Proceedings of the Royal Philosophical Society of Glasgow Volume 6

Proceedings of the Royal Philosophical Society of Glasgow Volume 6

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1868 edition. Excerpt: ...and therefore its momentum is constant for difi'erent velocities of the ring. To this must be added, as was proved by Poisson, a quantity equal to half its own amount, as an equivalent for the inertia of the external fluid; and the sum is the whole effective momentum of the motion. Hence we see not only that the whole effective momentum is independent of the velocity of the ring, but that its amount is the same as the magnetic moment in the corresponding ring electro-magnet. The same result is, of course, obtained by the Green's integral referred to above. The synthetical method just explained is not confined to the case of a single circular ring specially referred to, but is equally applicable to a number of rings of any form, detached from one another, or linked through one another, in any way, or to a single line knotted to any degree and quality of " multiple continuity," and joined continuously, so as to have no end. In every possible such case the motion of the fluid at every point, whether of the vortex core or of the fluid filling all space round it, is perfectly determined by Helmholtz's formulae, when the shape of the core is given. And the synthetic investigation now explained proves that the effective momentum of the whole fluid motion agrees, in magnitude and direction, with the magnetic moment of the corresponding electro-magnet. Hence, still considering, for simplicity, only an infinitely thin line of core, let this line be projected on each of three planes at right angles to one another. The areas of the plane circuits thus obtained (to be reckoned, according to De Morgan's rule when automic, as they will generally be) are the components of' momentum perpendicular to these three planes....
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Product details

  • Paperback | 178 pages
  • 189 x 246 x 10mm | 327g
  • United States
  • English
  • black & white illustrations
  • 1236765850
  • 9781236765857