Mathematical and Physical Papers Volume 1

Mathematical and Physical Papers Volume 1

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 edition. Excerpt: ...parallelepiped of the solid, and for, q, J the angles between the planes meeting in these edges respectively, the parallelepiped being so chosen that it becomes strained into a cube of unit dimensions, when the solid is in the particular state at which we wish to investigate its thermo-elastic properties. Transactions of the Royal Society, June 15, 1854. t Transactions of the Royal Society of Edinburgh, March 17, 1851. and if we suppose x, y, z, f, r), f to differ infinitely little from -o Vo 2o lo.o. respectively, the actual state (x, y, z, 97, f) will be one in which the body is strained from the state (x0 ya, z0, ? V0 O tne edges of tbe CUDe Deing elongated by x-x0, y-y0, z--z0, and the angles meeting in three conterminous edges receiving augmentations of --f0, Tj--rj0, --f0. It is clear, since the altered angles differ each infinitely little from a right angle, that the strains represented by f--f0, i--%, f--f0 involve no change of volume, and are simple deformations, each of a perfectly definite kind, in the planes YOZ, ZOX, XOY respectively, and that the change of volume due to the six coexistent strains is actually an infinitely small augmentation amounting to 194. Considering still x--x0 &c. as each very small, we have the following development by Maclaurin's theorem, the zero suffixes to the differential coefficients being used for brevity to denote the values of the different coefficients at (x y0, z0, f0, 0, 0). + 2 dag)/'--+2 ()--- --- + 2---6)+-,0-U --U +2-(f-+2 (s ).-("-+&c-(18) 195. According to the system of variables which we have adopted, as set forth in 193, when x--x0 &c. are each infinitely small, x...
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Product details

  • Paperback | 178 pages
  • 189 x 246 x 10mm | 327g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 123655390X
  • 9781236553904