A Treatise on the Motion of Vortex Rings: An Essay to which the Adams Prize was Adjudged in 1882, in the University of CambridgeMacmillan, 1883 - 124 síđur |
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Common terms and phrases
anchor ring angle angular velocity approximately atom consisting atom of hydrogen atom theory axis Boyle's law C₁ central line centre circular vortex ring coefficient collision compound cos˛ cose cross section deflection direction of motion direction-cosines dt dt dyad element equation expression fluid hence integral intersect the shortest k˛t˛ kinetic energy line of vortex mean velocity molecule momentum monad motion of CD number of links parallel paths plane quantities radial velocity radius vector shew shortest distance sin e sin˛ sine Sir William Thomson small compared Substituting suppose surface three primaries transverse section values velocity of translation velocity perpendicular velocity potential vibration vortex CD vortex columns vortex core vortex ring vortices αγη αδη γη δη ζα ζβ ηθ ηψ λ˛ ω₁
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Síđa iii - A TREATISE ON THE MOTION OF VORTEX RINGS. An Essay to which the Adams Prize was adjudged in 1882 in the University of Cambridge. By JJ THOMSON, Fellow of Trinity College, Cambridge, and Professor of Experimental Physics in the University.
Síđa 107 - ... ring, the total pressure over the surface is nil. When a ring approaches such a surface it begins to expand, so that if we consider a finite portion of the surface the total pressure upon it due to the ring will have a finite value when the ring is close enough. In a closed cylinder any vortexring approaching the plane end will expand out along the surface, losing in speed as it so does, until it reaches the cylindrical boundary, along which it will crawl back, on rebounding, to the other end...
Síđa 107 - WHEN a vortex-ring is approaching a plane large in comparison to the dimensions of the ring, the total pressure over the surface is nil. When a ring approaches such a surface it begins to expand, so that if we consider a finite portion of the surface the total pressure upon it due to the ring will have a finite value when the ring is close enough. In a closed cylinder any vortexring approaching the plane end will expand out along the surface, losing in speed as it so does, until it reaches the cylindrical...
Síđa 118 - ... to form a stable compound. This agrees with chemical facts, as Lothar Meyer in his Modernen Theorien der Chemie, 4th Edition, p. 196, states that no compound consisting of more than six atoms of one element combined with only one of another is known to exist in the gaseous state, and that a gaseous compound of tungsten, consisting of six atoms of chlorine united to one of tungsten does exist. Though in direct combination, the simplest compound is the one that would naturally be formed ; yet other...
Síđa 113 - Williamson, according to which the molecules of a compound gas are supposed not to always consist of the same atoms of the elementary gases, but that these atoms are continually changing partners. In order, however, that the compound gas should be something more than a mechanical mixture of the elementary gases of which it is composed, it is evidently necessary that the mean time during which an atom is paired with another of a different kind, which we shall call the paired time, should be large...
Síđa 111 - ... Graham, is of an entirely different kind from the passage of gases through capillary tubes, and is more nearly analogous to the flow of a gas through a small hole in the thin plate. "When the diameter of the hole and the thickness of the plate are both small compared with the length of the free path of a molecule, then, as Sir William Thomson has shown, any molecule which comes up to the hole on either side will be in very little danger of encountering another molecule before it has got fairly...
Síđa 112 - ... the one in front, then if, when it overtakes it, the shortest distance between the circular axes of the rings be small compared with the radius of either ring, the rings will not separate, the shortest distance between their circular axes will remain approximately constant, and these circular axes will rotate round another circle midway between them, while this circle moves forward with a velocity of translation which is small compared with the linear velocity of the vortex rings round it. We...
Síđa 2 - It will be seen that the work is almost entirely kinematical : we start with the fact that the vortex ring always consists of the same particles of fluid (the proof of which, however, requires dynamical considerations), and we find that the rest of the work is kinematical. This is further evidence that the vortex theory of matter is of a much more fundamental character than the ordinary solid particle theory; since the mutual action of two vortex rings can be found by kinematical principles, whilst...
Síđa 117 - ... of only one of these rings, others of two of the rings linked together, or else of a continuous curve with two loops, others of three, and so on...
Síđa 1 - ... laws of Hydrodynamics all the properties of bodies as consequences of the motion of this fluid. It is thus evidently of a very much more fundamental character than any theory hitherto started ; it does not, for example, like the ordinary kinetic theory of gases, assume that the atoms attract each other with a force which varies as that power of the distance т.