Retrograde motion

“ If physical phenomena were due exclusively to the movements of atoms whose mutual attraction depended only on the distance, it seems that all these phenomena should be reversible; if all the initial velocities were reversed, these atoms, always subjected to the same forces, ought to go over their trajectories in the contrary sense, just as the earth would describe in the retrograde sense this same elliptic orbit which it describes in the direct sense, if the initial conditions of its motion had been reversed. ”

“ In this way the motion of the wheel about its centre, would, in some situations, counterbalance the general motion of the centre, and make the planet retrograde, while, on the whole, the westerly motion would prevail. Just as if we suppose that a person, holding a lamp in his hand in the dark, and at a 140 distance, so that the lamp alone is visible, should run on turning himself round; we should see the light sometimes stationary, sometimes retrograde, but on the whole progressive. ”

“ As a result of this circular movement the particles of matter tend to become globular from contact with one another. Two species of matter are thus formed, one larger and globular, which continue their circular motion with a constant tendency to fly from the centre of the axis of rotation, the other composed of the clippings resulting from the grinding process. These smaller "filings" from the main bodies, becoming smaller and smaller, gradually lose their velocity and accumulate in the centre of the vortex. ”

“ There is an instantaneous axis of rotation, i.e. by a suitable Lorentz transformation one can achieve that all points of a straight line are at rest.
6) All points of the body have a constant "rest distance" with respect to a certain point located upon the instantaneous axis, the center of rotation.
Except the identification of these general properties of the definition, I have computed some special motions, among them the case that a point of the body carries out a uniformly-accelerated motion (hyperbolic motion) , and that the body is arbitrarily rotating about the direction of translation. ”

“ According to the formula, t = 2π √d/e, we should expect that a particle would make each semi-vibration in an equal time, and from a knowledge of the density and elastic moduli of a body this time might be calculated. Although the time of a semi-oscillation may be constant, we must bear in mind that, like the bob of a pendulum during each of its swings, the particle starts from rest, increases in velocity until it reaches the middle portion of its half swing, from which it gradually decreases in speed until it reaches zero, when it again commences a similar motion in the opposite direction. ”

“ The laws which govern the descent of bodies by gravity, being reversed, will be applicable to the ascent of bodies projected upwards. If a body be projected directly upwards with any given velocity, it will rise to the height from which it should have fallen to acquire that velocity. The earth’s attraction will, in this case, gradually deprive the body of the velocity which is communicated to it at the moment at which it is projected. Consequently, the phenomenon will be that of retarded motion. ”

“ It is accordingly clear that the acceleration or retardation of rotation is felt. The acceleration operates as a stimulus. The sensation, however, like almost all sensations, though it gradually decreases, lasts perceptibly longer than the stimulus. Hence the long continued apparent rotation after the stopping of the apparatus. The organ, however, which causes the persistence of this sensation must have its seat in the head, since otherwise the axis of apparent rotation could not assume the same motion as the head. ”

“ And if they do not balance each other, the inevitable result must be a rotation of the whole mass of the rarer medium in one direction. But preponderating momentum in one direction, having caused rotation of the medium in that direction, the rotating medium must in its turn gradually arrest such flocculi as are moving in opposition, and impress its own motion upon them; and thus there will ultimately be formed a rotating medium with suspended flocculi partaking of its motion, while they move in converging spirals towards the common centre of gravity. ”

“ This last supposition implies that, calling the two bodies A and B for brevity, the motion of the centre of inertia of B relatively to A must, when the distance between them was great, have been directed with great exactness to pass through the centre of inertia of A; such great exactness that the rotational momentum or moment of momentum after collision was no more than to let the sun have his present slow rotation when shrunk to his present dimensions. ”

“ If it be so placed that it must either remain at rest or ascend, it is clear, from the laws of equilibrium, that no motion derived from gravitation can take place; if it may descend, it must either continue to descend forever with a finite velocity, which is impossible,334 or it must first descend and then ascend with a vibratory motion, and then the case will be reducible to that of a pendulum, where it is obvious that no new motion is generated, and that the friction and resistance of the air must soon destroy the original motion. ”

“ Such are the inertia, the gravity or magnetism of bodies. For an occasional or periodical variation of intensity in any force is evidently productive of motion, which requires only to be accumulated or applied, and the apparatus for applying it cannot be considered as a machine for perpetual motion. Neither in strictness can any machine whose motion is derived from the rotation of the earth, and the consequent change of seasons and rotation of events, be so considered, because it does not generate, but only communicates. ”

“ Surely no more rigid, constant and unalterable cause could be conceived of than that of the normal motion of the particles of a medium among themselves, which, by an inevitable automatic adjustment arrange their motions so as to produce the effects of gravity. ”

“ Such a freely moving cavity radiation, separated form outer space by thin rigid reflective walls, provides a good example of a rigid body, whose laws of motion completely differ from those of ordinary mechanics. Although it differs, considered superficially, in no way from other rigid bodies and also possesses a certain inertial mass and obeys the law of inertia, its mass changes significantly with temperature and it also depends in a certain specifiable way from the magnitude of the velocity as well as from the direction of the moving force in respect to the velocity. ”

