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acceleration

acceleration

acceleration Sentence Examples

  • The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving.

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  • The acceleration therefore remains the same, and the velocity is unaltered.

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  • Since the difference between the acceleration of gravity at the pole and at the equator is about 2%, the correction for latitude will be quite sensible in an instrument which might be used at various times in high and low latitudes.

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  • The acceleration of a falling body is naturally attributed to the presence of the earth; and, though the body approaches the earth in the course of its fall, it is easily recognized that the conditions under which it moves are only very slightly affected by this approach.

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  • - If W 1 is the weight of the train in pounds and a the acceleration in feet per second, the force required to produce the acceleration is f = Wi a / g (19) And if V is the average speed during the change of velocity implied by the uniform acceleration a, the rate at which work is done by this force is fV= W1Va /g (20) or in horse-power units Time occupied in the change - 13 - 0 113.

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  • The alternate delay and acceleration of the eclipses are then merely apparent; they represent the changes in the length of the light-journey as the stars perform their wide circuit.

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  • When the service is frequent enough to give a good power factor continuously, the steam locomotive cannot compete with the electric motor for the purpose of quick acceleration, because the motors applied to the axles of a train may for a short time absorb power from the central station to an extent far in excess of anything which a locomotive boiler can supply.

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  • During some revolutions there was evidence of a slight acceleration of the return, and during others there was not.

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  • By using a formula that takes into account the acceleration of gravity, you calculate the time it takes for an object to fall to the ground.

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  • Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.

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  • The rapid variation of certain groups of animals or the acceleration of certain organs is also not evidence of the sudden appearance of new adaptive characters.

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  • The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity.

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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

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  • The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.

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  • Sometimes, as on the Central London railway, the acceleration of gravity is also utilized; the different stations stand, as it were, on the top of a hill, so that outgoing trains are aided at the start by having a slope to run down, while incoming ones are checked by the rising gradient they encounter.

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  • Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.

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  • Galileo proceeded to measure the motion of a body on a smooth, fixed, inclined plane, and found that the law of constant acceleration along the line of slope of the plane still held, the acceleration decreasing in magnitude as the angle of inclination was reduced; and he inferred that a body, moving on a smooth horizontal plane, would move with uniform velocity in a straight line if the resistance of the air, and friction due to contact with the plane, could be eliminated.

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  • " When I say," says Mach, " that a body A exerts a force on a body B, I mean that B, on coming into contraposition with A, is immediately affected by a certain acceleration with respect to A."

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  • " When I say," says Mach, " that a body A exerts a force on a body B, I mean that B, on coming into contraposition with A, is immediately affected by a certain acceleration with respect to A."

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  • In addition to the foregoing list, various special locomotive types have been developed for suburban service, where high rates of acceleration and frequent stops are required.

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  • Motion is obtained from a continuous-current generator driven by an alternating motor with a very heavy fly-wheel, a combination known as the Ilgner transformer, which runs continuously with a constant draught on the generating station, the extremely variable demand of the winding engine during the acceleration period being met by the energy stored in the fly-wheel, which runs at a very high speed.

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  • Motion is obtained from a continuous-current generator driven by an alternating motor with a very heavy fly-wheel, a combination known as the Ilgner transformer, which runs continuously with a constant draught on the generating station, the extremely variable demand of the winding engine during the acceleration period being met by the energy stored in the fly-wheel, which runs at a very high speed.

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  • The acceleration of the departure of the Japanese is shown by the fact that in the eighteen months (July 1904 to January 1906) occurred 19,114 of the 42,313 departures in the sixty-six months from July 1900 to January 1906.1 After 1906, owing to restrictions by the Japanese government, immigration to Hawaii greatly decreased.

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  • The principal condition operating in the design of locomotives intended for local services with frequent stops is the degree of acceleration required, the aim of the designer being to produce an engine which shall be able to bring the train to its journey speed in the shortest time possible.

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  • It has since been discovered, however, that the magnitude of the acceleration in question is not exactly the same at different places on the earth, the range of variation amounting to about 2%.

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  • Since high average speed on a line with frequent stops depends largely on rapidity of acceleration, the tendency in modern equipment is to secure as great an output of power as possible during the accelerating period, with corresponding increase in weight available for adhesion.

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  • The reader should, however, notice that what is generally called electric force is the analogue in electricity of the so-called acceleration of gravity in mechanics, whilst electrification or quantity_of electricity is analogous to mass.

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  • This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in mathematics a function depends on a variable; and that even Newton's third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.

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  • Rate at which work is done against acceleration.

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  • (2) The acceleration of the element at the origin is - n 2 sin nt; so that the force which would have to be applied to the parts where the density is D' (instead of D), in order that the waves might pass on undisturbed, is, per unit of volume, (D' - D)n 2 sin nt.

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  • These considerations also indicate what a difficult matter it is to find the exact rate of working against the resistances, because of the difficulty of securing conditions which eliminate the effect both of the gradient and of acceleration.

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  • If G is the acceleration of gravity at the equator and g that at any latitude X, then g= G(IFo�o0513 sin 2 X).

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  • (5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

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  • if r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.

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  • From about 1880 the prevailing temper had changed; within a decade of this date the change had become great; since then the influence of Old Testament criticism has grown with increased acceleration.

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  • He attained correct views as to the character of centrifugal force in connexion with Galileo's theory; and, when the fact of the variation of gravity (Galileo's acceleration) in different latitudes first became known from the results of pendulum experiments, he at once perceived the possibility of connecting such a variation with the fact of the earth's diurnal rotation relatively to the stars.

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  • Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

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  • Assuming such a base to exist, Newton admitted at the outset the difficulty of identifying it, but pointed out that the key to the situation might be found in the identification of forces; that is to say, in the mutual character of laws of acceleration as applied to any given body and any other by whose presence its motion is influenced.

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  • The total acceleration of any particle is that obtained by the superposition of the component accelerations derived from its association with the other particles of the system severally in accordance with this law.

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  • A force is said to act upon each of two particles forming a pair, its magnitude being the product of mass and component acceleration of the particle on which it acts, and its direction that of this component acceleration.

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  • As a law of acceleration of the planets relatively to the sun, its approximate agreement with Kepler's third law of planetary motion follows readily from a consideration of the character of the acceleration of a point moving uniformly in a circle.

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  • Differences of acceleration due to the attractions of the sun and moon are not important for terrestrial systems on a small scale, and can usually be ignored, but their effect (in combination with the rotation of the earth) is very apparent in the case of the ocean tides.

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  • A small body hanging by a string, at rest relatively to the earth, moves relatively to this base uniformly in a circle; that is to say, with constant acceleration directed towards the earth's axis.

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  • What is done is to divide the resultant force due to gravitation into two components, one of which corresponds to this acceleration, while the other one is what is called the "weight" of the body.

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  • Weight is in fact not purely a combination of forces, in the sense in which that term is defined in connexion with the laws of motion, but corresponds to the Galileo acceleration with which the body would begin to move relatively to the earth if the string were cut.

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  • This represents about two-thirds of the total variation of Galileo's acceleration between the equator and the poles, the balance being due to the ellipticity of the figure of the earth.

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  • The impetus which the indirect process and the acceleration of civilization in the 15th and 16th centuries gave to the iron industry was so great that the demands of the iron masters for fuel made serious inroads on the forests, and in 1558 an act of Queen Elizabeth's forbade the cutting of timber in certain parts of the country for iron-making.

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  • Now if a be the amplitude expressed in millimetres, and t the period expressed in seconds, then the maximum velocity of an earth particle as it vibrates to and fro equals 27ra/t, whilst the maximum acceleration equals 4,r 2 0 2.

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  • (ga 2 /2b); or if the height of the centre of gravity of a column like a gravestone above the base on which it rests is y, and x is the horizontal distance of this centre from the edge over which it has turned, then the acceleration or suddenness of motion which caused its overthrow is measured, as pointed out by C. D.

