Osborne Reynolds

“ It is not that the drop merely forces itself down under the surface, but, in descending, carries down with it a mass of water which, when the ring is one inch in diameter, would be an oblate spheroid, having a larger axis of two inches and a lesser of about one and a half inch. For it is well known that the vortex ring is merely the core of the mass of fluid which accompanies it, the shape of which is much the same as that which would be formed by winding string through and through a curtain-ring until it was full. ”

“ This, then, is the structure of the universe, except in the comparatively indefinitely small spaces in which there is matter;—grains in normal piling, of which the size, mean path, relative velocity and mean pressure are defined, and extend to infinity. Could anything be more simple?
In place of an elastic medium, of density approximating to empty space, we have this definite granular structure of the universe, elastic and of density ten thousand times that of water. ”

“ Friction, or resistance to tangential shifting of matter over matter, whatever the mode and arrangement, differs greatly according to the materials, but, like all material resistance, is essentially limited. ”

“ Thus for the last hundred years the idea of the structure of the universe, or the luminiferous ether, which has prevailed, is that of space occupied by an incompressible elastic jelly yielding to tangential stress, having a density which is all but indefinitely small. ”

“ The differential equations for the equilibrium of the lubricant are what the differential equations of viscous fluid in steady motion become when subject to the conditions necessary for lubrication as already defined— (1) the velocity is below the critical value; (2) at the surfaces the velocity of the fluid is that of the solid; (3) the thickness of the film is small compared with the lateral dimensions of the surfaces and the radii of curvature of the surfaces. ”

“ The singular surfaces which we call molecules are individuals, which, although they may cohere, cannot pass through each other and thus although the only mass, that of the medium, is changing every instant, at the extreme rates already mentioned, these singular surfaces or molecules preserve their individuality, the realization of which is a further tax on the imagination. ”

“ LUBRICATION. Our knowledge of the action of oils and other viscous fluids in diminishing friction and wear between solid surfaces from being purely empirical has become a connected theory, based on the known properties of matter, subjected to the definition of mathematical analysis and verified by experiment. ”

“ Then as the general result of the research, in spaces in which the piling is normal, which spaces are almost indefinitely greater than those occupied by matter, it is shown, that there is one and only one conceivable purely mechanical system capable of accounting for all the physical evidence, as we know it, in the universe. ”

“ Hence in the case of lubrication the velocities of the fluid at the surfaces of the solids are those of the solid. In as far as the presence of the lubricant is necessary, such properties as cause oil in spite of its surface tension to spread even against gravity over a bright metal surface, while mercury will concentrate into globules on the bright surface of iron, have an important place in securing lubrication where the action is intermittent, as in the escapement of a clock. ”

“ And thus we may have the fullest confidence that the structure is purely mechanical, and that ideas, such as I have endeavoured to sketch, will ultimately prevail, displacing for ever such metaphysical conceptions as that of action at a distance, and accomplishing that ideal which, from the time of Thales and Plato, has excited the highest philosophical interest. ”

“ Also, the theoretical division of the law of frictional resistance into two laws—one dealing with the limit of rest, and the other asserting that the friction of motion, which is invariably less in similar circumstances than that of rest, is independent of the velocity of sliding—involves the theoretical assumption that there is no asymptotic law of diminution of the resistance, since, starting from rest, the rate of sliding increases. ”

“ The dilatation diminishes as the centres of the negative inequalities approach, and work is done by the pressure, outside the singular surfaces, to bring the singular surfaces of the negative inequalities together.
The efforts to cause the approach of the centres correspond, exactly, to the gravitation of matter if matter represents the absence of mass, and thus the inversion of preconceived ideas is complete. Matter is measured by the absence of the mass necessary to complete the normal piling. And the effort to bring the negative inequalities together is also an effort on the mass to recede ”

“ Thus Tower, being unaware of the discovery of the criterion, which was published in the same year as his reports, was thrown off the scent in his endeavour to verify the evidence he had obtained as to the finite thickness of the film by varying the velocity. He remarks in his first report that, “according to the theory of fluid motion, the resistance would be as the square of the velocity, whereas in his results it did not increase according to this law.” ”

