Force field

“ Those who believe in force exerted at a distance without a means of communication have more elbow-room. They may assume attractive and repelling forces, perhaps oblique and tangential forces they may assume that these forces vary according to laws, simple or very complex they may wholly deny the existence of anything but force, and grant extension and inertia to a field of force regulated in a special fashion. ”

“ When the direction and magnitude of the force are the same throughout space and do not vary with time, the field of force is called uniform. Uniform fields of force are very difficult to obtain; the simplest illustration we can think of would be that given by a river flowing with constant speed along a rectilinear course. The force exerted by the current would of course remain the same in magnitude and in direction at all points in the river; and for this reason the field of force produced by the current would constitute a uniform field. ”

“ Together with inertial forces, something comes into light which was until now be interpreted as the "geometrical structure": the "guidance field", as something real, as an acting power of shaking force in some cases. ”

“ The beautiful illustration of the presence of magnetic force afforded by this experiment, naturally tends to make us think of the lines of force as something real, and as indicating something more than the mere resultant of two forces, whose seat of action is at a distance, and which do not exist there at all until a magnet is placed in that part of the field. ”

“ Clearly the artificial field of force is associated with curvature of track, and we can lay down the following rule:—
Whenever the observer's track through the four-dimensional world is curved he perceives an artificial field of force. ”

“ So far we have considered the cancellation of a field of gravitation, but we may also consider the creation of a field of force in empty space far from matter. Thus, if a hollow chest be subjected to a variable acceleration through empty space, a variable field of force (inertial force) will be experienced by an observer in the chest’s interior. ”

“ The difference of potential between any two points is called an electromotive force. The lines of force are necessarily perpendicular to the surface. When the lines of force and the equipotential surfaces are straight, parallel, and equidistant, we have a uniform field. The intensity of the field is shown by the number of lines passing through unit area, and the rate of variation of potential by the number of equipotential surfaces cutting unit length of each line of force. ”

“ Nothing material could exist, except instantaneously, in the field of force filling the axis of the Black's Cone of Battle; a field beside which the exact center of a multi-billion-volt flash of lightning would constitute a dead area. ”

“ It is evident that the conditions in the broad field of military operations correspond in kind, if not in degree, to the earlier hypothesis, and that the law deduced therefrom, that the fighting strength of a force can be represented by the square of its numerical strength, does, in its essence, represent an important truth. ”

“ For, let there be an overbalancing of the aggregating force in ever so little or much, an equivalent of the opposing force must thereafter find some other work to do, and the field is effectually given up to the mighty agency that combines, and constructs, and brings order out of chaos.
So long and in proportion as the forming worlds continue to contract their dimensions, the rotations and revolutions increase in their velocity. ”

“ The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. ”

“ An observer who is sitting eccentrically on the disc is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body . But the observer on the disc may regard his disc as a reference-body which is "at rest"; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. ”

“ But even in elementary mechanics an important natural force appears, which does not seem to operate in this manner. Gravitation is not resolvable into a succession of molecular blows. A massive body, such as the earth, seems to be surrounded by a field of latent force, ready, if another body enters the field, to become active, and transmit motion. ”

“ Let two spheres of radius be connected together so that their centres kept at a distance , and let them be suspended in a uniform magnetic field, then, although each sphere by itself would have been in equilibrium at any part of the field, the disturbance of the field will produce forces tending to make the balls set in a particular direction. ”

“ Let the axis of be the axis of revolution, and let the angular velocity be . Let the magnetism of the field be represented in quantity by , inclined at an angle to the direction of , in the plane of .
Let be the radius of the spherical shell, and the thickness. Let the quantities be the electro-tonic functions at any point of space; symbols of magnetic quantity and intensity; of electric quantity and intensity. Let be the electric tension at any point,
.............. ”

“ In 1846 he published his famous book on The Correlation of Physical Forces, the leading ideas of which he had already put forward in his lectures: its fundamental conception was that each of the forces of nature—light, heat, electricity, &c.—is definitely and equivalently convertible into any other, and that where experiment does not give the full equivalent, it is because the initial force has been dissipated, not lost, by conversion into other unrecognized forces. ”

“ So that if the excess of motion or velocity in the power is so great as to overcome all that resistance which commonly arises from the friction or attraction of contiguous bodies, as they slide by one another, or from the cohesion of bodies that are to be separated, or from the weights of bodies that are to be raised: the excess of the force remaining, after all these resistances are overcome, will produce an acceleration of motion thereto, as well in the parts of the machine, as in the resisting body. ”

“ A big machine is not needed to carry one through the air. [25] There are forces in nature which may be readily used for such purpose. Tell me, what holds you to the Earth, and makes a stone fall to the ground?"
"Attraction of gravitation," said Rob, promptly.
"Exactly. That is one force I refer to," said the Demon. "The force of repulsion, which is little known, but just as powerful, is another that mankind may direct. Then there are the Polar electric forces, attracting objects toward the north or south poles. You have guessed something of this by the use of the compass, or electric needle. ”

