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oscillation

The next class of wave or oscillation detector is the magnetic detector depending upon the power of electric oscillations to affect the magnetic state of iron.

40In the case of the inductive mode of exciting the oscillations an important quantity is the coefficient of coupling of the two oscillation circuits.

44Instead of inserting the sensitive tube between the receiving antenna and the earth, he inserted the primary coil of a peculiar form of oscillation transformer and connected the terminals of the tube to the secondary circuit of the transformer.

2211575 of 1897), but it is not every form of oscillation transformer which is suitable for this purpose.

22These two circuits are so adjusted that the closed oscillation circuit, consisting of the condenser, primary coil 1 See German Patent of F.

22For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

22The lower ends of these wires are connected through the secondary coil of an oscillation transformer to an earth plate, or to a large conductor placed on or near the earth called a " balancing capacity."

26The secondary circuit of this last is either connected between an aerial A and the earth E, or it may be again in turn connected to a second pair of spark balls and these again to a second condenser oscillation transformer and the aerial A.

10In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him.

10Therefore, according to Kekule, the double linkages are in a state of continual oscillation, and if his dynamical notion of valency, or a similar hypothesis, be correct, then the difference between the 1.2 and 1.6 di-derivatives rests on the insufficiency of his formula, which represents the configuration during one set of oscillations only.

10This configuration is, according to Sachse, more stable than any other form; no oscillation is possible, the molecule being only able to move as a whole.

10The change of frequency of oscillation of radiating molecules placed in a magnetic field, which was discovered by P. Zeeman, and the observed polarization of the components, are all beautifully explained by the theory of H.

10(6) A strictly periodic oscillation of this kind occurs in the working of a steam engine, in which the walls of the cylinder are exposed to regular fluctuations of temperature with the admission and release of steam.

10The dotted boundary curves have the equation 0 =omx, and show the rate of diminution of the amplitude of the temperature oscillation with depth in the metal.

104 is o 60 in., at which depth the amplitude of the variation is reduced to less than one five-hundredth part (e 2 7r) of that at the surface, so that for all practical purposes the oscillation may be neglected beyond one wave-length At half a wave-length the amplitude is only 3 rd of that at the surface.

10The steam pressure in the heater may be periodically varied by the gauge in such a manner as to produce an approximately simple harmonic oscillation of temperature at the hot end, while the cool end is kept at a steady temperature.

10During a gale a slight oscillation is noticeable on the bridge itself and from the shore.

10As in the rest of the Mediterranean, tides are scarcely observable; but at several points on the west and south coasts a curious oscillation in the level of the waters, known to the natives as the marrobbio (or marobia), is sometimes noticed, and is said to be always preceded by certain atmospheric signs.

10libra, a balance), a slow oscillation, as of a balance; in astronomy especially the seeming oscillation of the moon around her axis, by which portions of her surface near the edge of the disk are alternately brought into sight and swung out of sight.

10It is the oscillation which Mill manifests between the conception of his formula as it is actually applicable to concrete problems in practice, and the conception of it as an expression of a theoretical limit to practical procedure.

10In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him.

10The dotted boundary curves have the equation 0 =omx, and show the rate of diminution of the amplitude of the temperature oscillation with depth in the metal.

104 is o 60 in., at which depth the amplitude of the variation is reduced to less than one five-hundredth part (e 2 7r) of that at the surface, so that for all practical purposes the oscillation may be neglected beyond one wave-length At half a wave-length the amplitude is only 3 rd of that at the surface.

10During a gale a slight oscillation is noticeable on the bridge itself and from the shore.

10As in the rest of the Mediterranean, tides are scarcely observable; but at several points on the west and south coasts a curious oscillation in the level of the waters, known to the natives as the marrobbio (or marobia), is sometimes noticed, and is said to be always preceded by certain atmospheric signs.

10In almost all climes the tortoise and the frog are among the precursors and heralds of this season, and birds fly with song and glancing plumage, and plants spring and bloom, and winds blow, to correct this slight oscillation of the poles and preserve the equilibrium of nature.

10jars or of Leyden panes immersed in oil or some form of air condenser, and the inductance coil or primary circuit of the oscillation transformer consists of a few turns of highly insulated wire wound on a frame and immersed in oil.

