Motion study

“ It is true that metaphysicians hold that in the strictest sense absolute motion is not only unknowable but unthinkable, but we may say at least that the above method permits theoretically the detection of absolute translational motion in the same sense that a study of centrifugal forces enables us to detect absolute rotational motion. ”

“ More important astronomically—and probably intrinsically also—is what he calls the science of local motion,80 which deals with the motion of bodies. 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. ”

“ For instance, one of the cases which we can observe is, that where rotatory motion is continued for a very long time, and where the velocity very slowly diminishes, as the motion of a wheel or spinning top. ”

“ Again, let us suppose that instead of inexact observations made on the movements occurring in daily experience, we make exact experiments on movements specially arranged to yield measured results; what is the postulate underlying every experiment? Uniform velocity is defined as motion through equal spaces in equal times. How do we measure equal times? By an instrument which can be inferred to mark equal times only if the oscillations of the pendulum are isochronous; which they can be proved to be only if the first and second laws of motion are granted. ”

“ When a body has only a motion of translation all the particles of which it is composed move with equal swiftness, and also in parallel directions; and by the first law of motion, every particle put in such motion will constantly move with the same velocity in the same direction, unless it be prevented by some external cause.
Rotation.
By a motion of rotation, a body without changing its place, turns round on an axis passing through its centre of gravity. ”

“ 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. ”

“ Out of these studies of moving bodies was gradually developed a correct notion of several important general laws of mechanics—laws a knowledge of which was absolutely essential to the progress of physical science. The belief in the rotation of the earth made necessary a clear conception that all bodies at the surface of the earth partake of that motion quite independently of their various observed motions in relation to one another. ”

“ Cavendish Laboratory, Cambridge, 19th March, 1879 Sir, I have received with much pleasure the table of the satellites of Jupiter which you have been so kind as to send me, and I am encouraged by your interest in the Jovial system to ask you if you have made any special study of the apparent retardation of the eclipses as affected by the geocentric position of Jupiter.
I am told that observations of this kind have been somewhat put out of fashion by other methods of determining quantities related to the velocity of light, but they afford the only method, so far as I know, of getting any estimate of the direction and magnitude of the velocity of the sun with respect to the luminiferous medium. ”

“ 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. ”

“ Almost of necessity, therefore, motion appears to us as the most important physical factor. Moreover, mechanical properties may be discovered in all physical events. The sounding bell trembles, the heated body expands, the electrified body attracts other bodies. Why, therefore, should we not attempt to grasp all events under their mechanical aspect, since that is so easily apprehended and most accessible to observation and measurement? ”

“ The First Law of Motion.—The first law of motion is, that When a body moves not acted upon by any force, it will go on perpetually in a straight line, and with a uniform velocity. Now what is the real ground of our assent to this proposition? That it is not at first sight a self-evident truth, appears to be clear; since from the time of Aristotle to that of Galileo the opposite assertion was held to be true; and it was believed that all bodies in motion had, by their own nature, a constant tendency to move more and more slowly, so as to stop at last. ”

“ 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. ”

“ 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. ”

“ Furthermore, change of motion never takes place abruptly; if its direction is changed, it is always through a curve without angles; if its velocity alters, it is by degrees. The gradual changes which are constantly taking place are conceived by geometers to be compounded together according to the rules of the parallelogram of forces. ”

“ Here, then, we have at once a physical basis for Newton's Second Law of Motion, the results of which are entirely in harmony with observation and experiment, and whose conception fully satisfies all the Rules of Philosophy; as it is simple in conception, fully agrees with observation and experiment, and satisfactorily explains the Second Law of Motion sought to be explained. ”

“ Once, while performing one of these experiments, and after rotating so long that I was no longer conscious of the movement, I suddenly caused the apparatus to be stopped, whereupon I immediately felt and saw myself with the whole box rapidly flung round in rotation in the opposite direction, although I knew that the whole apparatus was at rest and every outward point of reference for the perception of motion was wanting. Every one who disbelieves in sensations of movement should be made acquainted with these phenomena. ”

“ In the “classical” mechanics so-called of the Baroque, founded by Galileo and Newton, an irreproachable solution of the motion-problem on dynamic lines has been sought again and again. The history of the concept of force, which has been stated and restated with all the tireless passion of a thought that feels its own self endangered by a difficulty, is nothing but the history of endeavours to find a form that is unimpeachable, mathematically and conceptually, for motion. ”

