Daedalus; Proceedings of the American Academy of Arts and Sciences Volume 46

Daedalus; Proceedings of the American Academy of Arts and Sciences Volume 46

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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. 1912 edition. Excerpt: ...the initial vector discharging p. d. in the circuit considered, OE0 the initial vector emf. of self-induction, and O/0 the initial vector discharging current, corresponding respectively to the vectors of the same denomination in Figure 8. These three vectors, starting at the positions shown, at the moment when the condenser of 4 microfarads, after being charged at 1000 volts p. d., is released through /= 0.1 henry and r = 500 ohms, run along the hyperbola fflIT, in the positive direction, with uniform hyperbolic angular velocity O = 1936.492 hyps, per second. That is, the sectorial areas described by each vector in each second of time are constant and equal to 1936.492 hyperbolic radians, taking the length of the semi-axis OI0 as unity. Consequently, at any instant, the sectorial areas E0OI0 and T0OTf0 remain equal to that shown, this area being the hyperbolic angle of either, and equal to 1.03172 hyps. = gdr1 50. 46'. 06." As the three vectors OEv OI0 and O U0 rotate with this uniform angular velocity in contact with the hyperbola, they continually approach the asymptote OA', without ever actually reaching it The resultant, or vector sum of OU and OE0 is Or = 2582 volts, and is equal to the initial vector product of the discharging current OT0 and the resistance r of the circuit. This vector also rotates with uniform hyp. angular velocity CI, over the rectangular hyperbola h r h', in the direction rh, corresponding to Or, Figure 8. As in Figure 8, the negative of vector Or, or--T0 r, should be drawn in the direction 70 0; but is omitted from the diagram for economy of space. It may be demonstrated that this negative extension of Or, rotating positively over a rectangular hyperbola, the image of h r A', will always be in vector...show more

Product details

  • Paperback | 212 pages
  • 189 x 246 x 11mm | 386g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236762215
  • 9781236762214