11When used as a receiver for wireless telegraphy Marconi inserted the oscillation coil of this detector in between the earth and a receiving antenna, and this produced one of the most sensitive receivers yet made for wireless telegraphy.

11- A, antenna; P S, jigger or oscillation transformer; C, condenser; 0, Fleming oscillation valve; B, working battery; T, telephone; R, rheostat; E, earth-plate.

11The receiving arrangement consists of an antenna which is connected to earth through the primary coil of an oscillation transformer and a variable inductance.

11This receiver therefore, like the transmitter, consists of an open and a closed electric oscillation circuit inductively connected together; also the two circuits of the receiver must be syntonized or tuned both to each other and to those of the transmitter.'

11When the methods for effecting this had been worked out practically it finally led to the inventions of Slaby, Braun and others being united into a system called the Telefunken system, which, as regards the transmitter, consisted in forming a closed oscillation circuit comprising a condenser, spark gap and inductance which at one point was attached either directly or through a condenser to the earth or to an equivalent balancing capacity, and at some other point to a suitably tuned antenna.

11At the receiving station the differences in these systems depend chiefly upon variations in the actual form of the oscillation detector used, whether it be a loose contact or a thermal, electrolytic or magnetic detector.

11His solution of the celebrated problem of the "centre of oscillation" formed in itself an important event in the history of mechanics.

11The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

11For his demonstration in 1851 of the diurnal motion of the earth by the rotation of the plane of oscillation of a freely suspended, long and heavy pendulum exhibited by him at the Pantheon in Paris, and again in the following year by means of his invention the gyroscope, he received the Copley medal of the Royal Society in 1855, and in the same year he was made physical assistant in the imperial observatory at Paris.

11In its course it passes through a glass tube wound over with two coils of wire; one of these is an oscillation coil through which the oscillations to be detected pass, and the other is in connexion with a telephone.

12D and spark gap, has the same natural time period of oscillation as the open circuit consisting of the antenna, secondary coil and adjustable inductance.

00The oscillations are controlled either by a key inserted in the primary circuit of the exciting induction coil or transformer, or by a key cutting in and out of the primary condensers or throwing inductance in and out of the closed oscillation circuit.

00The transformer T has its secondary or high-pressure terminals connected to spark balls S1, which are also connected by a circuit consisting of a large glass plate condenser C, and the primary circuit of an air-core transformer called an oscillation transformer.

00Fleming invented in 1904 a detector called an oscillation valve or glow lamp detector made as follows: 1 A small carbon filament incandescent lamp has a platinum plate or cylinder placed in it surrounding or close to the filament.

00Such an oscillation valve was first used by Fleming as a receiver for wireless telegraph purposes in 1904 as follows: - In between the receiving antenna and the earth is placed the primary coil of an oscillation transformer; the secondary circuit of this transformer contains a galvanometer in series with it, and the two together are joined between the external negative terminal of the carbon filament of the above-described lamp and the insulated platinum plate.

00His transmitter consists of a nearly closed oscillating circuit comprising a condenser or battery of Leyden jars, a spark gap, and the primary coil of an oscillation transformer consisting of one turn of thick wire wound on a wooden frame.

00The centric hypothesis has been applied to these rings by Bamberger and others; but as in the previous rings considered, the ordinary (3) (4) (5) representation with double and single linkages generally represents the syntheses, decompositions, &c.; exceptions, however, are known where it is necessary to assume an oscillation of the double linkage.

00C. C. Baly regards colour as due to " isorropesis " or an oscillation between the residual affinities of adjacent atoms composing the molecule.

00This oscillation may be represented in the case of acridine and fluorescein as This theory brings the property of fluorescence into relation with that of colour; the forms which cause fluorescence being the coloured modifications: ortho-quinonoid in the case of acridine, paraquinonoid in the case of fluorescein.

00This tautomerism may be of a twofold nature :-(I) it may involve the mere oscillation of linkages, as in acridine; or (2) it may involve the oscillation of atoms, as in fluorescein.

00trepidare, to tremble), a term meaning, in general, fear or trembling, but used technically in astronomy for an imagined slow oscillation of the ecliptic, having a period of 7000 years, introduced by the Arabian astronomers to explain a supposed variation in the precession of the equinoxes.