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  • Atwood's published works, exclusive of papers contributed to the Philosophical Transactions, for one of which he obtained the Copley medal, are as follows: - Analysis of a Course of Lectures on the Principles of Natural Philosophy (Cambridge, 1784); Treatise on the Rectilinear Motion and Rotation of Bodies (Cambridge, 1784), which gives some interesting experiments, by means of which mechanical truths can be ocularly exhibited and demonstrated, and describes the machine, since called by Atwood's name, for verifying experimentally the laws of simple acceleration of motion; Review of the Statutes and Ordinances of Assize which have been established in England from the 4th year of King John, 1202, to the 37th of his present Majesty (London, 1801), a work of some historical research; Dissertation on the Construction and Properties of Arches (London, 1801), with supplement, pt.

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  • Halley's most notable scientific achievements were - his detection of the "long inequality" of Jupiter and Saturn, and of the acceleration of the moon's mean motion (1693), his discovery of the proper motions of the fixed stars (1718), his theory of variation (1683), including the hypothesis of four magnetic poles, revived by C. Hansteen in 1819, and his suggestion of the magnetic origin of the aurora borealis; his calculation of the orbit of the 1682 comet (the first ever attempted), coupled with a prediction of its return, strikingly verified in 1759; and his indication (first in 1679, and again in 1716, Phil.

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  • Acceleration of gravity.

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  • PART 11.KINETIcs coefficients with respect to the time; thus the velocity may be represented by i~ and the acceleration by fi or x.

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  • There is another formula for the acceleration, in which u is regarded as a function of the position; thus = ~ u~.

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  • In the case of a constant force, the acceleration or x is, according to (1), constant, and we have say, the general solution of which is x=1/8ati+At+B.

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  • We may take it as an experimental result, although the best evidence is indirect, that a particle falling freely under gravity experiences a constant acceleration which at the same place is the same for all bodies.

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  • This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 322 feet per second.

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  • If u be the acceleration at unit distance, the equation of motion becomes the solution of which may be written in either of the forms x=A cos et+B sin ut, x=a cos (rt+~), (6)

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  • If the inclination of the string to the vertical does not exceed a few degrees, the vertical displacement of the particle is of the second order, so that the vertical acceleration may be neglected, and the tension of the string may be equated to the gravity mg of the particle.

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  • If u be the acceleration at unit distance, we have du u u~=~1 (5)

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  • The unit of acceleration is the acceleration of a point which gains unit velocity in unit time; it is accordingly denoted by LT2.

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  • The dimensions of, -n/x~ are those of an acceleration; hence the dimensions of u are L3Ti.

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  • Another important example is that of a particle subject to an acceleration which is directed always towards a fixed point 0 and is proportional to the distance from 0.

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  • If u be the acceleration at unit distance, the component accelerations parallel to axes of x and y through 0 as origin will be ux, uy, whence ~ = ~sy.

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  • The acceleration is towards the vertical through the point of suspension, and is equal to g~/l, approximately, if r denote distance from this vertical.

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  • mately, and the tangential acceleration at P is therefore dv/dt or 1.

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  • Again, the velocity parallel to the normal at P changes from o to vi,l, ultimately, so that the normal acceleration is vd~,&/dt.

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  • If P be the acceleration towards 0, we have dv dr v~=P~,, (3)

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  • In the case of a central force, with 0 as pole, the transverse, acceleration vanishes, so that r2dO/dt=h,, (15)

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  • where P, as before, denotes the acceleration towards 0.

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  • The locus of the point V is called the hodograp/z (q.v.); and it appears that the velocity of the point V along the hodograph represents in magnitude and in directon tbt acceleration in the original orbit.

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  • The acceleration of the centre is therefore the same as if the plane were smooth and the mass of the sphere were increased by C/a.

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  • Thus the centre of a sphere rolling under gravity on a plane of inclination a describes a parabola with an acceleration g sin a/(I+C/Ma)

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  • Neglecting the vertical acceleration we have P=gpx, whence a f ay\

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  • Graphical methods of analysis founded on this way of representing velocity and acceleration were developed by R.

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  • Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

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  • It should be understood that the instantaneous centre considered in the preceding paragraphs is available only for estimating relative velocities; it cannot be used in a similar manner for questions regarding acceleration.

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  • That is to say, although the instantaneous centre is a centre of no velocity for the instant, it is not a centre of no acceleration, and in fact the centre of no acceleration is in general a quite different point.

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  • 125) have plane motion and the acceleration of any point C be given in magnitude and direction, the acceleration of any c other point B is the vector sum of X

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  • the acceleration of C, the radial n acceleration of B about C and the A

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  • tangential acceleration of B about C.

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  • Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

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  • angles to Ct; then the vector sum of these three magnitudes is Ab, and this vectol represents the acceleration of the point B.

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  • The magnitude of the radial acceleration is given by the expression vi/BC, v being the velocity of the point B about the point C. This velocity can always be found from the velocity diagram of the chain of which the link forms a part.

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  • If dw/dt is the angular acceleration of the link, dw/dt X CB is the tangential acceleration of the point B about the point C. Generally this tangential acceleration is unknown in magnitude, and it becomes part of the problem to find it.

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  • An important property of the diagram is that if points X and x are taken dividing the link CB and the whole acceleration of B about C, namely, cb in the same ratio, then Ax represents the acceleration of the point X in magnitude and direction; cb is called the acceleration image of the rod.

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  • In applying this principle to the drawing of an acceleration diagram for a mechanism, the velocity diagram of the mechanism must be first drawn in order to afford the means of calculating the several radial accelerations of the links.

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  • Then assuming that the acceleration of one point of a particuar link of the mechanism is known together with the corresponding configuration of the mechanism, the two Vectors Ac and ct can be drawn.

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  • Examples, completely worked out, of velocity and acceleration diagrams for the slider crank chain, the four-bar chain, and the mechanism of the Joy valve gear will be found in ch.

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  • When a weight is reciprocated, the equal and opposite force required for its acceleration at any instant appears as an unbalanced force on the frame of the machine to which the weight belongs.

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  • In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.

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  • A more accurate though still approximate expression for the force on the frame due to the acceleration of the piston whose weight is W is given by w2r cos 0 + r cos 20

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  • An excess of the effort exerted on any piece, above that which is necessary to balanoe the resistance, is accompanied with acceleration; a deficiency of the effort, with retardation.

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  • An excess of effort above resistance involves an excess of energy exerted above work perfor~ned; that excess of energy is employed in producing acceleration.

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  • When a machine undergoes alternate acceleration and retardation, so that at certain instants of time, occurring at the end of intervals called periods or cycles, it returns to its original speed, then in each of those periods or cycles the alternate excesses of energy and of work neutralize each other; and at the end of each cycle the principle of the equality of energy and work stated in 87, with all, its consequences, is verified exactly as in the case of machines of uniform speed.

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  • At intermediate instants, however, other principles have also to be taken into account, which are deduced from the second law of motion, as applied to direct deviation, or acceleration and retardation.

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  • Energy of Acceleration and Work of Retardation for a Shifting Body.Let w be the weight of a body which has a motion of translation in any path, and in the course of the interval of time ~t let its velocity be increased at a uniform rate of acceleration from v1 to v2.

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  • The rate of acceleration will be dv/dt = const.

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  • = (v, vi) ~t; and to produce this acceleration a uniform effort will be required, expressed by P=w(vivi)g~t (7)

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  • To find the energy which has to be exerted to peoduce the acceleration from v1 to Vi, it is to be observed that the distance through which the effort P acts during the acceleration is L~s= (vi+vi)~t/2;

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  • consequently, the energy of acceleration is P.~s = w(v, ci) (v1+vi)12g = w(v, v11)2g, (72)

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  • Energy Stored and Restored by Deviations of Velocity.Thus a body alternately accelerated and retarded, so as to be brought back to its original speed, performs work during its retardation exactly equal in amount to the energy exerted upon it during its acceleration; so that that energy may be considered as stored during the acceleration, and restored during the retardation, in a manner analogous to the operation of a reciprocating force (~ 108).

