Fresnel and His Followers; A Criticism to Which Are Appended Outlines of Theories of Diffraction and Transversal Vibration

Fresnel and His Followers; A Criticism to Which Are Appended Outlines of Theories of Diffraction and Transversal Vibration

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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. 1849 edition. Excerpt: ...dAtf n Af + dx 2 + dy 2' + dz 2 5 dl.. f S.. d2l... Ax Ay + AxAz 4-----AyAz + &c., dxdy dxdz dydz and similar expressions for A17 and A ." Then "adopting the hypothesis of symmetrical distribution, and thus rejecting the sums of products of odd dimensions in Ax, Ay, Az; rejecting also products of the same terms of four dimensions as insensibly small," he reduces the equations to an integrable form. But it is obvious that this process is entirely fallacious, as Mr. Kelland appears to have subsequently abandoned this theory, and to have adopted that which I have discussed in the preceding paper. depending upon a false approximation. Instead of Ax, Ay, Az being so small that products involving the fourth powers of those quantities may be neglected as insensible, these quantities may have any magnitude whatever. This is so obvious that I cannot but feel some surprise that such a method should ever have been proposed. Mr Kelland, however, is not singular in this error. "Mr. Tovey (in his first papers in the Journal of Science, Vol. Viti. pp. 7, 270, 500)," as Professor Powell informs us, " after establishing the fundamental equations, proceeds to develop, rj, as each a function of Ax. He thus finds., . d2Z Ax2. At, = v-Ax +------+ &c., dx dx2 1.2 and similar expressions for At) and A ."--Now we can make no use of this series for Af, for, in the first place, as Ax may have any magnitude, we are not sure that even the whole series would be an equivalent for Aij, and a fortiori we cannot take a limited number of its terms to represent that quantity.--"Sir John Lubbock (Journal of Science, Vol. xi. Nov. 1837) developing Ap as a function of r, . dp. d'p Ar2. Ap =-f Ar...show more

Product details

  • Paperback | 56 pages
  • 189 x 246 x 3mm | 118g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 123654143X
  • 9781236541437