“ If is the velocity of the moving system, the speed of light, and if , then all dimensions parallel to the direction of motion shall be contracted in the ratio , the dimensions normal to the direction of motion shall remain unchanged. ”

“ IN the sciences of Mechanics and Physical Astronomy, Motion and Force are the direct and primary objects of our attention. But there is another class of sciences in which we endeavor to reduce phenomena, not evidently mechanical, to a known dependence upon mechanical properties and laws. In the cases to which I refer, the facts do not present themselves to the senses as modifications of position and motion, but as secondary qualities, which are found to be in some way derived from those primary attributes. ”

“ Now if the globes are not homogeneous, the space described by the denser globe must be augmented in the ratio of the density. For the motion, with an equal velocity, is greater in the ratio of the density, and the time (by this Proposition) is augmented in the ratio of motion directly, and the space described in the ratio of the time.
Corollary 5. And if the globes move in different mediums, the space, in a medium which, caeteris paribus, resists the most, must be diminished in the ratio of the greater resistance. ”

“ In 1831 Mechanics' Magazine printed an article contributed by a correspondent who signed himself "Ed. Vocis Rationis." He claimed to have invented a very powerful Perpetual Motion Machine.
His enthusiasm is as interesting as his device is absurd. We give the article as published in full:
I propose to endeavor to show how my plan of perpetual motion could be applied to practical and useful purposes. ”

“ Such motion is communicated in exact proportion to the vastly varied complexities of the matter of your worlds, and out of this proportionate communication arise the movements and the laws of movement of all the stars and planets, all of which movements and laws of movement are amenable to calculation. Much of this is already known to you, and the day will probably come when your men of science will be able to calculate the proper motion of the remotest star that your instruments can discover with as much precision as they now calculate the motions of your moon. ”

“ We might restate the first law of motion in the form "Every body tends to move in the track in which it actually does move, except in so far as it is compelled by material impacts to follow some other track than that in which it would otherwise move." ”

“ Some refer it to the approach to the centre; others say that there is a certain extension of the centrical medium, which, closing behind the body, pushes it forwards. For the present, it is enough for us to demonstrate certain properties of Accelerated Motion, the acceleration being according to the very simple Law, that the Velocity is proportional to the Time. And if we find that the properties of such motion are verified by the motions of bodies descending freely, we may suppose that the assumption agrees with the laws of bodies falling freely by the action of gravity.”14
14 Gal. ”

“ 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. ”

“ A complex mechanical system may be capable of motion in several distinct modes or types, and the motions corresponding to each such type may be arranged as before in families. For the sake of simplicity I will suppose that only two types are possible, so that there will only be two families; and the rotational momentum is to be constant. ”

“ Let us now consider the movements of rotation, which follow from wounds of portions of the encephalon. They are of two distinct types: the one is a rotary movement round a circle, the other a motion of rolling or spinning. In the first case, the animal remains in his normal attitude, but tends always to go to one side, and describe an orbit more or less extended. In the second case, the animal can progress but little in moving himself. When he attempts to move, he is forced into a revolving motion, and turns on himself like a ball. ”

“ 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. ”

“ The science of the mathematics of motion deals with the speed of one and its trajectory, the speed of another and its trajectory, and of their collisions, and for this purpose it has to deal with the measure of their relations, and forever relation is considered and thus an illusion is sometimes produced, when motion itself seems to be wholly relation. ”

“ The analysis is more complex than that of Laplace, where the mutual attraction of the ocean was neglected, but this was perhaps inevitable. Our first task is to form the equations of motion and continuity, which will be equally applicable to all forms of the theory.
§ 15. Equations of Motion.—Let be the radius vector, colatitude and east longitude of a point with reference to an origin, a polar axis and a zero-meridian rotating with a uniform angular velocity from west to east. ”

“ Motion as speed is constant in the particle. The particle, of whatever order it may be in the members of the hierarchy, is accelerated by deflecting its particles. The principles or laws of dynamics are all corollaries of this fundamental law; hence dynamics may be taught as a deductive science. Thus we have the mathematics of number, the mathematics of space, and the mathematics of motion, all fundamentally deductive sciences. ”

“ Sect. 2.—Generalization of the Third Law of Motion.—Centre of Oscillation.—Huyghens.
The Third Law of Motion, whether expressed according to Newton’s formula (by the equality of Action and Reaction) , or in any other of the ways employed about the same time, easily gave the solution of mechanical problems in all cases of direct action; that is, when each body acted directly on others. But there still remained the problems in which the action is indirect;—when bodies, in motion, act on each other by the intervention of levers, or in any other way. ”