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  • Let e denote the quantity by which the energy exerted in each cycle of the working of the machine alternately exceeds and falls short of the work performed, and which has consequently to be alternately stored by acceleration and restored by retardation of the flywheel.

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  • * To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.

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  • For a given link, this force isthe resultant of all the accelerating forces distributed through the substance of the material of the link required to produce the requisite acceleration of each particle, and the determination of this force depends upon the principles of the two preceding sections.

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  • Let a be the acceleration of be the angular acceleration about the axis through the Centre of gravity; then the K I1~~ the centre of gravity and let A

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  • force required to produce the - translation of the centre of - gravity is F =Wa/g, and the - couple required to produce the - angular acceleration about the Centre of gravity is M = IA/g, FiG.

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  • When the link forms part of a mechanism the respective accelerations of two points in the link can be determined by means of the velocity and acceleration diagrams described in 82, it being understood that the motion of one link in the mechanism is prescribed, for instance, in the steam-engines mechanism that the crank shall revolve uniformly.

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  • Let the acceleration of the two points B and K therefore be supposed known.

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  • The problem is now to find the acceleration a and A.

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  • 49), and set out Ob equal to the acceleration of B and Oh equal to the acceleration of K.

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  • Og is then the acceleration of the centre of gravity and the force F can therefore be immediately calculated.

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  • To find the angular acceleration A, draw kI, bt respectively parallel to and at right angles to the link KB.

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  • Then tb represents the angular acceleration of the point B relatively to the point K and hence tb/KB is the value of A, the angular acceleration of the link.

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  • directions of acceleration of B and K to Z meet in 0; draw a circle through the three 0

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  • The methods of the two preceding sections may be used when the acceleration of two points in the rod are known.

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  • moves with uniform velocity, so that if a is its angular velocit and r its radius, the acceleration is ar in a direction along the cran arm from the crank pin to the centre of the shaft.

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  • The acceleration of a second point, usually taken at the centre of the crosshead pin, can be found by the principles of 82, but several special geometrical constructions have been devised for this purpose, notably the construction of Klein,i discovered also independently by Kirsch.i But probably the most convenient is the construction due to G.

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  • Then, the crank standing at any angle with the line of stroke, draw LP at right angles to the connecting rod, PN at right angles to the line of stroke OB and NA at right angles to the connecting rod; then AO is the acceleration of the point B to the scale on which KO represents the acceleration of the point K.

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  • The finding of F may be continued thus: join AK, then AK is the acceleration image of the rod, OKA being the acceleration diagram.

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  • Hence Og represents the acceleration of the centre of gravity and, the weight of the connecting J.

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  • 800 and 1004, extracted from Caussin's translation of Ibn Junis, the eclipses and occultations of Bullialdus, Gassendi, and Hevelius, of the French astronomers at Paris and St Petersburg, and of Flamsteed at Greenwich, and deduced a secular acceleration of 8.8", agreeing well with the theoretical value.

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  • The average date of the break-up is April 11 th at Tver, and 14 days later about Kostroma, from which point a regular acceleration is observed (April 16th at Kazan, April 7th at Tsaritsyn, and March 17th at Astrakhan).

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  • for determining the acceleration of the Pendulum in Lat.

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  • Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.

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  • If W is the weight required to depress the attracted disk into the same sighted position when the plates are unelectrified and g is the acceleration of gravity, then the difference of potentials of the conductors tested is expressed by the formula V - V'=(d - d') /87 W where S denotes the area of the attracted disk.

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  • We Will Assume That When, As In Most Cases, Viscosity Maybe Neglected, The Mass (M) Of A Drop Depends Only Upon The Density (V), The Capillary Tension (T), The Acceleration Of Gravity (G), And The Linear Dimension Of The Tube (A).

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  • The " Dimensions " Of The Quantities On Which M Depends Are: A= (Mass)' (Length) 3, T = (Force)' (Length) ' = (Mass)' (Time) 2, G = Acceleration = (Length)' (Time) ', Of Which M, A Mass, Is To Be Expressed As A Function..

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  • If, as is sometimes stated, the tension of a vertical film were absolutely the same throughout, the middle parts would of necessity fall with the acceleration of gravity.

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  • Acceleration >>

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  • Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.

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  • They are carried across the disk by the sun's rotation, partaking in the equatorial acceleration; they also show marked displacements of their own, whether with, or relative to, the neighbouring photosphere does not appear; at the beginning of their life they usually outrun the average daily rotation appropriate to their latitude.

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  • The equation of light is the time taken by light to traverse the sun's mean distance from the earth; it can be found by the acceleration or retardation of the eclipses of Jupiter's satellites according as Jupiter is approaching opposition or conjunction with the sun; a recent analysis shows that its value is 498.6", which leads to the same value of the parallax as above, but the internal discrepancies of the material put its authority upon a much lower level.

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  • gravity of the long body CD, and be the centre of gravity of the three vertical forces acting downwards at the points x i, and considered as weights collected at those points; then if be above the line z i y i it can be shown that this arrangement of the knife-edges of CD favours the" acceleration " principle, and is suited to act with and assist an " accelerating " steelyard, and similarly if the point h2 be above the line z 2 y 2 in the case of the short body EF.

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  • In the following year his memoir on the secular acceleration of the moon's mean motion partially invalidated Laplace's famous explanation, which had held its place unchallenged for sixty years.

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  • He compiled the Hakimite Tables of the planets, and observed at Cairo, in 977 and 978, two solar eclipses which, as being the first recorded with scientific accuracy, 4 were made available in fixing the amount of lunar acceleration.

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  • of Jupiter and Saturn in 1784, and of the " secular acceleration " of the moon in 1787.

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  • The lunar acceleration, too, obtains ultimate compensation, though only after a vastly protracted term of years.

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  • The first step in constructing this theory was taken by Laplace, who showed that the secular acceleration was produced by the secular diminution of the earth's orbit.

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  • But Adams in 1853 1 showed that the previous computations of the acceleration were only a rude first approximation, and that a more rigorous computation reduced the result to about one-half.

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  • It was therefore surprising when, in 1877, Simon Newcomb found, by a study of the lunar eclipses handed down by Ptolemy and those observed by the Arabians - data much more reliable than the vague accounts of ancient solar eclipses - that the actual apparent acceleration was only about 8.3".

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  • The following is a summary of the present state of the question: The theoretical value of the acceleration, assuming the day to be constant, is .....

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  • - Combined with the question of secular acceleration is another which is still not entirely settled - that of inequalities of long period in the mean motion of the moon round the earth.

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  • The most plausible explanation is that, like the discrepancy in the secular acceleration, the observed deviation is only apparent, and arises from slow fluctuations in the earth's rotation, and therefore in our measure of time produced by the motion of great masses of polar ice and the variability of the amount of snowfall on the great continents.

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  • A similar though much smaller acceleration in the annual rate of increase after the Carlist Wars of 187476 is largely attributable to the prosperity caused by railway development between 1877 and 1887.

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  • the nation was well able to make good the numerical losses involved by a serious war; that its numbers tend to increase steadily; and that the rate of increase has hitherto shown a marked acceleration in periods of commercial expansion.

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  • acceleration of a particle moving in a circle.

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  • acceleration of electrons by Langmuir waves which are excited by the pump wave.

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  • disable Hardware Sound acceleration To disable hardware sound acceleration: Click Start, and then click Run.

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  • Skids are caused by harsh handling of the vehicle; harsh braking, acceleration or steering.

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  • The only way you can actually calculate the acceleration of the trolley is by using a ticker timer.

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  • As an example, consider the equation for the velocity v of an object that undergoes an acceleration a for a time t.

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  • Hydrostatic equation: An equation expressing the vertical pressure forces in balance with the gravitational acceleration.