“ It matters not that other and disturbing forces exist outside or inside the space these bodies revolve in, because if this force must be considered as acting uniformly—applying itself to each of these bodies in a way to produce a perfect equation on all, it is as if this outside force were non-existing. ”

“ The problem before us is how to communicate an initial force of 12,000 yards per second to a shell of 108 inches in diameter, weighing 20,000 pounds. Now when a projectile is launched into space, what happens to it? It is acted upon by three independent forces: the resistance of the air, the attraction of the earth, and the force of impulsion with which it is endowed. Let us examine these three forces. The resistance of the air is of little importance. The atmosphere of the earth does not exceed forty miles. ”

“ The north and south lines of force are produced, we believe, by what you call magnetism, and the east and west lines of force by some power that is generated by the earth's rotation,—some say it is electricity. ”

“ In the next place, let the masses remain unaltered, but let the distance between them be doubled, then the force will be reduced fourfold. Let the distance be tripled, then the force will be reduced ninefold, and so on. ”

“ The action of the forces therefore, considered by themselves, is here exactly the same as, or exactly corresponding to, their action in the case of the satellite. There exists however the difference that there all external forces are independent of each other, while here the action of an external force becomes at once the cause of the opposite action of a molecular force. ”

“ According to our rule, we must begin by asking what is the immediate use of thinking about force; and the answer is, that we thus account for changes of motion. If bodies were left to themselves, without the intervention of forces, every motion would continue unchanged both in velocity and in direction. ”

“ These centres through which the force can enter are therefore actually necessary to the existence of the vehicle, and so are in operation in every one, but they may be whirling with very different degrees of activity. Their particles may be in comparatively sluggish motion, just forming the necessary vortex for the force and no more, or they may be glowing and pulsating with living light so that an enormously greater amount of force passes through them, with the result that various additional faculties and possibilities are opened to the ego as he functions on that plane. ”

“ Let us suppose the particles of the medium to fly back from the globe with a force which is neither the greatest nor yet none at all, but with a certain mean force; then the resistance of the globe will be in the same mean ratio between the resistance in the first case and the resistance in the second. ”

“ We have learned the direction and the measure of the deflection, which a revolving body continually suffers, and its resistance to which is termed centrifugal force. The direction is toward the center, and the measure is the versed sine of the angle. ”

“ The conception of a force as something which pushes or pulls is familiar to every one. Equally familiar is the conception of an intervening link by which a force is transmitted from one body to another. If I pull a bucket of water out of a well the push exerted by the water on the bottom of the pail is transmitted to my hand by a very simple series of links. The bottom of the bucket pulls at its sides, these pull at the handle, the handle pulls the rope, and that finally pulls at my hand. We have here a transmission of force by links, all of which are in bodily contact. ”

“ During all these years in which he has given exhibitions of the operation of his generators, liberators, and disintegrators, in turn, each being an improvement, successively, on the preceding one, no one has attempted to give to the public any theory, or even so much as a sensible conjecture, of the origin of the force. ”

“ In the beginnings of physical science we read of the power of inertia, for instance, of the force of acceleration, of molecules, of centripetal and centrifugal force, as of facts which definitely exist ”

“ We are dissatisfied with the explanation founded on the hypothesis of attractive and repellent forces directed towards the magnetic poles, even though we may have satisfied ourselves that the phenomenon is in strict accordance with that hypothesis, and we cannot help thinking that in every place where we find these lines of force, some physical state or action must exist in sufficient energy to produce the actual phenomena. ”

“ As an example of an identical force acting during periods of time successively equal to 1, 2, or 3, we may take three guns of the same calibre, but of lengths equal to 1, 2, and 3, and of which the charges, or rather, their propulsive forces, are identical and constant. ”

“ MASS AND RESISTANCE.—Owing to the fact that resistance acts with such a retarding force on an object of small mass, and it is difficult to set up a rapid motion in an object of great density, lightness in flying machine structures has been considered, in the past, the principal thing necessary. ”

“ So if a force acts on a planet, it produces a change in velocity that is proportional to the force and in the same direction as the force. His law of inertia is that any body, persists in its state of rest or of uniform motion in a straight line, unless affected by an outside force. ”

“ Now, since the power of gravity and the resistance of the air will always be greater than any force of projection we can give a body, the latter must be gradually overcome, and the body brought to the ground; but the stronger the projectile force, the longer will those powers be in subduing it, and the farther will the body go before it falls. ”

“ He took for his subject Force, he made a plea for the accurate use of terms in mechanical science, a reform which has progressed much since that time. He says that force, defined as the rate of change of momentum in a body is also the space-variation of potential energy. ”

“ You will then readily understand, that the heavy material to which surface-bred mortals allude as probably constituting the interior of the earth, is, in fact, nothing but the manifestation of a matter-supporting force, as exemplified in the sphere of attractive energy, the seat of which we are soon to encounter on [Pg 338] our journey. Likewise the mutual attraction of the heavenly bodies is not a property solely of their material part, but an expression in which both the force-spheres and the matter collected thereon take part. ”