Circular 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. ”

“ And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect ”

“ If a circle made by a movent moved with simple motion be commensurable to another circle made by a point which is carried about by the same movent, all the points of both the circles will at some time return to the same situation.—7.. If a sphere have simple motion, its motion will more dissipate heterogeneous bodies by how much it is more remote from the poles.—8. If the simple circular motion of a fluid body be hindered by a body which is not fluid, the fluid body will spread itself upon the superficies of that body.—9. ”

“ The Effects which distinguish absolute from relative motion are, the forces of receding from the axe of circular motion. For there are no such forces in circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then fill'd with water, and held at rest together with the water ”

“ In simple motion, every strait line taken in the body moved is so carried, that it is always parallel to the places in which it formerly was.—2. If circular motion be made about a resting centre, and in that circle there be an epicycle, whose revolution is made the contrary way, in such manner that in equal times it make equal angles, every strait line taken in that epicycle will be so carried, that it will always be parallel to the places in which it formerly was.—3. ”

“ For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. ”

“ And the case is the same if the second impulse were made upon any other place of the æquator of the first motion; and also if the first impulse were made upon any place in the equator of the motion which would be generated by the second impulse alone; and therefore also when both impulses are made in any places whatsoever; for these impulses will generate the same circular motion, as if they were impressed together and at once in the place of the intersections of the equators of those motions, which would be generated by each of them separately. ”

“ If we limit our attention to the motion in a single plane perpendicular to the axis of the cylinder, we have something which is almost identical with a diagrammatic representation of the changes in distribution in phase of an ensemble of systems of one degree of freedom, in which the motion is periodic, the period varying with the energy, as in the case of a pendulum swinging in a circular arc. ”

“ He that understands the natures of the circular pendulum and circular motion, will easily understand the whole ground of this principle, and will know where to find direction in nature for the true stating thereof. ”

“ A person to whom the double circular motion is familiar in the lathe naturally looks upon one circle moving upon another as in simple motion, if the second circle be fixed to the revolving radius, so that one and the same point of the moving circle travels upon the fixed circle. ”

“ If a body, in a medium whose density is reciprocally as the distances of places from the centre, revolves in any curve AEB (Figure 3.) about that centre, and cuts the first radius AS in the same angle in B as it did before in A, and that with a velocity, that shall be to its first velocity in A reciprocally in a subduplicate ratio of the distances from the centre (that is, as AS to a mean proportional between AS and BS) that body will continue to describe innumerable similar revolutions BFC, CGD, &c. ”

“ Wherefore it is not requisite that the natural motions of natural bodies should be onely Circular. Next, I do not understand, why a Circular Motion cannot be gotten naturally without a precedent right motion; for, in my opinion, corporeal motions may be round or circular, without being or moving straight before; and if a straight line doth make a circle, then an imperfect figure makes a perfect ”

“ 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. ”

“ Indeed, since circular motion is against the nature of these four elements, there must be some other different body to whose nature it is conformable. There must thus be some simple and primary body, whose nature it is to be carried round in a circle, as earth is carried downwards and fire upwards. ”

“ So that, if motion first by nature belong to a body first by nature, if circular motion (as being perfect) be prior to rectilinear motion, and if rectilinear motion belong to a first or a simple body, as we see both in fire and in earth, — we may be sure à fortiori that circular motion belongs to a simple body, and that there is, besides the four elements here, prior to them and more divine than them, a different body cf special nature and essence. ”

“ 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. ”

“ The matter between any two sphærical superficies concentrical to the vortex will never be accelerated; because that matter will be always transferring the motion it receives from the matter nearer the centre to that matter which lies nearer the circumference. ”

“ For, a circular as well as a progressive motion being communicated to it by that stroak, its parts on that side, where the motions conspire, must press and beat the contiguous Air more violently than on the other, and there excite a reluctancy and reaction of the Air proportionably greater. ”

“ The cylindrical curve round the stem of a plant binds its fibres together; while the ascent of the stem is in lines of various curvature: so the curve of the horizon and of the apparent heaven, of the rainbow, etc.: and though the reader might imagine that the circular orbit of any moving body, or the curve described by a sling, was a curve of motion, he should observe that the circular character is given to the curve not by the motion, but by the confinement: the circle is the consequence not of the energy of the body, but of its being forbidden to leave the centre ”