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  • The semicircular canals of the inner ear sense changes in angular acceleration.

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  • Polar Moment of Inertia The resistance of an object to rotational acceleration.

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  • For 3D acceleration, Tempest supports up to 1152 x 870 @ 16-bit color or 832 x 624 @ 24-bit color.

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  • This testing allows for rapid acceleration of TCE induced failures.

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  • The unit of measure for lateral acceleration, or " road-holding.

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  • acceleration vector drawing for a four bar linkage.

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  • acceleration lane for the slip road where we joined.

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  • Citroen says that this gives it a 0-60mph acceleration time of just over six seconds and a top speed in excess of 155mph.

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  • And out on the highway, this 7% increase in drive force makes for outstandingly strong roll-on acceleration.

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  • To reduce the hardware acceleration: Open the Control Panel.

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  • These features are formed as a result of particle acceleration in the hairpin field structure of the distant tail.

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  • Enhanced waves in these regions could play a major role in electron acceleration to relativistic energies during periods of prolonged substorm activity.

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  • Keywords: Solid state physics, Lattice dynamics, Lattice sums, convergence acceleration, Incomplete gamma Function.

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  • angular acceleration.

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  • armature coils and a commutator, its inertia is small, allowing rapid acceleration and deceleration.

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  • bremsstrahlung radiation produced by the acceleration of charged particles.

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  • brisk effortless acceleration.

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  • centripetal acceleration, then it equals delta-V / delta-t.

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  • Faster street bike acceleration cheats With any street motorcycle, use weight control and hold back to wheelie.

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  • convergence acceleration, Incomplete gamma Function.

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  • Or turning off Hardware Acceleration in the nVidia decoder?

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  • At the rear is a limited slip differential with a 3.46 to 1 ratio to reduce rear wheel slip under acceleration.

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  • earthquake hazard maps like this are more often expressed in terms of ground acceleration.

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  • Fall, and then comment on the acceleration due to gravity... Worm Theory Why do endgames take so long?

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  • hardware acceleration yet.

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  • earthquake hazard maps like this are more often expressed in terms of ground acceleration.

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  • I. FTY720 selectively decreases the number of circulating mature lymphocytes by acceleration of lymphocyte homing.

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  • kinematics of a particle in a plane including the case when velocity or acceleration depends on time (but excluding use of acceleration.

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  • Acceleration is quite leisurely, with 11 seconds needed to reach 60mph.

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  • I. FTY720 selectively decreases the number of circulating mature lymphocytes by acceleration of lymphocyte homing.

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  • oxytocin induction or acceleration, and prostaglandin E2 gel induction.

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  • portends acceleration of efforts to packetize its sales manager core network.

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  • And it makes a lovely throaty rasp under acceleration and a staccato backfire when you lift off the throttle.

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  • roll-on acceleration.

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  • We respectfully request the Court of Justice to give consideration to the acceleration of its preliminary ruling in this case.

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  • Sudden acceleration of a car, forward or backward causes a loud screech of the tires, even on dirt or wet roads.

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  • The acceleration of the news cycle by necessity leads to less careful checking, while competition leads to more sensationalism.

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  • The RX 400h is very sprightly for a two-ton milk float, posting better acceleration times than a standard Alfa GT.

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  • This problem is an investigation of the influence of acceleration heating on the behavior of a mechanical room thermostat.

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  • Good mid-range torque gives excellent acceleration, try an MGB GT V8.

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  • whistler mode chorus associated with electron acceleration to relativistic energies.

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  • This one really zings, as the claimed 0-62mph acceleration figure of 4.8 seconds shows.

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  • (2) The acceleration of the element at the origin is - n 2 sin nt; so that the force which would have to be applied to the parts where the density is D' (instead of D), in order that the waves might pass on undisturbed, is, per unit of volume, (D' - D)n 2 sin nt.

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  • It is a fundamental result in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height of v 2 /2g centimetres, where g represents the numerical value of the acceleration produced by gravity in centimetre-second units.

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  • Now, if m represent the mass of the body in grammes its weight will be mg dynes, for it will require a force of mg dynes to produce in it the acceleration denoted by g.

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  • (5) Resistance due to acceleration, represented by Ra.

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  • The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving.

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  • Rate at which work is done against acceleration.

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  • - If W 1 is the weight of the train in pounds and a the acceleration in feet per second, the force required to produce the acceleration is f = Wi a / g (19) And if V is the average speed during the change of velocity implied by the uniform acceleration a, the rate at which work is done by this force is fV= W1Va /g (20) or in horse-power units Time occupied in the change - 13 - 0 113.

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  • The principal condition operating in the design of locomotives intended for local services with frequent stops is the degree of acceleration required, the aim of the designer being to produce an engine which shall be able to bring the train to its journey speed in the shortest time possible.

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  • The acceleration, a, which may be supposed uniform, is 1.465.

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  • The average acceleration in feet per second is measured by the fraction Change of speed in feet per sec. 60.07-58.6 64 tons; and to obtain the horse-power the boiler will be one of the largest that can be built to the construction gauge.

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  • After acceleration to the journey speed of 30 m.

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  • per hour the horse-power required is reduced to about one-third of that required for acceleration alone.

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  • 17 at a speed corresponding to the average speed during the acceleration a, G the gradient, g the acceleration due to gravity, and V the velocity of the train in feet per second.

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  • In this expression it is assumed that the acceleration is uniform, and this assumption is sufficiently accurate for any practical purpose to which the above formula would be applieu in the ordinary working of a locomotive.

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  • If a is variable, then the formula must be applied in a series of steps, each step corresponding to a time interval over which the acceleration may be assumed uniform.

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  • These considerations also indicate what a difficult matter it is to find the exact rate of working against the resistances, because of the difficulty of securing conditions which eliminate the effect both of the gradient and of acceleration.

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  • In addition to the foregoing list, various special locomotive types have been developed for suburban service, where high rates of acceleration and frequent stops are required.

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  • When the service is frequent enough to give a good power factor continuously, the steam locomotive cannot compete with the electric motor for the purpose of quick acceleration, because the motors applied to the axles of a train may for a short time absorb power from the central station to an extent far in excess of anything which a locomotive boiler can supply.

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  • per hour, according to the distance between stations Later practice takes advantage of the great increase in power that can be temporarily developed by electric motors during the period of acceleration; this, in proportion to the weight of the train to be hauled, gives results much in advance of those obtained on ordinary steam railways.

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  • Since high average speed on a line with frequent stops depends largely on rapidity of acceleration, the tendency in modern equipment is to secure as great an output of power as possible during the accelerating period, with corresponding increase in weight available for adhesion.

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  • Sometimes, as on the Central London railway, the acceleration of gravity is also utilized; the different stations stand, as it were, on the top of a hill, so that outgoing trains are aided at the start by having a slope to run down, while incoming ones are checked by the rising gradient they encounter.

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  • Since the difference between the acceleration of gravity at the pole and at the equator is about 2%, the correction for latitude will be quite sensible in an instrument which might be used at various times in high and low latitudes.

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  • If G is the acceleration of gravity at the equator and g that at any latitude X, then g= G(IFo�o0513 sin 2 X).

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  • As notable instances may be mentioned Laplace's discoveries relating to the velocity of sound and the secular acceleration of the moon, both of which were led close up to by Lagrange's analytical demonstrations.

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  • The year 1787 was rendered further memorable by Laplace's announcement on the 19th of November (Memoirs, 1786), of the dependence of lunar acceleration upon the secular changes in the eccentricity of the earth's orbit.

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  • Now 2 area 17r=2Xr; so that, in order to reconcile the amplitude of the primary wave (taken as unity) with the half effect of the first zone, the amplitude, at distance r, of the secondary wave emitted from the element of area dS must be taken to be dS/Xr (1) By this expression, in conjunction with the quarter-period acceleration of phase, the law of the secondary wave is determined.