00It was in this same year that he received the singular diplomatic mission to Frederick which nobody seems to have taken seriously, and after his return the oscillation between Brussels, Cirey and Paris was resumed.

00Having studied mathematics under John Machin and John Keill, he obtained in 5708 a remarkable solution of the problem of the " centre of oscillation," which, however, remaining unpublished until May 5754 (Phil.

00In the last resort, therefore, Spencer fails to deduce philosophically not only the necessity of progress, but also its compatibility with the evolution-dissolution oscillation, and even the general possibility of conceiving the world as a process.

00In addition to this it is necessary to have an extra system of fixed guides at the surface and at the bottom, where it is necessary to keep the cage steady during the operations of loading and landing, there being a much greater amount of oscillation during the passage of the cage than with fixed guides.

00The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...

00(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

00For the scientific problems connected with oscillation see Mechanics and Oscillograph.

00He also demonstrated that mutations have this special or distinctive character, that they repeat in the same direction without oscillation or retrogression.

00They determined to reinvestigate the motion of y Draconis; the telescope, constructed by George Graham (1675-1751), a celebrated instrument-maker, was affixed to a vertical chimneystack, in such manner as to permit a small oscillation of the eyepiece, the amount of which, i.e.

00The oscillation of the earth's axis may arise in two distinct ways; distinguished as " nutation of the axis " and " variation of latitude.

00" Nutation, the only form of oscillation imagined by Bradley, postulates that while the earth's C A FIG.

00Defining oscillation as is usual in spectroscopic measurement by wave-length, the visible spectrum is found to extend from about 7700 to 3900 A.

00A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants.

00The spectra experimented on by Paschen were band spectra, but as these split up into fine lines the possibility of homogeneous radiation in pure thermal oscillation may be considered as established.

00This represents a forced oscillation whose period 27r/o1, coincides with that of the disturbing force; and the phase agrees with that of the force, or is opposed to it, according as c1i2u; i.e.

00marion (as in the case of the pendulum), this solution can only be accepted as a representation of the initial stages of the forced oscillation.

00This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.

00To find the forced oscillation due to a periodic force we have tl+k+ux-f cos(rjt+e).

00Thus, assuming that the period of a small oscillation of a given pendulum at a given place is a definite quantity, we see that it must vary as ~ (l/g).

00The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.

00sin 4, we find for the period (r) of a complete oscillation r= 4f ~4=~V- f1/8~r~ ~1 _Ii~in1~

00The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.

00This occurs only when the period (21r/w) of revolution of the arm lies between the two periods (2ii-/p, 27r/q) of oscillation when the arm is fixed.

00If we produce OG to P, making OP =1, the point P is called the centre of oscillation; the bob of a simple pendulum of length OP suspended from 0 will keep step with the motion of P, if properly started.

00This shows that if the body were swung from a parallel axis through P the new centre of oscillation would be at 0.

00For different parallel axes, the period of a small oscillation varies as ~i, or ~f (GO+OP); this is least, subject to the condition (4), when GO=GP=,c. The reciprocal relation between the centres of suspension and oscillation is the basis of Katers method of determining g experimentally.

00If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.

00To find the small oscillation about a state of steady precession in which the axis makes a constant angle a with the vertical, we write O=a+X, and neglect terms of the second order in x.

00In a free oscillation we have Qi, Qi,.

00The oscillation of M then resembles that of a particle at a distance a from one end of a string of length a+b fixed at the ends and subject to a tension mg.

00It is essential to the steady motion of every rapidly rotating piece in a machine that its axis of rotation should not merely traverse its centre of gravity, but should be a permanent axis; for otherwise the centrifugal couples will increass friction, produce oscillation of the shaft and tend to make it leave its bearings.

00The needle, a piece of paddle-shaped paper thinly coated with silver foil, is suspended by a quartz fibre, its extreme lightness making it possible to use a very feeble controlling force without rendering the period of oscillation unduly great.

00In these researches he skilfully took advantage of the well-known property of reciprocity between the centres of suspension and oscillation of an oscillating body, so as to determine experimentally the precise position of the centre of oscillation; the distance between these centres was then the length of the ideal simple pendulum having the same time of oscillation.

