Relative motion

“ It is better form of speech to say that motion is absolute or relative when it is desired to call attention to one factor or the other, rather than to say that motion is an absolute or a relation.
The motion of particles is of such a nature that paths must impinge, and then collisions arise which give rise to impulse, or collision by which paths are deflected. ”

“ If a state of motion exists in a system of bodies, in which the components of the light vector are certain functions of relative coordinates and time t, thus also the functions that arise when we replace t by -t, represents the values of the components that correspond to a possible motion. ”

“ In conservation of matter, energy, what you will, in plenitude, in motion as only relative and so as always under a principle of uniformity and constancy or even immobility, in motion too as inclining to vibration, which suggests poise or tension, or to rotation, in which we see rest as well as motion, and finally, not to extend what might be a long list, in the infinity of space and time or of quantity, the physical sciences have hidden entrances for the silent, usually unnoticed admission of what is psychical. ”

“ In the physical world we are congnizant of but four elementary or primordial ideas, beside the inevitable Time and Space. They are Matter, Force, Position, and Motion. Of these, motion is simply change of position; and force is recognized as the agent in every change of motion. ”

“ Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.
I. ”

“ If the direction of the force be through the centre of gravity, it causes a progressive motion only, that is, if the body was at rest before, it will move forward in the direction of the impressed force. ”

“ For by compounding the proper motion of the body with that motion, which the impulse alone would rate, you'll have the motion with which the body will go off from a given place of impulse, in the direction of a right line given in position. ”

“ We must here remember that motion as speed is inherent and constant in the particle and that motion as path is always determined from without, but the particles within the body are all external to one another, and therefore the direction of motion which is internal to the body is in obedience to the laws of heredity, and the direction of motion which comes from without the body is heat, gravity and strain. ”

“ But whether or not momentum necessarily accompanies motion, it was shown above that the same reason for conceiving color to be solely a mode of motion equally obtains in our conception of matter, mass, or inertia, as a mode of motion; and that "all the reality we know" exists, primarily, in changing, but ever-existing, relations and contrasts of modes of motion. ”

“ It is, however, always in the same direction—the direction opposed to the earth's spin. When we speak then of the precessional motion of the earth, we usually think of the mean or average motion, since the motion gets quicker and slower every quarter year. ”

“ B. You perplex yourself by confounding the idea of circular motion, with that of motion in a right line; you must think only of the motion of a body round a fixed line, and you will find, that if the parts farthest from the centre had not the greatest velocity, those parts would not be able to keep up with the rest of the body, and would be left behind. Do not the extremities of the vanes of a windmill move over a much greater space, than the parts nearest the axis of motion? (plate 3. fig. 1.) ”

“ It means, in the first place, that the ultimate facts in physics must be events, rather than bodies in motion. A body is supposed to persist through a certain length of time, and its motion is only definite when we have fixed upon one way of dividing intervals between space and time. ”

“ The general law that the change of motion is proportional to the moving force and takes place in its direction, provided we take care always to regard the reaction of curves, surfaces, obstacles, &c., as so many real moving forces of (for a time) unknown magnitude, will always help us out of any dynamical scrape we may get into. ”

“ Free motion, arrested motion, the effort, the speed, and the direction of motion, such are the sensorial elements, which, in all probability, constitute the foundation of our ideas on space and its properties. ”

“ The science of dynamics is founded upon certain principles known as the laws of motion. The simplest of these principles asserts that a body once set moving in a straight line will continue to move on uniformly for ever in the same straight line, unless some force be permitted to act upon that body. For nature as we know it, this law seems to be fully proved. It has been tested in every way that we have been able to devise. ”

“ Motion. A continued and successive change of place, either of a whole body, or of the particles of [Pg 211] which a body is composed; the earth in revolving upon its axis only, would not change its place as a body, but all the particles of which it is composed, would revolve round a common axis of motion. In revolving in its orbit, its whole mass is constantly occupying a new portion of space. ”

“ The causes, as they exist at any moment, having produced a certain motion, that motion, becoming itself a cause, reacts upon the causes, and produces a change in them. By altering the distance and direction of the central body relatively to the planet, and the direction and quantity of the force in the direction of the tangent, it alters the elements which determine the motion at the next succeeding instant. ”

“ For that Motion which can continue long in one and the same part of a Body, can be propagated a long way from one part to another, supposing the Body homogeneal, so that the Motion may not be reflected, refracted, interrupted or disorder'd by any unevenness of the Body. ”

“ The law of the complex effect is explained, by being resolved into the separate laws of the causes which contribute to it. Thus, the law of the motion of a planet is resolved into the law of the acquired force, which tends to produce a uniform motion in the tangent, and the law of the centripetal force, which tends to produce an accelerating motion toward the sun; the real motion being a compound of the two. ”

“ Although the doctrine of motion in connexion with force, which is the subject of mechanics, is by far the most important form in which the consideration of motion enters into the formation of our sciences, the Pure Doctrine of Motion, which treats of space, time, and velocity, might be followed out so as to give rise to a very considerable and curious body of science. ”

“ So long as that which we term Matter is able to accept motion in any manner from any body that is either moving, or in a state of vibration, and not only accepts, but also transmits the vibratory, or the kinetic motion so called of the moving body, then that which accepts the motion is legitimately termed Matter. ”

