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.
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.
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.
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.
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.
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.
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.
During some revolutions there was evidence of a slight acceleration of the return, and during others there was not.
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.
The acceleration, a, which may be supposed uniform, is 1.465.
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.
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.
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.
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.
(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.
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.
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.
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.
(6) On a curved bridge the centrifugal load due to the radical acceleration of the train.
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.
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.
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%.
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.
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.
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.
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.
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.
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.
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?
, (7) and when q is stationary, the acceleration is normal to the surface H = constant, and the stream line is a geodesic.
- LAW OF Acceleration And Retardation Illustrated In The Evolution Of The Hind Feet Of The Horse.