vibrations of the current in an electric circuit, produced by moving the armature of an electromagnet included in the circuit nearer to or farther from the poles of the magnet.

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  • He proposed to make the armature partake of the vibrations of the atmosphere either by converting it into a suitable vibrator or by controlling its vibrations by a stretched membrane of parchment armature had the form of a hinged lever one end, which pressed against the centre.

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  • This alteration of charge caused a corresponding change in the mutual attraction of the plates of the condenser; hence the flexible plate was made to copy the vibrations of the diaphragm of the transmitter.

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  • It was very early recognized - and, indeed, is mentioned in the first patents of Bell, and in a caveat filed by Elisha Gray in the United States patent office only some two hours after Bell's application for a patent - that sounds and spoken words might be transmitted to a distance by causing the vibrations of a diaphragm to vary the resistance in the circuit.

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  • Both Bell and Gray proposed to do this by introducing a column of liquid into the circuit, the length or the resistance of which could be varied by causing the vibrations of the diaphragm to vary the depth of immersion of a light rod fixed to it and dipping into the liquid.

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  • 5 He proposed to introduce into the circuit a cell containing carbon powder, the pressure on which could be varied by the micro- vibrations of a diaphragm.

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  • By means of vibrations or shocks transmitted through the - Sub water, or by displacements in the balance or position of the animal, the otoliths are caused to impinge against the bristles of the sensory cells, now on one side, now on the other, causing shocks or stimuli which are transmitted by the basal nerve-fibre to the central nervous system.

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  • 6); and it has been suggested that the association of these two is analogous to the association of the rods and cones of the animal eye with their pigment layer, the light absorbed by the red pigment-spot setting up changes which react upon the refractive granule and being transmitted to the flagellum bring about those modifications in its vibrations by which the direction of movement of the organism is regulated.

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  • An ill-balanced load also exaggerates " plunging," and if the period of oscillation of the load happens to agree with the changes of contour or other inequalities of the track vibrations of a dangerous character, giving rise to so-called " sinuous " motion, may occur.

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  • Laplace (1801); Traite analytique des courbes et des surfaces du second degre (1802); Recherches sur l'integration des equations differentielles partielles et sur les vibrations des surfaces (1803); Traite de physique (1816); Recueil d'observations geodesiques, astronomiques et physiques executees en Espagne et Ecosse, with Arago (1821); Memoire sur la vraie constitution de l'atmosphere terrestre (1841); Traite elementaire d'astronomie physique (1805); Recherches sur plusieurs points de l'astronomie egyptienne (1823); Recherches sur l'ancienne astronomic chinoise (1840); Etudes sur l'astronomie indienne et sur l'astronomie chinoise (1862); Essai sur l'histoire generale des sciences pendant la Revolution (1803); Discours sur Montaigne (1812); Lettres sur l'approvisionnement de Paris et sur le commerce des grains (1835); Mélanges scientifiques et litteraires (1858).

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  • Soc.), regards the property as occasioned by internal vibrations within the molecule conditioned by a symmetrical double tautomerism, light of one wave-length being absorbed by one form, and emitted with a different wave-length by the other.

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  • The first group, named the " luminophore," is such that when excited by suitable aetherial vibrations emits radiant energy; the other, named the " fluorogen," acts with the luminophore in some way or other to cause the fluorescence.

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  • In remembrance of these victims of popular wrath Jalal-uddin founded the order of the Maulawi (in Turkish Mevlevi) dervishes, famous for their piety as well as for their peculiar garb of mourning, their music and their mystic dance (sama), which is the outward representation of the circling movement of the spheres, and the inward symbol of the circling movement of the soul caused by the vibrations of a Sufi's fervent love to God.

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  • When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot.

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  • According to the best determinations the value of elm does not exceed 1.8X Io', and T is of the order of Io 15 second, the period of luminous vibrations; hence OM/M must always be less than 109 H, and therefore the strongest fields yet reached experimentally, which fall considerably short of Io %, could not change the magnetic moment M by as much as a ten-thousandth part.

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  • a surface at which the primary vibrations are in one phase.

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  • Any obscurity that may hang over Huygens's principle is due mainly to the indefiniteness of thought and expression which we must be content to put up with if we wish to avoid pledging ourselves as to the character of the vibrations.

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  • The component vibrations at P due to the successive zones are thus nearly equal in amplitude and opposite in phase (the phase of each corresponding to that of the infinitesimal circle midway between the boundaries), and the series which we have to sum is one in which the terms are alternately opposite in sign and, while at first nearly constant in numerical magnitude, gradually diminish to zero.

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  • Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).

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  • This result was employed by Stokes as a criterion of the direction of vibration; and his experiments, conducted with gratings, led him to the conclusion that the vibrations 2 = 2?rv d4)/ d o- = ra (32); (33) .

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  • What is understood by a" tone " in this language is distinguished in reality, not by the number of sonorous vibrations which belong to it, but rather by a use of the vocal apparatus special to each.

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  • In acoustics he invented, about 1819, the improved siren which is known by his name, using it for ascertaining the number of vibrations corresponding to a sound of any particular pitch, and he also made experiments on the mechanism of voice-production.

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  • As a verb, the word means to stifle or check; hence damped vibrations or oscillations are those which have been reduced or stopped, instead of being allowed to die out naturally; the "dampers" of the piano are small pieces of feltcovered wood which fall upon the strings and stop their vibrations as the keys are allowed to rise; and the "damper" of a chimney or flue, by restricting the draught, lessens the rate of combustion.

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  • Japan also experiences a vast number of petty vibrations not perceptible without the aid of delicate instruments.