00Measurements at the Ripon Falls show that 18,000,000,000, or some 13% of this amount, is taken off by the Nile, and when allowance has been made for the annual rise and fall of the lake-level it is apparent that by far the greater part of the water which enters the nyanza is lost by evaporation; in fact, that the amount drawn off by the river plays a comparatively small part in the annual oscillation of the water surface.

00There is thus in the case of each planet an oscillation of the mean longitude which increases it and then diminishes it to its original value at the end of the period of 883 years.

00This apparent oscillation is called libration, and its amount on each side of the mean is commonly between 6° and 7°.

00The oscillation of the centre of power between Meath and Tir Eogain, according as the ardri belonged to the southern or northern Hy Neill, produced corresponding perturbations in the balance of parties among the minor kings.

00For the seven years of our record there is a very obvious oscillation in the temperature anomaly.

00amplitude of the primary oscillation has fallen to zero.

00At higher oscillation amplitudes, the test probe actually bounces on the surface to permit the investigation of impact phenomena.

00damped harmonic oscillation.

00Here, we consider the potentially deleterious effect of this oscillation on the qubit rotation.

00During the damped primary oscillation energy passes back and forth between the primary capacitor and the primary inductor.

00In contrast to other optical methods of the detection of Shear force interactions the fiber interferometer enables to measure the tip amplitude oscillation.

00I have investigated the modulation by the quasi-biennial oscillation of the tropical winds of the isentropic mixing in the tropics and subtropics.

00oscillation amplitude.

00oscillation frequency of 30 Hz.

00oscillation experiment CHORUS, at CERN.

00oscillation angle for all frames in each segment.

00In the case of normal mode vibration derived from a relaxation oscillation, we need low-frequency tuning of the attached oscillator.

00radian of oscillation " .

00relaxation oscillation, we need low-frequency tuning of the attached oscillator.

00Further, the signal may be a slowly varying low frequency anharmonic oscillation, or a high frequency sinusoid.

00Now 25 years is a short time in climate terms, only two complete cycles of the eleven year sunspot oscillation.

00systematics studies in the Near and Far Detectors as part of muon neutrino to electron neutrino oscillation analysis.

00telescope oscillation.

00The complex wavelet will evidence a constant power across the time duration of the oscillation.

00When at the limits of its swing, the pendulum is for an instant at rest, and all the energy of the oscillation is static or potential.

00When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.

00Instead of inserting the sensitive tube between the receiving antenna and the earth, he inserted the primary coil of a peculiar form of oscillation transformer and connected the terminals of the tube to the secondary circuit of the transformer.

0011575 of 1897), but it is not every form of oscillation transformer which is suitable for this purpose.

00These two circuits are so adjusted that the closed oscillation circuit, consisting of the condenser, primary coil 1 See German Patent of F.

00D and spark gap, has the same natural time period of oscillation as the open circuit consisting of the antenna, secondary coil and adjustable inductance.

00Fleming devised an arrangement in which a multiple transformation takes place, two oscillation circuits being interlinked inductively, and the last one acting inductively on the open or antenna circuit.

00Stone similarly devised a multiple inductive oscillation circuit with the object of forcing on the antenna circuit a single oscillation of definite frequency.'

00In the case of the inductive mode of exciting the oscillations an important quantity is the coefficient of coupling of the two oscillation circuits.

00The lower ends of these wires are connected through the secondary coil of an oscillation transformer to an earth plate, or to a large conductor placed on or near the earth called a " balancing capacity."

00jars or of Leyden panes immersed in oil or some form of air condenser, and the inductance coil or primary circuit of the oscillation transformer consists of a few turns of highly insulated wire wound on a frame and immersed in oil.

00The oscillations are controlled either by a key inserted in the primary circuit of the exciting induction coil or transformer, or by a key cutting in and out of the primary condensers or throwing inductance in and out of the closed oscillation circuit.

00The transformer T has its secondary or high-pressure terminals connected to spark balls S1, which are also connected by a circuit consisting of a large glass plate condenser C, and the primary circuit of an air-core transformer called an oscillation transformer.

00The secondary circuit of this last is either connected between an aerial A and the earth E, or it may be again in turn connected to a second pair of spark balls and these again to a second condenser oscillation transformer and the aerial A.