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  • That the amplitude of the secondary wave should vary as r1 was to be expected from considerations respecting energy; but the occurrence of the factor A1, and the acceleration of phase, have sometimes been regarded as mysterious.

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  • Thus, on the supposition that the irregularity of temperature t extends through a length 1, and produces an acceleration of a quarter of a wave-length, 4A=I I ltX102; or, if we take X = 5.3 X 10-5, it= 12, the unit of length being the centimetre.

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  • that at any point the tangent to the hodograph is parallel to the direction, and the velocity in the hodograph equal to the magnitude of the resultant acceleration at the corresponding point of the orbit.

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  • Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.

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  • Phil.): - Let x, y, z be the coordinates of P in the orbit,, r t, those of the corresponding point T in the hodograph, then dx dy _ dz c= ' 71 - a' - at therefore Also, if s be the arc of the hodograph, ds = v = V V1 1) j dt + (dt2) dt Equation (1) shows that the tangent to the hodograph is parallel to the line of resultant acceleration, and (2) that the velocity in the hodograph is equal to the acceleration.

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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

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  • To determine the component acceleration of a particle, suppose F to denote any function of x, y, z, t, and investigate the time rate of F for a moving particle; denoting the change by DF/dt, DF = 1t F(x+uSt, y+vIt, z+wSt, t+St) - F(x, y, z, t) dt at = d + u dx +v dy+ w dz and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, z; but dF/dt, dF/dx, dF/dy, dF/dz (2) represent the rate of change of F at the time t, at the point, x, y, z, fixed in space.

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  • (5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

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  • if r denotes the radius of curvature of the stream line, so that I dp + dV - dH _ dq 2 q2 (6) p dv dv dv dv - r ' the normal acceleration.

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  • The osculating plane of a stream line in steady motion contains the resultant acceleration, the direction ratios of which are du du, du d i g d g 2 _ dH dx +v dy + dz - 2v?

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  • , (7) and when q is stationary, the acceleration is normal to the surface H = constant, and the stream line is a geodesic.

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  • With liquid of density p, this gives rise to a kinetic reaction to acceleration dU/dt, given by 7rp b 2 a 2 b l b d J = a 2 +b2 M' dU, if M' denotes the mass of liquid displaced by unit length of the cylinder r =b.

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  • Similarly, the inertia parallel to Oy and Oz is NW' - 1 B W', B C (b2 +-X, c 2 ab and A +C abc/ZP, Ao For a sphere a=b=c, Ao= Bo=Co =, 'a' = Q = = z, (9) U from (II), (16) so that the effective inertia of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration W - W', g (30) W+ aW Thus a spherical air bubble, in which W/W' is insensible, will begin to rise in water with acceleration 2g.

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  • The reader should, however, notice that what is generally called electric force is the analogue in electricity of the so-called acceleration of gravity in mechanics, whilst electrification or quantity_of electricity is analogous to mass.

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  • If a mass of M grammes be placed in the earth's field at a place where the acceleration of gravity has a value g centimetres per second, then the mechanical force acting on it and pulling it downwards is Mg dynes.

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  • The alternate delay and acceleration of the eclipses are then merely apparent; they represent the changes in the length of the light-journey as the stars perform their wide circuit.

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  • The velocity perpendicular to the axis of any point on the curve at a fixed distance x from 0 is dy_ (I ]) at A A The acceleration perpendicular to the axis is d2y = 2 2 dt 2 - A 2 sin A (x - Ut) The maximum pressure excess is the amplitude of ("6= Eu /U _ (E/U)dy/dt.

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  • The acceleration therefore remains the same, and the velocity is unaltered.

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  • There are two steel-clad series-wound motors of 36 B.H.P. For a test load of 120 tons the tractive force is 70 lb per ton, which is sufficient for acceleration, and maintaining speed against wind pressure.

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  • (6) On a curved bridge the centrifugal load due to the radical acceleration of the train.

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  • 3 parallel to AM; the energycurve AQE would be another straight line through A; the velocitycurve AvV, of which the ordinate v is as the square root of the energy, would be a parabola; and the acceleration of the shot being constant, the time-curve AtT will also be a similar parabola.

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  • of the charge may be suitable for the weight and acceleration of the shot.

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  • From about 1880 the prevailing temper had changed; within a decade of this date the change had become great; since then the influence of Old Testament criticism has grown with increased acceleration.

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  • (d) The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity.

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  • The number adopted for the value of the normal acceleration of gravity is 980.965 cm/sec-squared.

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  • His " law of acceleration " together with the complementary " law of retardation," or the slowing up in the development of certain characters (first propounded by E.

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  • Cope's philosophic contributions to palaeontology began in 1868 (see essays in The Origin of the Fittest, New York, 1887, and The Primary Factors of Organic Evolution, Chicago, 1896) with the independent discovery and demonstration among vertebrates of the laws of acceleration and retardation.

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  • The evolution consists first in progressive increase in size; second, in the acceleration of the median digit and retardation of the lateral digits, the latter becoming more and more elevated from the ground until finally in Equus (6) they are the lateral splints, which in the embryonic condition have vestigial cartilages attached representing the last traces of the lateral phalanges.

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  • - LAW OF Acceleration And Retardation Illustrated In The Evolution Of The Hind Feet Of The Horse.

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  • The above law of gradual evolution is perfectly consistent with a second principle, namely, that at certain times evolution is much more rapid than at others, and that organisms are accelerated or retarded in development in a manner broadly analogous to the acceleration or retardation of separate organs.

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  • The rapid variation of certain groups of animals or the acceleration of certain organs is also not evidence of the sudden appearance of new adaptive characters.

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  • ACCELERATION (from Lat.

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  • The acceleration of the departure of the Japanese is shown by the fact that in the eighteen months (July 1904 to January 1906) occurred 19,114 of the 42,313 departures in the sixty-six months from July 1900 to January 1906.1 After 1906, owing to restrictions by the Japanese government, immigration to Hawaii greatly decreased.

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  • This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in mathematics a function depends on a variable; and that even Newton's third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.

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  • Among the many difficulties which beset the question, not the least obvious was the length of time during which the Church must remain without a ruler, if - as Sigismund and the German nation demanded - the papal election were deferred till the completion of the internal reforms. The result was decided by the policy of the cardinals, who since May 1417 had openly devoted their whole energies to the acceleration of that election; and union was preserved by means of a compromise arranged by Bishop Henry of Winchester, the uncle of the English king.

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  • acceleration; that is to say, would move in a straight line, in such a manner that its velocity would increase by equal amounts in any two equal times.

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  • It has since been discovered, however, that the magnitude of the acceleration in question is not exactly the same at different places on the earth, the range of variation amounting to about 2%.

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  • He went on to deal with the case of projectiles, and was led to the conclusion that the motion in this case could be regarded as the result of superposing a horizontal motion with uniform velocity and a vertical motion with constant acceleration, the latter identical with that of a merely falling body; the inference being that the path of a projectile would be a parabola except for deviations attributed to contact with the air, and that in a vacuum this path would be accurately followed.

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  • They had practically the effect of suggesting an entirely new view of the subject, namely, that a body uninfluenced by other matter might be expected to move, relatively to some base or other, with uniform velocity in a straight line; and that, when it does not move in this way, its acceleration is the feature of its motion which the surrounding conditions determine.

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  • The acceleration of a falling body is naturally attributed to the presence of the earth; and, though the body approaches the earth in the course of its fall, it is easily recognized that the conditions under which it moves are only very slightly affected by this approach.

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  • He attained correct views as to the character of centrifugal force in connexion with Galileo's theory; and, when the fact of the variation of gravity (Galileo's acceleration) in different latitudes first became known from the results of pendulum experiments, he at once perceived the possibility of connecting such a variation with the fact of the earth's diurnal rotation relatively to the stars.

