Elastic medium

“ And as, when applying those laws to the elastic medium air, we are able to infer the phenomena of sound, so by arguing in a similar manner concerning ether we are able to infer the existence of light phenomena corresponding to what do occur. All that we do is to take an elastic substance, increase its elasticity immensely, and denude it of gravity and some other properties of matter, but we must retain sufficient likeness to matter to allow of deductive calculations. ”

“ Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed. ”

“ And therefore in mediums of equal density and elastic force, all the pulses are equally swift. Now if the density or the elastic force of the medium were augmented, then, because the motive force is increased in the ratio of the elastic force, and the matter to be moved is increased in the ratio of the density, the time which is necessary for producing the same motion as before will be increased in the subduplicate ratio of the density, and will be diminished in the subduplicate ratio of the elastic force. ”

“ A medium, in order to be available at all, must transmit actions across it in time ; therefore there must be postulated for it the property of inertia, — of the same kind as ordinary matter possesses, for there can hardly be a more general kind, — and also the property of elasticity or statical resistance to change either of position or of form. In ordinary matter the elasticity has reference solely to deformation; while in the constitution here assumed for the æther there is perfect fluidity as regards form, but elastic resistance to rotational displacement. ”

“ Let us first apply the elastic theory to the case of the so-called vacuum. If we write for the amplitude measured in the middle between two nodal planes, the velocities of displacement will be as and the kinetic energy will be represented by where is a constant depending on the density of the medium. The potential energy, which consists in distortion of the medium, may be represented by where is a constant depending on the rigidity of the medium. ”

“ So the physicists, not to be out-done by any fairies, make their ether indefinitely elastic, and their theory lands them just here, with a medium filling all space, thousands of times more elastic than steel, and thousands on thousands of times less dense than hydrogen gas. ”

“ And accordingly, so long as our purpose is morphological, so long as what we seek to explain is regularity and definiteness of form, it matters little if we should happen, here or there, to confuse surface tension with elasticity, the contractile forces manifested at a liquid surface with those which come into play at the complex internal surfaces of an elastic solid. ”

“ It possesses so-called elasticity of bulk. In the case of water having a free surface there is, as we have seen, a resistance to any change of level in the surface. This may be called an elasticity of surface form. Whenever an elastic material is strained or deformed, energy has to be expended on it to create the deformation. Thus to wind up a watch-spring, stretch a piece of indiarubber, compress some air, or bend a bow, requires an energy expenditure. ”

“ Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of an elastic fluid. Hard bodies are in the next degree elastic; if two ivory, or hardened steel balls are struck together, the parts at which they touch, will be flattened; but their elasticity will make them instantaneously resume their former shape. ”

“ The yield-point may be raised, as, for instance, in wire which has been hardened by stretching, but the elasticity is much impaired, and it is only within very narrow limits, if at all, that proportionality between stress and strain is found. Subsequent prolonged rest gradually restores the elasticity, and after a sufficient number of weeks or months the metal is found to be elastic up to a point which may be much higher than the original elastic limit. ”

“ The elasticity of all the diameters of any plane perpendicular to the axis of a prism of rock crystal, may be considered as being sensibly the same.
2nd. All the planes parallel to the axis are far from possessing the same elastic state; but if any three of these planes be taken, restricting ourselves only to this condition, that the angles which they form with each other are equal, then their elastic state is the same. ”

“ In some substances the limit is reached with slight distortion, while others are perfectly elastic even when greatly stretched. India rubber is an example of a body having perfect elasticity through wide limits. Glass has great elastic force but its limit of elasticity is soon reached. Substances like India rubber may be said to have great "stretchability," but little elastic force. In physics, elasticity refers to the elastic force rather than to ability to endure stretching. ”

“ Degrees of Elasticity in Different Substances.—Some substances have so very little elasticity that they are practically considered as having none. Lead is one of these. A rod of lead when bent remains so, and a leaden ball does not rebound. While aeriform substances are the most compressible of all, they are also the most elastic. Air compressed returns to its usual condition the moment that it is relieved from the pressure, and with a force proportioned to the amount of the pressure. So it is with steam and the gases. ”

“ Here, then, out of matter possessing rigidity, but absolutely devoid of elasticity, we have made a perfect model of a spring in the form of a spring balance. Connect millions of millions of particles by pairs of rods such as these of this spring balance, and we have a group of particles constituting an elastic solid; exactly fulfilling the mathematical ideal worked out by Navier, Poisson, and Cauchy, and many other mathematicians, who, following their example, have endeavored to found a theory of the elasticity of solids on mutual attraction and repulsion between a group of material particles. ”

“ What is the elastic curve?—the curve into which an elastic line forms itself under the pressure of a weight—is a problem which had been proposed by Galileo, and was fully solved, as a mathematical problem, by Euler and others.
But beams in practice are not mere lines: they are solids. And their resistance to flexure, and the amount of it, depends upon the resistance of their internal parts to extension and compression, and is different for different substances. ”

“ The elastic state of these plates cannot present such remarkable differences as those we have observed in the preceding series; for, being all cut round the axis of greatest elasticity, they can only contain in their plane that of least or that of mean elasticity, or lastly, those intermediate between these limits, which do not vary greatly from each other. ”