“ Every point in the body describes a circle about the axis, and returns to its original position after each complete revolution. But if the axle itself be in motion, the paths of the different points of the body will no longer be circular or re-entrant. Even the velocity of rotation about the axis requires a careful definition, and the proposition that, in all motion about a fixed point, there is always one line of particles forming an instantaneous axis, is usually given in the form of a very repulsive mass of calculation. ”

“ There is but one circle; there are an infinite number of ovals. Any original impulse would give some oval, but only one particular impulse, determinate in velocity and direction, will give a circle. If we suppose the planet to be originally projected, it must be projected perpendicularly to its distance from the sun, and with a certain precise velocity, in order that the motion may be circular. ”

“ The same sign which thus indicates the source of motion indicates likewise the species of motion, whether it be continuous or reciprocating, circular or progressive, &c. The same system of signs further indicates the nature of the mechanical connexion between the mover and the thing moved, whether it be permanent and invariable (as between the two arms of a lever) , or whether the mover and the moved are separate and independent pieces, as is the case when a pinion drives a wheel; also whether the motion of one piece necessarily implies the motion of another ”

“ 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 onwards in infinitum ”

“ 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. ”

“ But change the problem from geometry to dynamics, by supposing a particle to move on the surface of a smooth sphere under the action of a force tending to the center, as that exerted by an elastic string in a state of tension; then it is equally easy to prove that this particle, when started in any direction, will describe a great circle—that is, its motion will be such that the distance traversed by it in passing from its point of departure to any point in its path will be the shortest distance between those points. ”

“ And therefore in clocks, if forces were impressed by some machine upon the pendulum which preserves the motion, and so compounded with the force of gravity, that the whole force tending downwards should be always as a line produced by applying the rectangle under the arc TR and the radius AR to the line TN, all the oscillations will become isochronous. ”

“ When a body, like the ball at the end of the string, revolves in a circle, the centre of the circle is called the centre of its motion, and the body is said to revolve in a plane; because a line extended from the revolving body, to the centre of motion, would describe a plane, or flat surface.
When a body revolves round itself, as a ball suspended by a string, and made to spin round, or a top spinning on the floor, whilst it remains on the same spot; this revolution is round an imaginary line passing through the body, and this line is called its axis of motion. ”

“ Every body that moves in any curve line described in a plane, and by a radius, drawn to a point either immovable, or moving forward with an uniform rectilinear motion, describes about that point areas proportional to the times, is urged by a centripetal force directed to that point. ”

“ They comprised myriads of infinitesimal points, ostensibly motionless but actually moving very lazily: an individual point moved at most by a two-minute arc in an hour, and that not in a straight line but as it were oscillating about its own center of motion. ”

“ Therefore, a homogeneous and perfect globe will not retain several distinct motions, but will unite all those that are impressed on it, and reduce them into one; revolving, as far as in it lies, always with a simple and uniform motion about one single given axis, with an inclination perpetually invariable. And the inclination of the axis, or the velocity of the rotation, will not be changed by centripetal force. ”

“ The larger the circle described by b the more is the spring stretched, and the greater is the force with which b is attracted towards the centre. This experiment proves that the force necessary to retain a body in a circular path must be increased when the speed is increased. ”

“ If the distances of the pulses or their lengths are greater in one medium than in another; let us suppose that the correspondent parts describe spaces, in going and returning, each time proportional to the breadths of the pulses: then will their contractions and dilatations be equal. And therefore if the mediums are homogeneous, the motive elastic forces, which agitate them with a reciprocal motion, will be equal also. Now the matter to be moved by these forces is as the breadth of the pulses; and the space thro' which they move every time they go and return, is in the same ratio. ”

“ 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. ”

“ 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. ”

“ The manner in which you compound these different momenta to obtain their resultant strikes me as so novel that my mind is left in no small confusion. I do not refer to the composition of two uniform motions, even when unequal, and when one takes place along a horizontal, the other along a vertical direction; because in this case I am thoroughly convinced that the resultant is a motion whose square is equal to the sum of the squares of the two components. The confusion arises when one undertakes to compound a uniform horizontal motion with a vertical one which is naturally accelerated. ”