00In the early experiments Marconi connected the sensitive tube in between the receiving antenna and the earth plate, but, as already mentioned, in subsequent forms of apparatus he introduced the primary coil of a peculiar form of oscillation transformer into the antenna circuit and connected the ends of the sensitive tube to the terminals of the secondary circuit of this " jigger " (fig.

00The next class of wave or oscillation detector is the magnetic detector depending upon the power of electric oscillations to affect the magnetic state of iron.

00In its course it passes through a glass tube wound over with two coils of wire; one of these is an oscillation coil through which the oscillations to be detected pass, and the other is in connexion with a telephone.

00When used as a receiver for wireless telegraphy Marconi inserted the oscillation coil of this detector in between the earth and a receiving antenna, and this produced one of the most sensitive receivers yet made for wireless telegraphy.

00Fleming invented in 1904 a detector called an oscillation valve or glow lamp detector made as follows: 1 A small carbon filament incandescent lamp has a platinum plate or cylinder placed in it surrounding or close to the filament.

00Such an oscillation valve was first used by Fleming as a receiver for wireless telegraph purposes in 1904 as follows: - In between the receiving antenna and the earth is placed the primary coil of an oscillation transformer; the secondary circuit of this transformer contains a galvanometer in series with it, and the two together are joined between the external negative terminal of the carbon filament of the above-described lamp and the insulated platinum plate.

00On the other hand, if a closed oscillation circuit is constructed having capacity and considerable inductance, then oscillations can be set up in it by very small periodic electromotive forces provided these have a frequency exactly agreeing with that of the condenser circuit.

00- A, antenna; P S, jigger or oscillation transformer; C, condenser; 0, Fleming oscillation valve; B, working battery; T, telephone; R, rheostat; E, earth-plate.

00His transmitter consists of a nearly closed oscillating circuit comprising a condenser or battery of Leyden jars, a spark gap, and the primary coil of an oscillation transformer consisting of one turn of thick wire wound on a wooden frame.

00The receiving arrangement consists of an antenna which is connected to earth through the primary coil of an oscillation transformer and a variable inductance.

00This receiver therefore, like the transmitter, consists of an open and a closed electric oscillation circuit inductively connected together; also the two circuits of the receiver must be syntonized or tuned both to each other and to those of the transmitter.'

00When the methods for effecting this had been worked out practically it finally led to the inventions of Slaby, Braun and others being united into a system called the Telefunken system, which, as regards the transmitter, consisted in forming a closed oscillation circuit comprising a condenser, spark gap and inductance which at one point was attached either directly or through a condenser to the earth or to an equivalent balancing capacity, and at some other point to a suitably tuned antenna.

00At the receiving station the differences in these systems depend chiefly upon variations in the actual form of the oscillation detector used, whether it be a loose contact or a thermal, electrolytic or magnetic detector.

00An 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.

00Therefore, according to Kekule, the double linkages are in a state of continual oscillation, and if his dynamical notion of valency, or a similar hypothesis, be correct, then the difference between the 1.2 and 1.6 di-derivatives rests on the insufficiency of his formula, which represents the configuration during one set of oscillations only.

00This configuration is, according to Sachse, more stable than any other form; no oscillation is possible, the molecule being only able to move as a whole.

00The centric hypothesis has been applied to these rings by Bamberger and others; but as in the previous rings considered, the ordinary (3) (4) (5) representation with double and single linkages generally represents the syntheses, decompositions, &c.; exceptions, however, are known where it is necessary to assume an oscillation of the double linkage.

00C. C. Baly regards colour as due to " isorropesis " or an oscillation between the residual affinities of adjacent atoms composing the molecule.

00This oscillation may be represented in the case of acridine and fluorescein as This theory brings the property of fluorescence into relation with that of colour; the forms which cause fluorescence being the coloured modifications: ortho-quinonoid in the case of acridine, paraquinonoid in the case of fluorescein.

00This tautomerism may be of a twofold nature :-(I) it may involve the mere oscillation of linkages, as in acridine; or (2) it may involve the oscillation of atoms, as in fluorescein.