“ He builds up on the basis of his early experiments (§ 116) a theory of falling bodies, in which occurs for the first time the important idea of uniformly accelerated motion, or uniform acceleration, i.e. motion in which the moving body receives in every equal interval of time an equal increase of velocity. He shews that the motion of a falling body is—except in so far as it is disturbed by the air—of this nature, and that, as already stated, the motion is the same for all bodies, although his numerical estimate is not at all accurate. ”

“ During the entire of the descent, electric matter is vacating the rear and medium of space entering, consequently the fall is accelerated. Now as the body cannot fall of itself; as descending motion is of increasing velocity, while motion in every other direction is retarded; and, because all descent has the same centripetal direction, so should there be some distinct cause to produce these conspicuous effects, which, to trace, suggest the following hypothesis ”

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

“ Then I say that all the momentum of the falling body is along the vertical and is a maximum when it falls in that direction; the momentum is less along DA and still less along EA, and even less yet along the more inclined plane FA. Finally on the horizontal plane the momentum vanishes altogether; the body finds itself in a condition of indifference as to motion or rest; has no inherent tendency to move in any direction, and offers no resistance to being set in motion. ”

“ In the case of a body in visible rectilinear motion on the earth's surface, this change takes place very soon—if the motion be rotatory, such as that of a heavy revolving top, it may, perhaps, continue longer before it is ultimately stopped, by means of the surrounding air, and by friction of the pivot; if it be oscillatory, as in the pendulum, or vibratory, as in a musical instrument, we have seen that the air and internal friction are at work, in one shape or another, to carry it off, and will ultimately succeed in converting it into heat. ”

“ We can compare its field with an angle-lever, its material parts with the shell. Neither the electromagnetic momentum of one part, nor the mechanical momentum of the other part, is parallel to the velocity, therefore both need a torque for their translatory motion. However, since momentum as a whole is parallel to velocity, both momentum components (perpendicular to the velocity) are oppositely equal to one another, and the same holds thus for the torque. ”

“ In the case of a connected system in motion, the configuration is continually changing at a rate depending on the velocities so that we can no longer assume that the momentum is the time-integral of the force which acts on it. ”

“ If in the one case the springs are made more and more stiff, and in the other case the angular velocities of the fly wheels are made greater and greater, the periods of the vibrational constituents of the motion will become shorter and shorter, and the amplitudes smaller and smaller, and the motions will approach more and more nearly those of two perfectly rigid groups of material points moving through space and rotating according to the well known mode of rotation of a rigid body having unequal moments of inertia about its three principal axes. ”

“ Now we imagine the motion as altered by an external force , for instance by a homogeneous electric or magnetic field. Angular forces and rotation are excluded by us; we satisfy the equations of motion, when we accordingly alter the momentum vector of force , and let the motion be parallel to the respective direction of the momentum vector. ”

“ Thus it appears, that whenever the state of a body is changed either from rest to uniform rectilinear motion or vice versa, or from one state of uniform rectilinear motion to another, differing from that either in velocity or direction, or in both, the phenomenon is produced by that peculiar modification of force whose action continues but for a single instant, and which has been called an impulse. ”

“ If, therefore, we can determine the direction of motion of the wave particle in the first semiphase, and its maximum velocity, we can obtain, from any selected point, a line (that of emergence of the shock) somewhere in which, if prolonged beneath the earth, the focus must have been; and if we can obtain like results for two or more selected points, we decide the position and the depth of the focus, which must be in the intersection of the several lines of direction of the wave particle motion at each point, when prolonged downwards. ”

“ Hence from the times of the oscillations in unequal arcs in a resisting medium, may be known the times of the oscillations in a non-resisting medium of the same specific gravity. For the difference of the times will be to the excess of the time in the lesser arc above the time in a non-resisting medium, as the difference of the arcs to the lesser arc. ”

“ Supposing an original state of rest, about to pass into motion in obedience to the disturbing forces, the currents commencing at the centre will follow the lines of most rapidly-decreasing density; seeing that the inertia will be least in those lines. That is to say, there will be a current from the centre towards each pole, along the axis of rotation; and the space thus continually left vacant will be filled by the collapse of matter coming in at right angles to the axis. ”

“ In order to illustrate the theory of rotation experimentally, we must have a body balanced on its centre of gravity, and capable of having its principal axes and moments of inertia altered in form and position within certain limits. ”

“ If particles could exist without speed there would be no change and no motion; or if there was but one particle with speed there would be only rectilineal motion, but as there are many particles with speed they collide and deflect one another; deflected speed is directed motion. The first phase of directed motion is thus change of direction in free particles. Here we have persistence in speed and change in direction by which persistence is divided into portions by events of collision, and this manifests time. ”

“ If a body be drawn back parallel to the beam, and released so as to swing against another swinging body, both will have motion. This motion will, in some cases be a rebounding motion, as in the case of a small elastic body swinging against and striking a larger elastic body, but in all cases the sum total of the momentum after the impingement is the same as before. ”