Mathematical and Physical Papers

Mathematical and Physical Papers

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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. 1880 edition. Excerpt: ...is considered is very great compared with the depth of the fluid, we may without sensible error neglect the difference between the horizontal motions of different particles in the same vertical line, or in other words suppose the particles once in a vertical line to remain in a vertical line: we may also neglect the vertical, compared with the horizontal effective force.. These considerations extremely simplify the problem; and the theory of long waves is very important from its bearing on the theory of the tides. Lagrangers solution of the problem in the case of a fluid of uniform depth is well known. It is true that Lagrange fell into error in extending his solution to cases to which it does not apply; but there is no question as to the correctness of his result when properly restricted, that is when applied to the case of long waves only. There are however many questions of interest connected with this theory which have not been considered by Lagrange. For instance, what will be the velocity of propagation in a uniform canal whose section is not rectangular? How will the form of the wave be altered if the depth of the fluid, or the dimensions of the canal, gradually alter? In a paper read before the Cambridge Philosophical Society in May 1837.J, the late Mr Green has considered the motion of long waves in a rectangular canal whose depth and breadth alter very slowly, but in other respects quite arbitrarily. Mr Green arrived at the following results: --If 0 be the breadth, and 7 the depth of the canal, then the height of the wave cc /3i yi, the horizontal velocity of the particles in a given phase of their motion cc /3 y% the length of the wave x 7, and the velocity of propagation = JgyWith respect to the height of the wave, Mr Russell..show more

Product details

  • Paperback | 104 pages
  • 189 x 246 x 6mm | 200g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236885465
  • 9781236885463