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Transactions of the Cambridge Philosophical Society Volume 15

Transactions of the Cambridge Philosophical Society Volume 15


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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. 1894 Excerpt: ... of number (i) above the fourth we obtain from (40) as an approximate formula The abscissae supplying the subsequent maxima ordinates are the roots of (34). Thus the corresponding positions of the layer coincide with the node surfaces. For the ratios of the first to the subsequent maxima ordinates, and so for the ratios of the first to the subsequent maxima changes of pitch, I find 1: -162: -090: 062... From considerations as to the values of those maxima of J (x) which answer to large values of x, of an exactly analogous nature to those discussed in 67, it may be proved that a fairly close approximation to the maximum change of pitch of number (j) in the note of number (t), i and j being both greater than 4, is supplied by dk (dV m1-m = 18-51 4) x 4-935 In this formula j may equal but cannot exceed i, as the number of maxima, being equal to the number of node surfaces, including the axis, is equal to the number of the note. 76. When the layer whose m differs from that of the remainder is of given thickness the curve showing the variation of the change of pitch with kab is B fig. 7, the equation to which is (53). The abscissae supplying the maxima ordinates are the roots greater than zero of (2a?-1) /, ()-uJ (x) = 0 (63). For the first two roots I find approximately-9408 and 3 9594. It is easily proved that the positions of the layer answering to the maxima changes of pitch whose numbers exceed 2 lie outside of but very close to the corresponding node surfaces. The positions of the layer answering to the first two maxima are given in the following table for the first four notes and the usual values of er: --As the second maximum ordinate is very nearly equal to all the subsequent maxima, and is decidedly greater than the first, I have includ...


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Product Details
  • ISBN-13: 9781130582000
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 120
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 1130582000
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 227 gr

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