Reciprocating motion

“ Is it to cause a body to act in such a manner that the reaction shall be greater than the action itself, and by that means generate force by the accumulation of the surplus? Or, can the motion communicated be greater than that lost by the agent? ”

“ If the law of action of these several forces is the same in the case of moving matter as in the case of moving electricity, then their motions also will be the same. The moving forces are called the action and the opposing forces are called the reaction, and Newton’s third law of motion says: Action is equal to the opposing reaction. ”

“ We see, therefore, that if between a particular impression and a particular motion associated with it, there is established a connexion producing what is called reflex action, the law that motion follows the line of least resistance, and that, if the conditions remain constant, resistance in any direction is diminished by motion occurring in that direction, supplies an explanation. ”

“ 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. ”

“ Thus, in order to determine the case of the direct action of bodies upon one another, we require no new law of motion. The equality of action and reaction, which enters necessarily into every conception of mechanical operation, combined with the measure of action as given by the third law of motion, enables us to trace the consequences of every case, whether of pressure or of impact. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ A few simple experiments will help us to fix in our minds the great fact of the convertibility of force. Starting with actual visible motion, correlation requires that when it disappears as motion, it should reappear as heat, light, or electricity. If the moving body be elastic like this rubber ball, then its motion is not destroyed when it strikes, but is only changed in direction. ”

“ We find such truths universally established and assented to among the cultivators of science, and among speculative men in general. All mechanicians agree that reaction is equal and opposite to action, both when one body presses another, and when one body communicates motion to another. All reasoners join in the assertion, not only that every observed change of motion has had a cause, but that every change of motion must have a cause. ”

“ 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. ”

“ 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. ”

“ It seems safe to look forward to the time when the conception of attractive and repulsive forces, having served its purpose as a useful piece of scientific scaffolding, will be replaced by the deduction of the phenomena known as attraction and repulsion, from the general laws of motion. ”

“ It would have been scarcely possible to discover the law that every body in motion tends to continue moving in a straight line, by an induction from instances in which the motion is deflected into a curve, by being compounded with the effect of an accelerating force. ”

“ If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ They are two functions of the co-operant forces, one dynamic, the other static; although markedly distinguishable as functions, we know that they are simply the co-operant forces now unbalanced and now balanced; what we call Rest is also a product of moving forces, each of which is operant, and will issue in a definite resultant when its counter-force is removed. Motion and Rest are correlatives, and both belong to the sphere of Kinetics. ”

“ The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. ”

“ 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. ”

“ Another more common distribution of the perpetual chain of causes and effects, which constitute the motions, or changing configurations, of the natural world, is into active and passive. Thus, if a ball in motion impinges against another ball at rest, and communicates its motion to it, the former ball is said to act, and the latter to be acted upon. ”

“ 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. ”

“ When A moves towards B, it is evident that B has the power directly or indirectly of drawing or attracting A; and when you notice this, and measure the law of the motion, and discover that A moves as if attracted towards B by some simple law, you will easily be enabled to ascertain what will take place if the motion continue. ”

“ From that time forth, all phenomena have been conceived as motion or modes of motion, only differing essentially one from the other in so far as motions may differ—that is to say, in the masses of the moving particles, their velocities, and their trajectories. The external world has appeared essentially homogeneous; it has fallen a prize to mechanics. Above all, there is heterogeneity in ourselves. ”

“ Motion as well as Matter being fixed in quantity, it would seem that the change in the distribution of Matter which Motion effects, coming to a limit in whichever direction it is carried, the indestructible Motion thereupon necessitates a reverse distribution. ”

“ 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. ”

“ After one force has put a body in motion, another force, it is true, may change its direction; but in such a case, it is not correct to say, that one force caused its motion and another the direction of that motion. For, in reality, both the motion of the body and its direction, result from the joint action of the two forces; or, in other words, each force contributes to the motion, and each to its direction. ”

“ In a similar manner philosophers demonstrate the first law of motion, or uniform velocity in a straight line, by showing that retardation, or divergence, is always in the definite ratio of the obstacles encountered by the moving body. ”

“ These facts and the principles out of which they grow are familiar to all who understand thoroughly, even the rudiments of physics; but to persons who are inclined to mechanics, but who have never had the advantages of the presentation of clear principles, they are confusing, and it is surprising that they have not become more fertile fields for Perpetual Motion workers. ”

“ By a like process the few which reach the Earth are again diffused through surrounding space. And on each occasion, such portions of the rays as are absorbed instead of reflected, undergo refractions that equally destroy their parallelism. More than this is true. By conflict with matter, a uniform force is in part changed into forces differing in their directions; and in part it is changed into forces differing in their kinds. When one body is struck against another, that which we usually regard as the effect, is a change of position or motion in one or both bodies. ”

“ No matter what their reciprocal interactions are, the path integral of their momenta is always minimal. Compared to traditional mechanics methods, the motion may be more difficult to calculate using our new method ”

“ From this same primordial truth, too, may be deduced the principle that motion once set up along any line, becomes itself a cause of subsequent motion along that line. The mechanical axiom that, if left to itself, matter moving in any direction will continue in that direction with undiminished velocity, is but an indirect assertion of the persistence of force ”

“ 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. ”

“ 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. ”

“ There is, in every case, a resistance to motion, which shows itself, not in preventing the motion, but in a reciprocal force, exerted backwards upon the agent by which the motion is produced. And this resistance resides in each portion of matter, for it is increased as we add one portion of matter to another. ”

“ To understand the demonstration of this corollary, we must premise this obvious principle, that when a body is acted upon by a motion of power parallel to a right line given in position, this power, or motion, has no effect to cause the body to approach towards that line, or recede from it, but to move in a line parallel to a right line only ”

“ 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. ”

“ Two such forces constitute what is known in mechanical science as a couple, which occasions rotatory instead of rectilinear motion, and can only be neutralised by an equal and opposite couple of forces. ”

“ 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. ”

“ Secondly, The motion and force are transmitted from the prime mover through the train of mechanism to the working piece or pieces, and during that transmission the motion and force are modified in amount and direction, so as to be rendered suitable for the purpose to which they are to be applied. ”