“ The word elastic, in physics, is the name given to the tendency which a body exerts, when distorted, to return to its original shape. Rubber possesses more elasticity than any other material known, it being possible to stretch a piece of rubber cord to eight or nine times its original length without fracture. Rubber also possesses the added requisite of lightness and will store up more energy than any form of steel spring. ”

“ The case is quite different in the elastic theory. Here the force from outside necessary to maintain in any element of volume the displacement is represented by In transparent bodies, therefore, it is directed toward the center. In metals, there is a component in the direction of the motion while the radial part of the force changes its direction and is often many times greater than the opposite force in transparent bodies. ”

“ The finishing of elastic fabrics is a process which demands great care, and has to be taken into calculation from the beginning of the web construction. Calculations must always be made as to what effect heat, moisture and sizing will have upon the covered up elastic threads, confined as they are in a multiple of small cavities and under high tension. As soon as the softening influence of heat and steam operate upon the covering of cotton yarn which confines these threads, the rubber strands begin to assert themselves and contraction at once takes place. ”

“ In making up sections of elastic webs for various purposes, particularly when required to be attached to garments, it is often found that the joinings are bulky and unsightly on account of their thickness. ”

“ The limits of perfect elasticity as regards change of shape, on the other hand, are very low, if they exist at all, for glasses and other hard, brittle solids; but a class of metals including copper, brass, steel, platinum are very perfectly elastic as regards distortion, provided that the distortion is not too great. The question can be tested by observation of the torsional elasticity of thin fibres or wires. ”

“ Also, in general, if something is broken, the pieces will not readily unite of themselves, when placed in contact. The natural elasticity of shape of the elastic molecules causes an initial repulsion. By suitable assumption regarding thickness, stiffness, &c., of these ring-like molecular forms, the differences between the "chemical affinity" of different molecules might doubtless be accounted for. ”

“ The immense differences in their weight almost disappear; the remains of difference in color that were left are lost. Transparency becomes universal, and they are all elastic. They now form but one set of substances, and the varieties of density, hardness, opacity, color, elasticity, and form, which render the number of solids and fluids almost infinite, are now supplied by a few slight variations in weight, and some unimportant shades of color. ”

“ Any object that has any degree of elasticity at all is apt, if struck or rubbed or otherwise set suddenly in motion, to start vibrating back and forth; the vibrations will nearly always be regular, and will occur at a rate that is the same for that particular object whenever it vibrates. The rate depends on the size, the character, and the degree of stretch of the object. Air is to all intents and purposes perfectly elastic ”

“ As they fall, the stored-up (potential) energy becomes kinetic and can be made to do work.
2. Storing of Energy through Elasticity.—Energy is stored also by doing work in opposition to elasticity, as in bending a bow or in winding a clock spring. The bending, twisting, stretching, or compressing of elastic substances puts them in a condition of strain which causes them to exert a pressure (called elastic force) that tends to restore them to their former condition. Energy stored by this means becomes active as the distorted or compressed substance returns to its former shape or volume. ”

“ The behaviour of an elastic solid body, strained within the limits of its elasticity, is entirely determined by the constants and if the body is isotropic, that is to say, if it has the same quality in all directions around any point. ”

“ To represent all the correlated quantities we should have to construct not only a diagram of moments but also a diagram of elastic deflexion and its so-called “curvature”; and the engineer would want to know something more about the material of the ligamentous tension-member—its modulus of elasticity in direct tension, its elastic limit, and its safe working stress.
In various ways our structural problem is beset by “limiting conditions.” Not only must rigidity be associated with flexibility, but also stability must be ensured in various positions and attitudes ”

“ The æther is a perfect fluid endowed with rotational elasticity; so in the first place we have — and this is the most difficult part of our undertaking — to construct a material model of a perfect fluid, which is a type of medium nowhere existing in the material world. ”

“ Tests of elasticity are made by subjecting wire of different materials but of the same dimensions to the same tension. The one changing least is said to have the greatest elastic force or elasticity. If greater forces are applied to the wire and then removed, one will finally be found that will permanently stretch the wire so that it will not return exactly to the former length. ”

“ Not, as people generally think the mere power of elongation, calling a thing elastic that can be pulled out like a piece of India-rubber. An elastic body in the popular sense is not an elastic body from the scientific point of view, and, strange as it may sound, glass is much more elastic than India-rubber. ”

“ It may be compared to an elastic band, but there is no intermediate tangible substance to influence bodies that are affected by it, and it remains in undying tension, unlike all elastic material substances known, neither losing nor acquiring energy as time passes. ”

“ Elastic Solid Theory.—In the earlier days of the wave theory it was supposed that the whole of space was filled with something which acted like an elastic solid material in which the vibrations of the atoms of a luminous body started waves in all directions, just as the vibrations of a marble embedded in a jelly would send out waves through the jelly. ”

“ Further, as the elasticity of the medium which regulates the pressure is proportional to the density, so the pressure must decrease, as the elasticity decreases--that is, as the electric potential decreases, or the electric density is diminished. ”

“ What I claim as my invention is: (1) In a corset, an elastic section composed of two thicknesses of cloth or material having tubes in combination with the spiral metal springs, E, inclosed by such tubes, and arranged in groups, to regulate the elasticity of the section, such groups being all composed of a single continuous spring passed back and forth through the tubes, and secured at its ends, substantially as described and shown. ”