00trepidare, to tremble), a term meaning, in general, fear or trembling, but used technically in astronomy for an imagined slow oscillation of the ecliptic, having a period of 7000 years, introduced by the Arabian astronomers to explain a supposed variation in the precession of the equinoxes.

00His solution of the celebrated problem of the "centre of oscillation" formed in itself an important event in the history of mechanics.

00The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

00It was in this same year that he received the singular diplomatic mission to Frederick which nobody seems to have taken seriously, and after his return the oscillation between Brussels, Cirey and Paris was resumed.

00Having studied mathematics under John Machin and John Keill, he obtained in 5708 a remarkable solution of the problem of the " centre of oscillation," which, however, remaining unpublished until May 5754 (Phil.

00In the last resort, therefore, Spencer fails to deduce philosophically not only the necessity of progress, but also its compatibility with the evolution-dissolution oscillation, and even the general possibility of conceiving the world as a process.

00The conditions favourable to the production of coal seem therefore to have been-forest growth in swampy ground about the mouths of rivers, and rapid oscillation of level, the coal produced during subsidence being covered up by the sediment brought down by the river forming beds of sand or clay, which, on re-elevation, formed the soil for fresh growths, the alternation being occasionally broken by the deposit of purely marine beds.

00In addition to this it is necessary to have an extra system of fixed guides at the surface and at the bottom, where it is necessary to keep the cage steady during the operations of loading and landing, there being a much greater amount of oscillation during the passage of the cage than with fixed guides.

00The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...

00(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

00For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the circuital relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

00As the oscilla swung in the wind, oscillare came to mean to swing, hence in English "oscillation," the act of swinging backwards and forwards, periodic motion to and fro, hence any variation or fluctuation, actual or figurative.

00For the scientific problems connected with oscillation see Mechanics and Oscillograph.

00He also demonstrated that mutations have this special or distinctive character, that they repeat in the same direction without oscillation or retrogression.

00They determined to reinvestigate the motion of y Draconis; the telescope, constructed by George Graham (1675-1751), a celebrated instrument-maker, was affixed to a vertical chimneystack, in such manner as to permit a small oscillation of the eyepiece, the amount of which, i.e.

00The oscillation of the earth's axis may arise in two distinct ways; distinguished as " nutation of the axis " and " variation of latitude.

00" Nutation, the only form of oscillation imagined by Bradley, postulates that while the earth's C A FIG.

00He reverted to his early idea of a nutation of the earth's axis, and was rewarded by the discovery that the earth did possess such an oscillation (see Astronomy).

00Defining oscillation as is usual in spectroscopic measurement by wave-length, the visible spectrum is found to extend from about 7700 to 3900 A.

00A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants.

00The change of frequency of oscillation of radiating molecules placed in a magnetic field, which was discovered by P. Zeeman, and the observed polarization of the components, are all beautifully explained by the theory of H.

00The spectra experimented on by Paschen were band spectra, but as these split up into fine lines the possibility of homogeneous radiation in pure thermal oscillation may be considered as established.

00(6) A strictly periodic oscillation of this kind occurs in the working of a steam engine, in which the walls of the cylinder are exposed to regular fluctuations of temperature with the admission and release of steam.

00The steam pressure in the heater may be periodically varied by the gauge in such a manner as to produce an approximately simple harmonic oscillation of temperature at the hot end, while the cool end is kept at a steady temperature.

00libra, a balance), a slow oscillation, as of a balance; in astronomy especially the seeming oscillation of the moon around her axis, by which portions of her surface near the edge of the disk are alternately brought into sight and swung out of sight.

00For his demonstration in 1851 of the diurnal motion of the earth by the rotation of the plane of oscillation of a freely suspended, long and heavy pendulum exhibited by him at the Pantheon in Paris, and again in the following year by means of his invention the gyroscope, he received the Copley medal of the Royal Society in 1855, and in the same year he was made physical assistant in the imperial observatory at Paris.

00It is the oscillation which Mill manifests between the conception of his formula as it is actually applicable to concrete problems in practice, and the conception of it as an expression of a theoretical limit to practical procedure.

00This represents a forced oscillation whose period 27r/o1, coincides with that of the disturbing force; and the phase agrees with that of the force, or is opposed to it, according as c1i2u; i.e.