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  • Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

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  • Assuming such a base to exist, Newton admitted at the outset the difficulty of identifying it, but pointed out that the key to the situation might be found in the identification of forces; that is to say, in the mutual character of laws of acceleration as applied to any given body and any other by whose presence its motion is influenced.

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  • The total acceleration of any particle is that obtained by the superposition of the component accelerations derived from its association with the other particles of the system severally in accordance with this law.

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  • A force is said to act upon each of two particles forming a pair, its magnitude being the product of mass and component acceleration of the particle on which it acts, and its direction that of this component acceleration.

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  • Instead of the operation of superposing accelerations, we may compound the several forces acting on a particle by the parallelogram law (see Mechanics) into what may be called the resultant force, the total acceleration of the particle being the same as if this alone acted.

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  • As a law of acceleration of the planets relatively to the sun, its approximate agreement with Kepler's third law of planetary motion follows readily from a consideration of the character of the acceleration of a point moving uniformly in a circle.

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  • Differences of acceleration due to the attractions of the sun and moon are not important for terrestrial systems on a small scale, and can usually be ignored, but their effect (in combination with the rotation of the earth) is very apparent in the case of the ocean tides.

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  • A small body hanging by a string, at rest relatively to the earth, moves relatively to this base uniformly in a circle; that is to say, with constant acceleration directed towards the earth's axis.

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  • What is done is to divide the resultant force due to gravitation into two components, one of which corresponds to this acceleration, while the other one is what is called the "weight" of the body.

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  • Weight is in fact not purely a combination of forces, in the sense in which that term is defined in connexion with the laws of motion, but corresponds to the Galileo acceleration with which the body would begin to move relatively to the earth if the string were cut.

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  • This represents about two-thirds of the total variation of Galileo's acceleration between the equator and the poles, the balance being due to the ellipticity of the figure of the earth.

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  • The impetus which the indirect process and the acceleration of civilization in the 15th and 16th centuries gave to the iron industry was so great that the demands of the iron masters for fuel made serious inroads on the forests, and in 1558 an act of Queen Elizabeth's forbade the cutting of timber in certain parts of the country for iron-making.

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  • Now if a be the amplitude expressed in millimetres, and t the period expressed in seconds, then the maximum velocity of an earth particle as it vibrates to and fro equals 27ra/t, whilst the maximum acceleration equals 4,r 2 0 2.

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  • (ga 2 /2b); or if the height of the centre of gravity of a column like a gravestone above the base on which it rests is y, and x is the horizontal distance of this centre from the edge over which it has turned, then the acceleration or suddenness of motion which caused its overthrow is measured, as pointed out by C. D.

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  • Atwood's published works, exclusive of papers contributed to the Philosophical Transactions, for one of which he obtained the Copley medal, are as follows: - Analysis of a Course of Lectures on the Principles of Natural Philosophy (Cambridge, 1784); Treatise on the Rectilinear Motion and Rotation of Bodies (Cambridge, 1784), which gives some interesting experiments, by means of which mechanical truths can be ocularly exhibited and demonstrated, and describes the machine, since called by Atwood's name, for verifying experimentally the laws of simple acceleration of motion; Review of the Statutes and Ordinances of Assize which have been established in England from the 4th year of King John, 1202, to the 37th of his present Majesty (London, 1801), a work of some historical research; Dissertation on the Construction and Properties of Arches (London, 1801), with supplement, pt.

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  • Halley's most notable scientific achievements were - his detection of the "long inequality" of Jupiter and Saturn, and of the acceleration of the moon's mean motion (1693), his discovery of the proper motions of the fixed stars (1718), his theory of variation (1683), including the hypothesis of four magnetic poles, revived by C. Hansteen in 1819, and his suggestion of the magnetic origin of the aurora borealis; his calculation of the orbit of the 1682 comet (the first ever attempted), coupled with a prediction of its return, strikingly verified in 1759; and his indication (first in 1679, and again in 1716, Phil.

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  • Acceleration of gravity.

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  • PART 11.KINETIcs coefficients with respect to the time; thus the velocity may be represented by i~ and the acceleration by fi or x.

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  • There is another formula for the acceleration, in which u is regarded as a function of the position; thus = ~ u~.

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  • Its gradient represents the acceleration, and the area (Jzidl) included between any two ordinates represents the space described in the fnterval between the corresponding instants (see fig.

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  • In the case of a constant force, the acceleration or x is, according to (1), constant, and we have say, the general solution of which is x=1/8ati+At+B.

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  • We may take it as an experimental result, although the best evidence is indirect, that a particle falling freely under gravity experiences a constant acceleration which at the same place is the same for all bodies.

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  • This acceleration is denoted by g; its value at Greenwich is about 981 centimetre-second units, or 322 feet per second.

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  • If u be the acceleration at unit distance, the equation of motion becomes the solution of which may be written in either of the forms x=A cos et+B sin ut, x=a cos (rt+~), (6)

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  • If the inclination of the string to the vertical does not exceed a few degrees, the vertical displacement of the particle is of the second order, so that the vertical acceleration may be neglected, and the tension of the string may be equated to the gravity mg of the particle.

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  • If u be the acceleration at unit distance, we have du u u~=~1 (5)

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  • The unit of acceleration is the acceleration of a point which gains unit velocity in unit time; it is accordingly denoted by LT2.

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  • The dimensions of, -n/x~ are those of an acceleration; hence the dimensions of u are L3Ti.

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  • Another important example is that of a particle subject to an acceleration which is directed always towards a fixed point 0 and is proportional to the distance from 0.

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  • If u be the acceleration at unit distance, the component accelerations parallel to axes of x and y through 0 as origin will be ux, uy, whence ~ = ~sy.

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  • The acceleration is towards the vertical through the point of suspension, and is equal to g~/l, approximately, if r denote distance from this vertical.

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  • mately, and the tangential acceleration at P is therefore dv/dt or 1.

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  • Again, the velocity parallel to the normal at P changes from o to vi,l, ultimately, so that the normal acceleration is vd~,&/dt.

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  • If P be the acceleration towards 0, we have dv dr v~=P~,, (3)

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  • In the case of a central force, with 0 as pole, the transverse, acceleration vanishes, so that r2dO/dt=h,, (15)

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  • where P, as before, denotes the acceleration towards 0.

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  • The locus of the point V is called the hodograp/z (q.v.); and it appears that the velocity of the point V along the hodograph represents in magnitude and in directon tbt acceleration in the original orbit.

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  • This gives the acceleration of m as modified by the inertia of the wheel.

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  • The acceleration of the centre is therefore the same as if the plane were smooth and the mass of the sphere were increased by C/a.

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  • Thus the centre of a sphere rolling under gravity on a plane of inclination a describes a parabola with an acceleration g sin a/(I+C/Ma)

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  • Neglecting the vertical acceleration we have P=gpx, whence a f ay\

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  • Graphical methods of analysis founded on this way of representing velocity and acceleration were developed by R.

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  • Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

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  • It should be understood that the instantaneous centre considered in the preceding paragraphs is available only for estimating relative velocities; it cannot be used in a similar manner for questions regarding acceleration.

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  • That is to say, although the instantaneous centre is a centre of no velocity for the instant, it is not a centre of no acceleration, and in fact the centre of no acceleration is in general a quite different point.

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  • The general principle on which the method of drawing an acceleration diagram depends is that if a link CB (fig.

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  • 125) have plane motion and the acceleration of any point C be given in magnitude and direction, the acceleration of any c other point B is the vector sum of X

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  • the acceleration of C, the radial n acceleration of B about C and the A

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  • tangential acceleration of B about C.

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  • Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

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  • angles to Ct; then the vector sum of these three magnitudes is Ab, and this vectol represents the acceleration of the point B.

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  • The magnitude of the radial acceleration is given by the expression vi/BC, v being the velocity of the point B about the point C. This velocity can always be found from the velocity diagram of the chain of which the link forms a part.