“ If the medium is stationary and the molecules are moving with the earth, the grains within the surfaces do not partake of the mean motion of these surfaces, being continuously replaced by other grains by the action of propagation, by which the singular surfaces in their motion are continually absorbing the grains in front and leaving those behind without any mean effect on the motion of the grains. ”

“ The actual size of these rings depends on the size and speed of the drops. They steadily increase as they descend, and before they stop they have generally attained a diameter of from one to two inches, or even more. ”

“ Apart from the displacement of mass, the complex inequality differs from the gravitating inequalities.
In the complex inequalities the parameter of the dilatation is not the diameter of the grain, but is one half the linear dimension of the volume of the grain displaced taken as spherical.
The intensity of the efforts to revert, in the case of a complex inequality is the product of the pressure multiplied by the product of the volumes of the positive and negative inequalities, and again by the parameter. ”

“ However, in the attempts at generalization which followed the reformation of science, opportunity was afforded for such discrepancies in the mere enunciation of the circumstances in which the so-called laws of friction of motion are supposed to apply. The circumstances in which the great amount of empirical research was conducted as to the resistance between the clean, plane, smooth surfaces of rigid bodies moving over each other under pressure, invariably include the presence of air at atmospheric pressure around, and to some extent between, the surfaces ”

“ Strained normal piling implies that, although the shape of the medium is strained, so that the distances of the grains from their twelve neighbours are no longer equal—since the successive layers of grain in the normal piling instead of being flat are subject to slight spherical curvature—the strains are such as do not allow any change of neighbours; so that when the strain is removed each grain will find itself in normal piling with the same neighbours. ”

“ The range of the limits in available materials has a primary place in determining mechanical possibilities, and from the earliest times they have demanded the closest attention on the part of all who have to do with structures or with machines, the former being concerned to find those materials and their arrangements which possess the highest limits, and the latter the materials in which the limits are least. ”

“ By the first of these conditions all the terms having ρ as a factor may be neglected, and the equations thus become the equations of equilibrium of the fluid; as such, they are applicable to fluid whether incompressible or elastic, and however the pressure may affect the viscosity. ”

“ To show that there is an effort to expand the bag, while the pinch is on, it is only necessary to bring the bag into communication with a pressure-gauge, when the mercury shows that the pressure in the bag is only half of that of the atmosphere outside the bag. ”

“ Then, since the space occupied by inequalities is almost indefinitely small compared to the space in normal piling, it appears, even if there are as many positive inequalities as there are negative inequalities, the positive will present no evidence, being scattered, while the negative inequalities being brought together by gravitation, are in evidence. ”

“ The actions between such spheres is outside all experience. But it follows, since there is no elasticity, that for the conservation of energy, when these spheres, or grains, as they will now be called, come into collision, they will exchange their momenta, on the instant, and thus displace momentum and energy by instantaneous conduction. ”

“ The system being neither more nor less than an arrangement of indefinite extents of spherical grains in normal piling, so close that the grains cannot change their neighbours, although continually in relative motion with one another; the grains being of changeless shape and size. Thus constituting, to a first approximation, an elastic medium, with six axes symmetrically placed, see Fig. ”

“ Putting the bag between two vertical plates and slightly shaking and squeezing, so as to keep the sand at its densest, it still has a free surface and it can, in this way, be spread out until it is a broad flat plate; it is still soft, as long as it is squeezed, but when the pressure is removed the elasticity of the bag tends to draw it back to its rounded form, changing the shape, enlarging the interstices and absorbing the excess of water. This is soon gone and the bag remains a flat cake with peculiar properties; to pressures on its
Fig. ”

“ The downward slope in the upper chase being uniform for a small distance beyond the position of the stop; then varying, as an inverted S, so as to be horizontal at the level of the lower chase—when the stop is removed the balls start with nearly equal acceleration, then having accelerated, when they reach the steep slope they are separated. ”