00marion (as in the case of the pendulum), this solution can only be accepted as a representation of the initial stages of the forced oscillation.

00This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.

00To find the forced oscillation due to a periodic force we have tl+k+ux-f cos(rjt+e).

00Thus, assuming that the period of a small oscillation of a given pendulum at a given place is a definite quantity, we see that it must vary as ~ (l/g).

00The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.

00sin 4, we find for the period (r) of a complete oscillation r= 4f ~4=~V- f1/8~r~ ~1 _Ii~in1~

00The following table gives the period, for various amplitudes a, in terms of that of oscillation in an infinitely small arc about a vertical axis half-way between the points of attachment of the upper string.

00This occurs only when the period (21r/w) of revolution of the arm lies between the two periods (2ii-/p, 27r/q) of oscillation when the arm is fixed.

00If we produce OG to P, making OP =1, the point P is called the centre of oscillation; the bob of a simple pendulum of length OP suspended from 0 will keep step with the motion of P, if properly started.

00This shows that if the body were swung from a parallel axis through P the new centre of oscillation would be at 0.

00For different parallel axes, the period of a small oscillation varies as ~i, or ~f (GO+OP); this is least, subject to the condition (4), when GO=GP=,c. The reciprocal relation between the centres of suspension and oscillation is the basis of Katers method of determining g experimentally.

00If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.

00To find the small oscillation about a state of steady precession in which the axis makes a constant angle a with the vertical, we write O=a+X, and neglect terms of the second order in x.

00In a free oscillation we have Qi, Qi,.

00The oscillation of M then resembles that of a particle at a distance a from one end of a string of length a+b fixed at the ends and subject to a tension mg.

00It is essential to the steady motion of every rapidly rotating piece in a machine that its axis of rotation should not merely traverse its centre of gravity, but should be a permanent axis; for otherwise the centrifugal couples will increass friction, produce oscillation of the shaft and tend to make it leave its bearings.

00The needle, a piece of paddle-shaped paper thinly coated with silver foil, is suspended by a quartz fibre, its extreme lightness making it possible to use a very feeble controlling force without rendering the period of oscillation unduly great.

00In these researches he skilfully took advantage of the well-known property of reciprocity between the centres of suspension and oscillation of an oscillating body, so as to determine experimentally the precise position of the centre of oscillation; the distance between these centres was then the length of the ideal simple pendulum having the same time of oscillation.

00Measurements at the Ripon Falls show that 18,000,000,000, or some 13% of this amount, is taken off by the Nile, and when allowance has been made for the annual rise and fall of the lake-level it is apparent that by far the greater part of the water which enters the nyanza is lost by evaporation; in fact, that the amount drawn off by the river plays a comparatively small part in the annual oscillation of the water surface.

00There is thus in the case of each planet an oscillation of the mean longitude which increases it and then diminishes it to its original value at the end of the period of 883 years.

00This apparent oscillation is called libration, and its amount on each side of the mean is commonly between 6Ã‚° and 7Ã‚°.

00The oscillation of the centre of power between Meath and Tir Eogain, according as the ardri belonged to the southern or northern Hy Neill, produced corresponding perturbations in the balance of parties among the minor kings.

00A definition of Q is " Energy stored in the cavity divided by energy dissipated per radian of oscillation ".

00Further, the signal may be a slowly varying low frequency anharmonic oscillation, or a high frequency sinusoid.

00Now 25 years is a short time in climate terms, only two complete cycles of the eleven year sunspot oscillation.

00Electron neutrino identification and background systematics studies in the Near and Far Detectors as part of muon neutrino to electron neutrino oscillation analysis.

00The initial decorrelation in the recorded datasets was found to be determined by the telescope oscillation.

00The complex wavelet will evidence a constant power across the time duration of the oscillation.

00"Motion sickness: effect of the frequency of lateral oscillation."

00Nystagmus is a condition in which there is involuntary and rhythmic movement or oscillation of the eye.

00The frequency of the oscillation or movement and the amplitude of the oscillation also vary.

00An accentuated oscillation when looking up is seen in upbeat nystagmus.

00An analogous oscillation prevails in the pyrazol nucleus, for L.

01An analogous oscillation prevails in the pyrazol nucleus, for L.

01

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