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  • If dw/dt is the angular acceleration of the link, dw/dt X CB is the tangential acceleration of the point B about the point C. Generally this tangential acceleration is unknown in magnitude, and it becomes part of the problem to find it.

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  • An important property of the diagram is that if points X and x are taken dividing the link CB and the whole acceleration of B about C, namely, cb in the same ratio, then Ax represents the acceleration of the point X in magnitude and direction; cb is called the acceleration image of the rod.

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  • In applying this principle to the drawing of an acceleration diagram for a mechanism, the velocity diagram of the mechanism must be first drawn in order to afford the means of calculating the several radial accelerations of the links.

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  • Then assuming that the acceleration of one point of a particuar link of the mechanism is known together with the corresponding configuration of the mechanism, the two Vectors Ac and ct can be drawn.

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  • Examples, completely worked out, of velocity and acceleration diagrams for the slider crank chain, the four-bar chain, and the mechanism of the Joy valve gear will be found in ch.

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  • When a weight is reciprocated, the equal and opposite force required for its acceleration at any instant appears as an unbalanced force on the frame of the machine to which the weight belongs.

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  • In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.

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  • A more accurate though still approximate expression for the force on the frame due to the acceleration of the piston whose weight is W is given by w2r cos 0 + r cos 20

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  • An excess of the effort exerted on any piece, above that which is necessary to balanoe the resistance, is accompanied with acceleration; a deficiency of the effort, with retardation.

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  • An excess of effort above resistance involves an excess of energy exerted above work perfor~ned; that excess of energy is employed in producing acceleration.

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  • When a machine undergoes alternate acceleration and retardation, so that at certain instants of time, occurring at the end of intervals called periods or cycles, it returns to its original speed, then in each of those periods or cycles the alternate excesses of energy and of work neutralize each other; and at the end of each cycle the principle of the equality of energy and work stated in 87, with all, its consequences, is verified exactly as in the case of machines of uniform speed.

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  • At intermediate instants, however, other principles have also to be taken into account, which are deduced from the second law of motion, as applied to direct deviation, or acceleration and retardation.

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  • Energy of Acceleration and Work of Retardation for a Shifting Body.Let w be the weight of a body which has a motion of translation in any path, and in the course of the interval of time ~t let its velocity be increased at a uniform rate of acceleration from v1 to v2.

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  • The rate of acceleration will be dv/dt = const.

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  • = (v, vi) ~t; and to produce this acceleration a uniform effort will be required, expressed by P=w(vivi)g~t (7)

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  • To find the energy which has to be exerted to peoduce the acceleration from v1 to Vi, it is to be observed that the distance through which the effort P acts during the acceleration is L~s= (vi+vi)~t/2;

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  • consequently, the energy of acceleration is P.~s = w(v, ci) (v1+vi)12g = w(v, v11)2g, (72)

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  • Energy Stored and Restored by Deviations of Velocity.Thus a body alternately accelerated and retarded, so as to be brought back to its original speed, performs work during its retardation exactly equal in amount to the energy exerted upon it during its acceleration; so that that energy may be considered as stored during the acceleration, and restored during the retardation, in a manner analogous to the operation of a reciprocating force (~ 108).

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  • Let e denote the quantity by which the energy exerted in each cycle of the working of the machine alternately exceeds and falls short of the work performed, and which has consequently to be alternately stored by acceleration and restored by retardation of the flywheel.

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  • * To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.

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  • For a given link, this force isthe resultant of all the accelerating forces distributed through the substance of the material of the link required to produce the requisite acceleration of each particle, and the determination of this force depends upon the principles of the two preceding sections.

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  • Let a be the acceleration of be the angular acceleration about the axis through the Centre of gravity; then the K I1~~ the centre of gravity and let A

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  • force required to produce the - translation of the centre of - gravity is F =Wa/g, and the - couple required to produce the - angular acceleration about the Centre of gravity is M = IA/g, FiG.

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  • When the link forms part of a mechanism the respective accelerations of two points in the link can be determined by means of the velocity and acceleration diagrams described in 82, it being understood that the motion of one link in the mechanism is prescribed, for instance, in the steam-engines mechanism that the crank shall revolve uniformly.

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  • Let the acceleration of the two points B and K therefore be supposed known.

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  • The problem is now to find the acceleration a and A.

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  • 49), and set out Ob equal to the acceleration of B and Oh equal to the acceleration of K.

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  • Og is then the acceleration of the centre of gravity and the force F can therefore be immediately calculated.

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  • To find the angular acceleration A, draw kI, bt respectively parallel to and at right angles to the link KB.

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  • Then tb represents the angular acceleration of the point B relatively to the point K and hence tb/KB is the value of A, the angular acceleration of the link.

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  • directions of acceleration of B and K to Z meet in 0; draw a circle through the three 0

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  • The methods of the two preceding sections may be used when the acceleration of two points in the rod are known.

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  • moves with uniform velocity, so that if a is its angular velocit and r its radius, the acceleration is ar in a direction along the cran arm from the crank pin to the centre of the shaft.

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  • The acceleration of a second point, usually taken at the centre of the crosshead pin, can be found by the principles of 82, but several special geometrical constructions have been devised for this purpose, notably the construction of Klein,i discovered also independently by Kirsch.i But probably the most convenient is the construction due to G.

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  • Then, the crank standing at any angle with the line of stroke, draw LP at right angles to the connecting rod, PN at right angles to the line of stroke OB and NA at right angles to the connecting rod; then AO is the acceleration of the point B to the scale on which KO represents the acceleration of the point K.

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  • The finding of F may be continued thus: join AK, then AK is the acceleration image of the rod, OKA being the acceleration diagram.

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  • Hence Og represents the acceleration of the centre of gravity and, the weight of the connecting J.

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  • In an elaborate memoir 2 he showed that the ancient solar eclipses described by Herodotus, Thucydides, and others, which seemed to require an increased value of the secular acceleration of the moon's mean motion to bring them into line with modern results, might safely be neglected, the ambiguity of the accounts in each case rendering uncertain either the totality of the eclipse or the place from which it was visible.

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  • 800 and 1004, extracted from Caussin's translation of Ibn Junis, the eclipses and occultations of Bullialdus, Gassendi, and Hevelius, of the French astronomers at Paris and St Petersburg, and of Flamsteed at Greenwich, and deduced a secular acceleration of 8.8", agreeing well with the theoretical value.

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  • The average date of the break-up is April 11 th at Tver, and 14 days later about Kostroma, from which point a regular acceleration is observed (April 16th at Kazan, April 7th at Tsaritsyn, and March 17th at Astrakhan).

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  • for determining the acceleration of the Pendulum in Lat.

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  • Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.

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  • If W is the weight required to depress the attracted disk into the same sighted position when the plates are unelectrified and g is the acceleration of gravity, then the difference of potentials of the conductors tested is expressed by the formula V - V'=(d - d') /87 W where S denotes the area of the attracted disk.

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  • We Will Assume That When, As In Most Cases, Viscosity Maybe Neglected, The Mass (M) Of A Drop Depends Only Upon The Density (V), The Capillary Tension (T), The Acceleration Of Gravity (G), And The Linear Dimension Of The Tube (A).

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  • The " Dimensions " Of The Quantities On Which M Depends Are: A= (Mass)' (Length) 3, T = (Force)' (Length) ' = (Mass)' (Time) 2, G = Acceleration = (Length)' (Time) ', Of Which M, A Mass, Is To Be Expressed As A Function..

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  • If, as is sometimes stated, the tension of a vertical film were absolutely the same throughout, the middle parts would of necessity fall with the acceleration of gravity.

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  • Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.

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  • They are carried across the disk by the sun's rotation, partaking in the equatorial acceleration; they also show marked displacements of their own, whether with, or relative to, the neighbouring photosphere does not appear; at the beginning of their life they usually outrun the average daily rotation appropriate to their latitude.

