Uniform motion

“ 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. ”

“ If a globe revolve with a uniform motion about an axis of a given position in a similar and infinite quiescent fluid with an uniform motion, it will communicate a whirling motion to the fluid like that of a vortex, and that motion will by degrees be propagated onward in infinitum ”

“ The motion of a heavy body down a curve differs in an important respect from the motion down an inclined plane. Every part of the plane being equally inclined to the vertical direction, the effect of gravity in the direction of the plane is uniform; and, consequently, the phenomena obey all the established laws of uniformly-accelerated motion. ”

“ I do not assert that the motion of all moving bodies is in fact uniform, but that such is their tendency. If it is otherwise than uniform, there is some cause operating to disturb the uniformity to which it is naturally prone. ”

“ Uniform.—A body has uniform motion when its speed and direction of motion do not change. Uniform motion for extended periods is rarely observed. A train may cover, on an average, 40 miles per hour but during each hour its speed may rise and fall. ”

“ If two bodies pass through two lengths with uniform motion, the proportion of their times to one another will be compounded of the proportions of length to length, and impetus to impetus reciprocally taken; also the proportion of their impetus to one another will be compounded of the proportions of length to length, and time to time reciprocally taken.—8. If a body be carried on with uniform motion by two movents together, which meet in an angle, the line by which it passes will be a strait line, subtending the complement of that angle to two right angles.—9, &c. ”

“ 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. ”

“ The only answer the geometrician could give is that we must assume that space is uniform, so that wherever we form our triangles we obtain the same results. The same is true in mechanics. The laws of motion and inertia hold good of the pebble on the roadside, of the dust grains dancing in the sunbeam, and of distant stars in the milky way. ”

“ The astronomy of the ancients admitted none but uniform circular motions, and could therefore be completely cultivated by the aid of their elementary geometry. But the pure science of motion might be extended to all motions, however varied as to the speed or the path of the moving body. ”

“ The First Law of Motion asserts that the motion of a body, when left to itself will not only be uniform, but rectilinear also. This latter part of the law is indeed obvious of itself as soon as we conceive a body detached from all special reference to external points and objects. ”

“ Therefore a conception of matter, mass, inertia, or momentum, being solely a product of motion in the brain, and a conception of color being solely a product of motion in the brain, it is again self-evident that the only possible difference, between the primordial realities we call inertia and color, is difference in modes of motion. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Is it true that, as Newton imagined, the dynamical facts of motion, established empirically and illustrated in the experiment of the rotating bucket render absolute motion, hence absolute space, inevitable? ”

“ 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. ”

“ Every tremulous body in an elastic medium propagates the motion of the pulses on every side right forward; but in a non-elastic medium excites a circular motion. Case. 1. The parts of the tremulous body, alternately going and returning, do in going urge and drive before them those parts of the medium that lie nearest, and by that impulse compress and condense them; and in returning suffer those compressed parts to recede again, and expand themselves. ”

“ 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. ”

“ 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. ”

“ The spaces which a body describes by any finite force urging it, whether that force is determined and immutable, or is continually augmented or continually diminished, are in the very beginning of the motion one to the other in the duplicate ratio of the times. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Imagine curve lines to be described on any plane, and to revolve about any given axes passing through the centre of force, and by that revolution to describe curve superficies; and that the bodies move in such sort that their centres may be always found in those superficies. If those bodies reciprocate to and fro with an oblique ascent and descent; their motions will be performed in planes passing through the axis, and therefore in the curve lines by whose revolution those curve superficies were generated. ”

“ 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. ”

“ 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. ”

“ For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Upon which accounts, true motion does by no means consist in such relations. ”

“ The evidence of the motion of the Earth around its axis, as afforded by the swinging of a pendulum or the rotation of a sphere, is too interesting to be omitted. In mechanical philosophy, we have two terms of the same general meaning—the conservation of the plane of vibration—and the conservation of the axis of rotation. For the non-scientific reader, these terms require explanation, and in endeavouring to simplify this as much as possible, we must ask the indulgence of the Mechanical Philosopher. ”

“ That Bodies refract Light by acting upon its Rays in Lines perpendicular to their Surfaces. But in order to this Demonstration, I must distinguish the Motion of every Ray into two Motions, the one perpendicular to the refracting Surface, the other parallel to it, and concerning the perpendicular Motion lay down the following Proposition. ”

“ Any kind of centripetal force being supposed, and the centre of force, and any plane whatsoever in which the body revolves, being given, and the quadratures of curvilinear figures being allowed; it is required to determine the motion of a body going of from a given place, with a given velocity, in the direction of a given right line in that plane. ”

“ By the same reasoning if a body, acted on by forces tending to two or more centres in any the same right line CO, should describe in a free space any curve line ST; the area AOP would always proportional to the time. ”

“ 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. ”

“ Rotation and translation combined.A body may have at the same time both a progressive and rotatory motion, without either disturbing the other, and one may suffer a change from the action of some external force, while the other continues the same as before.
Force through centre of gravity, causes progressive motion only. ”

“ There can be nothing paradoxical in the relative motion of two bodies being disturbed when the motion of one or the other is modified by an external cause. Nor need I dwell on the case of relative motion referring to axes which rotate uniformly. ”

“ But, just because we have set aside the elements, atoms or what not, to which these movements had been affixed, we are no longer dealing with that movement which is the accident of a moving body, with that abstract motion which the mechanician studies and which is nothing, at bottom, but the common measure of concrete movements. ”