“ The continued action of the earth upon a falling body is equivalent to a series of forces, applied in successive instants, each tending to produce a certain constant quantity of motion; and the motion at each instant is the sum of the effects of the new force applied at the preceding instant, and the motion already acquired. In each instant a fresh effect, of which gravity is the proximate cause, is added to the effect of which it was the remote cause ”

“ Motion depends upon certain external disturbing and directing forces acting upon all matter; and, consequently, as every mode of action is determined by some excitement external to the body moved, motion cannot, philosophically, be regarded otherwise than as a peculiar affection of matter under determinable conditions. “We find,” says Sir Isaac Newton, “but little motion in the world, except what plainly flows from either the active principles of nature, or from the command of the willer.” ”

“ While it is true that from a purely visual standpoint the motion of a body will depend essentially on the frame of reference we select, and will vary when we change our frame from the earth to, say, the moon or the sun, yet owing to the generation of dynamical effects it is possible to decide in an absolute way whether the body is rotating or not. ”

“ Many modern physicists mythologize in this manner about motion, being unable to distinguish motion as an abstract property, because motion is formulated in terms of space and force in terms of parallelograms. ”

“ But since local motion, or an endeavour at it, is not included in the nature of matter, which is as much matter when it rests as when it moves; and since we see that the same portion of matter may from motion be reduced to rest, and after it hath continued at rest, so long as other bodies do not put it out of that state, may by external agents be set a moving again ”

“ If a body in a given time, by the force M impressed apart in the place A, should with an uniform motion be carried from A to B; and by the force N impressed apart in the same place, should be carried from A to C ”

“ And again, motion in a straight line and in a curve are no otherwise distinct than that the one is motion continuing in the same direction, the other is motion which at each instant changes its direction. There is, therefore, according to the principles I have stated, no absurdity in supposing that all motion may be produced in one and the same way, by the same kind of cause. ”

“ When a body in a state of uniform motion receives an impulse in a direction not coinciding with that of its motion, it will move uniformly after the impulse in an intermediate direction, which may be determined by the principles established for the composition of motion in the last chapter. ”

“ The communication of motion, its direction, the resistance it suffers, and its cessation, in a word, the whole doctrine of motion cannot be consistently explained or clearly understood without supposing the inertia of matter. Self-moving matter must have thought and design, because, whenever matter moves, it must move in some particular direction, and with some precise degree of velocity ”

“ No object at rest alters its position without the intervention of some conditions extraneous to itself; and when once in motion, no object returns to a state of rest, or alters either its direction or its velocity, unless some new external conditions are superinduced. ”

“ And therefore the same law takes place in a system consisting of many bodies as in one single body, with regard to their persevering in their state of motion or of rest. For the progressive motion, whether of one single body, or of a whole system of bodies, is always to be estimated from the motion of the centre of gravity. ”

“ Time is a polar positing of the primary act, and an endless repetition of this positing; through this originate individual things, whose succession is motion.
81. Primary motion is the result of primary polarity. All motion has originated from duplicity; consequently from the idea in a dynamic not a mechanical manner. A mechanical motion, which might be produced ad infinitum by mechanical impulses, is an absurdity. There is nowhere a purely mechanical motion; nothing, as it is at present in the word, has become so by impulse; an internal act, a polar tension lies at the bottom of all motion. ”

“ Motion itself, however, is not twofold in character; it is unity, but the result of duality. In time we have to distinguish the polar act of position, and the act of repeating this position, which is motion. ”

“ It is obvious that the motions of a pair of points may be varied in any manner, whether by direct or by lateral deviation, and yet that their comparative motion may remain constant, in consequence of the deviations taking place in the same proportions, in the same directions and at the same instants for both points. ”

“ Applying these general considerations to the case of motion, we find that, even within the sphere of immediate sense-data, it is necessary, or at any rate more consonant with the facts than any other equally simple view, to distinguish instantaneous states of objects, and to regard such states as forming a compact series. Let us consider a body which is moving swiftly enough for its motion to be perceptible, and long enough for its motion to be not wholly comprised in one sensation. ”

“ In the other class of motions, as when bodies are thrown up in the air, they are, on the contrary, moving from their own place. Now, this conception of a body moving toward its own place may justly be considered inappropriate; because, though it expresses a circumstance really found in some of the most familiar instances of motion apparently spontaneous, yet, first, there are many other cases of such motion, in which that circumstance is absent; the motion, for instance, of the earth and planets. ”

“ Give him any amount of material at rest, and he can not conceive of any method by which motion can disturb any part of it, unless such motion be mass motion communicated from without, or molecular motion, already existing within. He accounts for the phases of present motion in heavenly bodies, not for the primal cause of the actual movements or intrinsic properties they possess. ”

“ It would be easy to show that the fundamental laws of motion, in whatever form we state them, possess a very preeminent simplicity, compared with almost all others, which we might imagine as existing. ”

“ What can produce 45motion but motion itself? Into what can motion be converted, but motion? May not these forces, thus mutually convertible, be simply different modes of motion of the molecules of matter, precisely as mechanical motion is a motion of its mass? Thus was born the dynamic theory of force, first brought out in any completeness by Mr. Grove, in 1842, in a lecture on the “Progress of Physical Science,” delivered at the London Institution. In that lecture he said: “Light, heat, electricity, magnetism, motion, are all convertible material affections. ”