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  • The equation of light is the time taken by light to traverse the sun's mean distance from the earth; it can be found by the acceleration or retardation of the eclipses of Jupiter's satellites according as Jupiter is approaching opposition or conjunction with the sun; a recent analysis shows that its value is 498.6", which leads to the same value of the parallax as above, but the internal discrepancies of the material put its authority upon a much lower level.

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  • gravity of the long body CD, and be the centre of gravity of the three vertical forces acting downwards at the points x i, and considered as weights collected at those points; then if be above the line z i y i it can be shown that this arrangement of the knife-edges of CD favours the" acceleration " principle, and is suited to act with and assist an " accelerating " steelyard, and similarly if the point h2 be above the line z 2 y 2 in the case of the short body EF.

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  • In the following year his memoir on the secular acceleration of the moon's mean motion partially invalidated Laplace's famous explanation, which had held its place unchallenged for sixty years.

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  • He compiled the Hakimite Tables of the planets, and observed at Cairo, in 977 and 978, two solar eclipses which, as being the first recorded with scientific accuracy, 4 were made available in fixing the amount of lunar acceleration.

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  • of Jupiter and Saturn in 1784, and of the " secular acceleration " of the moon in 1787.

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  • The lunar acceleration, too, obtains ultimate compensation, though only after a vastly protracted term of years.

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  • C. Adams in 1853, nearly doubled the value of the acceleration deducible from them; and served to conceal a discrepancy with observation which has since given occasion to much profound research (see MooN).

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  • The first step in constructing this theory was taken by Laplace, who showed that the secular acceleration was produced by the secular diminution of the earth's orbit.

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  • But Adams in 1853 1 showed that the previous computations of the acceleration were only a rude first approximation, and that a more rigorous computation reduced the result to about one-half.

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  • It was therefore surprising when, in 1877, Simon Newcomb found, by a study of the lunar eclipses handed down by Ptolemy and those observed by the Arabians - data much more reliable than the vague accounts of ancient solar eclipses - that the actual apparent acceleration was only about 8.3".

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  • The following is a summary of the present state of the question: The theoretical value of the acceleration, assuming the day to be constant, is .....

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  • - Combined with the question of secular acceleration is another which is still not entirely settled - that of inequalities of long period in the mean motion of the moon round the earth.

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  • The most plausible explanation is that, like the discrepancy in the secular acceleration, the observed deviation is only apparent, and arises from slow fluctuations in the earth's rotation, and therefore in our measure of time produced by the motion of great masses of polar ice and the variability of the amount of snowfall on the great continents.

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  • A similar though much smaller acceleration in the annual rate of increase after the Carlist Wars of 187476 is largely attributable to the prosperity caused by railway development between 1877 and 1887.

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  • the nation was well able to make good the numerical losses involved by a serious war; that its numbers tend to increase steadily; and that the rate of increase has hitherto shown a marked acceleration in periods of commercial expansion.

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  • And it makes a lovely throaty rasp under acceleration and a staccato backfire when you lift off the throttle.

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  • We respectfully request the Court of Justice to give consideration to the acceleration of its preliminary ruling in this case.

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  • Sudden acceleration of a car, forward or backward causes a loud screech of the tires, even on dirt or wet roads.

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  • The acceleration of the news cycle by necessity leads to less careful checking, while competition leads to more sensationalism.

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  • A naive acceleration run was also setup with too little run off forcing the car skid off to the grass verge.

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  • The RX 400h is very sprightly for a two-ton milk float, posting better acceleration times than a standard Alfa GT.

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  • This problem is an investigation of the influence of acceleration heating on the behavior of a mechanical room thermostat.

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  • Good mid-range torque gives excellent acceleration, try an MGB GT V8.

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  • Evidence for enhanced substorm activity and whistler mode chorus associated with electron acceleration to relativistic energies.

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  • This one really zings, as the claimed 0-62mph acceleration figure of 4.8 seconds shows.

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  • By using aformulathat takes into account the acceleration of gravity, you can calculate the time it takes for an object to fall to the ground.

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  • By using a formula that takes into account the acceleration of gravity, you can calculate the time it takes for an object to fall to the ground.

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  • Most sports cars have good acceleration and braking, agile handling and varying levels of fuel economy.

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  • For lawyers who don't qualify for an attorney line of credit, fee acceleration can offer similar benefits.

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  • If your firm doesn't meet the requirements to qualify for a line of credit, a fee acceleration is another cost-effective solution for the cash flow difficulties of a plaintiff's lawyer.

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  • Fee acceleration purchases unpaid legal fees from settled cases and lawyers have money on hand as it is needed.

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  • Fee acceleration is an alternative that can be used instead of a line of credit.

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  • With a fee acceleration plan, a company buys the unpaid legal fees from cases that have settled.

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  • In a fee acceleration situation, the lawyer will agree to receive his or her fees early and the fee acceleration company would retain a certain amount for its services.

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  • If more power is needed such as during passing the computer will automatically cause the electric motor to provide the extra acceleration that is needed at the time.

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  • Drive consistently without speeding, quick acceleration and sudden braking.

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  • The most fuel efficient driving requires slow and steady acceleration.

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  • Acceleration: Acceleration is the increased rate of velocity in respect to time at which something moves.

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  • The school has also ramped up its continuing education and non-credit programs for those interested in rapid career acceleration.

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  • That long stretch of track will pass by in an instant through the intense acceleration, and as the coaster turns completely vertical ascending its primary hill it rolls through a 90 degree spiral.

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  • Clingman's Dome: The thrilling 350-foot long tube ride takes guests along a path that allows them to experience a range of acceleration and deceleration forces from the front, rear sides of the slide.

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  • Acceleration and braking aren't complicated at all, as they shouldn't be.

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  • Lighter characters, like Baby Mario, typically have good acceleration and poor top speed.

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  • The difference in handling, speed, and acceleration is noticeable between the cars so you'll feel comfortable in choosing one car over the other without wasting points.

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  • There were no DirectX video standards, no surround sound, and certainly no 3D acceleration.

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  • The Tours start out pretty easy with cars having minimal speed, acceleration and power.

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  • It is legal for the bank to make this demand in most states because mortgages contain "acceleration clauses."

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  • The acceleration clauses state that if a customer misses payments, the bank can "accelerate" the loan or demand full payment at any time.

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  • Once the bank demands full payment under the acceleration clause, in most cases it is too late to resume regular monthly payments.

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  • A person who receives a paycheck and then turns around and promptly spends most of it away is not the type of homeowner who will benefit from this type of mortgage acceleration program.

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  • Speedtrack Plate: The Speedtrack plate, as the name implies, is engineered to assist the quick movements and bursts of acceleration often necessary in soccer.

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  • Will you need a car with great acceleration and performance?

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  • Over time, the automaker discovered that, in certain models, the gas pedal could remain depressed after the driver removed his or her foot, causing unintended acceleration of the vehicle.

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  • Toyota began receiving complaints about acceleration issues in 2008, and the automaker began considering a recall at that time. 2008 also saw a Toyota recall of the 2008 Toyota Highlander SUV.

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  • Drivability - Pay attention to how well the car performs in acceleration and braking.

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  • The company also says that wear and tear on the gas pedal is the most likely cause of the acceleration problem.

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  • Simply put, the study looked at the differences between the effects of running and jumping on body acceleration distribution and oxygen uptake.

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  • An alternative is to do leg presses in the gym, but try to get that acceleration element into the picture as well.

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  • Acceleration - The aforementioned clapping is a type of ballistic training, where you train the explosiveness of the muscle.

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  • There's a strong correlation between acceleration and jumping ability, so make it a point to include sprinting drills into your routine regularly.

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  • If long term care becomes a necessity for a person with an acceleration rider, the money received to help pay for services is an advance on the death benefit due when the person dies.

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  • It's called an acceleration rider because it accelerates payment of the insurance policy's death benefit.

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  • During some revolutions there was evidence of a slight acceleration of the return, and during others there was not.

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