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
A₁ anchor ring angle angular velocity approximately atom theory axis B₁ Boyle's law C₁ central line centre circular vortex ring coefficient collision compound cos˛ cose cross section deflection differential direction of motion direction-cosines dt dt dx dy dz equation fluid hence hydrogen integral intersect the shortest k˛t˛ kinetic energy line of vortex molecule momentum motion of CD n˛ n˛ number of links parallel paths plane quantities radial velocity radius vector shew shortest distance sin n sin˛ Sir William Thomson small compared sphere Substituting suppose surface transverse section values velocity of translation velocity perpendicular velocity potential vibration vortex atom theory vortex CD vortex columns vortex core vortices αγη αδη β₁ δη ζα ζβ ηψ λ˛ ω₁
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Síđa 109 - ... 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 109 - 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 115 - Clausius and 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...
Síđa 120 - ... the definition of the terms monad, dyad, &c. Thus each vortex ring in the atom would correspond to a unit of affinity in the chemical theory of quantivalence. If we regard the vortex rings in those atoms consisting of more vortex rings than one as linked together in the most symmetrical way, then no element could have an atom consisting of more than six vortex rings...
Síđa 114 - ... 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 113 - ... 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 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 119 - ... 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 120 - ... element could have an atom consisting of more than six vortex rings at the most, so that no single atom would be capable of uniting with more than six atoms of another element so as to form a stable compound. This agrees with chemical facts, as Lothar Meyer in his Modernen Theorien der Chemie, 4th Edition, p.
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 T.