Transactions of the American Mathematical Society Volume 1

Transactions of the American Mathematical Society Volume 1

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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. 1900 edition. Excerpt: ...formulation of these boundary conditions so as to obtain a system of equations which can be readily solved. Such a system is system (3) of this section. It is of the same form as system (6) of II, the solution of which was obtained in that section. Equations (4) and (5) are thus obtained. Equation (5) is the most general solution, and when this equation becomes very nearly the same as equation (5) of I then the non-uniform conductor of this section becomes equivalent to its corresponding uniform conductor. This equivalence cannot be decided without a careful study of the wave-lengths and of the damping constants of waves of different periods. This study is recorded in the remaining portion of this section. This section is also entirely new. The work given in I and a portion of that given iu II, together with a description of experimental investigations bearing upon the same, were published in vol. XVI of the Transactions of the American Institute of Electrical Engineers for 1899. Additional experimental investigations bearing upon the principal problem, that is the problem of III, will be published in the near future. I. Wave Propagation Along A Uniform Linear Conductor. A. Waves of forced period. The conductor is a loop of wire A B (Fig. 1). At one point of the loop is a transmitting apparatus A, at the opposite point is a receiving apparatus B. The distance between A and B is I, equal to one-half the length of the whole loop. The distance of any element ds from A is s. (2) where Let L, R, and C, denote the inductance, resistance, and capacity, respectively, per unit length. Let y be the current at any point s. Then is the well known equation of propagation. To formulate the two boundary...show more

Product details

  • Paperback | 126 pages
  • 189 x 246 x 7mm | 240g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236966007
  • 9781236966001