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  • The frequency of these phenomena is in some degree a source of security, for the minor vibrations are believed to exercise a binding effect by removing weak cleavages.

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  • In the capital (Tokyo) the average yearly number of shocks throughout the 26 years ending in 1906 was 96, exclusive of minor vibrations, hut during the 50 years then ending there were only two severe shocks (i8S4 and 1894), and they were not directly responsible for any damage to life or limb.

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  • The weighing is conducted in the usual way by vibrations, except when the weight be small; it is then advisable to bring the pointer to zero, an operation rendered necessary by the damping due to the adhesion of water to the fibre.

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  • In this expression the first line may be supposed to represent the energy (or part of the energy) of s similar molecules of a kind which we shall call the first kind, the terms 2 (mu 2 +mv 2 +mw 2) being the kinetic energy of translation, and the remaining terms arising from energy of rotation or of internal motion, or from the energy, kinetic and potential, of small vibrations.

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  • In fact the proved tendency for the gas to pass into the " normal state " in which there is equipartition of energy, represents in this case nothing but the tendency for the translational energy to become dissipated into the energy of innumerable small vibrations.

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  • We find that this dissipation, although undoubtedly going on, proceeds with extreme slowness, so that the vibrations pass their energy on to the ether as rapidly as they acquire it, and the " normal state " is never established.

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  • If the source makes n vibrations in one second it is said to have " frequency " n.

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  • When a wave of sound travelling through one medium meets a second medium of a different kind, the vibrations of its own particles are communicated to the particles of the new medium, so that a wave is excited in the latter, and is propagated through it with a velocity dependent on the density and elasticity of the second medium, and therefore differing in general from the previous velocity.

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  • It may thus be brought into unison with any sound of which it may be required to determine the corresponding number of vibrations per second, as for instance the note A3, three octaves higher than the A which is indicated musically by a small circle placed between the second and third lines of the G clef, which A is the note of the tuning-fork usually employed for regulating concert-pitch.

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  • This, therefore, is the number of vibrations corresponding to the note A3.

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  • If we divide this by 2 3 or 8, we obtain 440 as the number of vibrations answering to the note A.

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  • If, then, we can determine the number m of revolutions performed by the plate in every second, we shall at once have the number of vibrations per second corresponding to the audible note by multiplying m by n.

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  • As an example of the application of this siren, suppose that the number of revolutions of the plate, as shown by the indices, amounts to 5400 in a minute, that is, to 90 per second, then the number of vibrations per second of the note heard amounts to 90n, or (if number of holes in each plate = 8) to 720.

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  • Thus may be obtained, either separately or in various combinations, the four notes whose vibrations are in the ratios of the above numbers, and which therefore form the fundamental chord (Cegc 1).

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  • The relation between the pitch of a note and the frequency of the corresponding vibrations has also been studied by graphic methods.

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  • Thus, if an elastic metal slip or a pig's bristle be attached to one prong of a tuningfork, and if the fork, while in vibration, is moved rapidly over a glass plate coated with lamp-black, the attached style touching the plate lightly, a wavy line will be traced on the plate answering to the vibrations to and fro of the FIG.

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  • The same result will be ob tained with a stationary fork and a movable glass plate; and, if the time occupied by the plate in moving through a given distance can be ascertained and the number of complete undulations exhibited on the plate for that distance, which is evidently the number of vibrations of the fork in that time, is reckoned, we shall have determined the numerical vibration value of the note yielded by the fork.

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  • Or, if the same plate be moved in contact with two tuning-forks, we shall, by comparing the number of sinuosities in the one trace with that in the other, be enabled to assign the ratio of the corresponding numbers of vibrations per second.

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  • If, at the same time, a tuning-fork of known number of vibrations per second be made to trace its own line close to the other, a comparison of the two lines gives the number corresponding to the sound under consideration.

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  • The phonograph may be regarded as an instrument of this class, in that it records vibrations on a revolving drum or disk.

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  • The motion of the fork is maintained by the clock acting through an escapement, and the dial registers both the number Koenig's of vibrations of the fork and the seconds, minutes and Tuning-fork hours.

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  • the total number of vibrations of the fork in any time may be accurately determined.

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  • If the fork makes exactly 32 vibrations and the wheel 8 revolutions in one pendulum beat, then the positions will be fixed, and every two seconds, the time of a complete pendulum vibration, he will see the two positions looked at flash out in succession at an interval of a second.

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  • Then the wheel makes 8 N + 1 revolutions in N clock beats, and the fork makes 32 N + 4 vibrations in the same time.

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  • Until the vibrations of a source have a frequency in the neighbourhood of 30 per second the ear can hear the separate impulses, if strong enough, but does not hear a note.

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  • ix.) used a string loaded at the middle point so that the higher tones were several octaves above the fundamental, and so not likely to be mistaken for it; he found that with 37 vibrations per second a very weak sensation of tone was heard, but with 34 there was scarcely anything audible left.

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  • A determinate musical pitch is not perceived, he says, till about 40 vibrations per second.

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  • It is shown below how the vibrations of a string may be deduced from stationary waves.

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  • Then, as we shall prove later, the vibrations of the string may be represented by the travelling of two trains in opposite directions each with velocity /tension=mass per unit length each half the height of the train represented in fig.

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  • This resonance is a particular example of the general principle that a vibrating system will be set in vibration by any periodic Forced VI force applied to it, and ultimately in the period of the force, its own natural vibrations gradually dying down.

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  • V i brat i ons thus excited are termed forced vibrations, and their amplitude is greater the more nearly the period of the applied force approaches that of the system when vibrating freely.

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  • The mathematical investigation of forced vibrations (Rayleigh,Sound, i.

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