A Treatise on Electricity and Magnetism Volume N . 1

A Treatise on Electricity and Magnetism Volume N . 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. 1892 edition. Excerpt: ...equation of the system of meridional planes to which the first system is reduced is _ = Q (sin ay (cos ay x' As regards the quantity /3, if we take the definition given in page 233, (7), we shall be led to an infinite value of the integral at the lower limit. In order to avoid this we define /3 in this particular case as the value of the integral cd,2 If we now put A, = c sin p, /3 becomes r-rr, i. e. log cot i (b; sin 6 r g8 g-- whence cos 4--i s (33) 2 and therefore sinf =-5-. (34) If we call the exponential quantity (e6 + eB) the hyperbolic cosine of /8, or more concisely the hypocosine of /3, or cosh /3, and if we call i (eB--e-B) the hyposine of /3, or sinh /3, and if in the same way we employ functions of a similar character analogous to the other simple trigonometrical ratios, then A2 = c sech /3, and the equation of the system of hyperboloids of one sheet is a?+y2 _ _ C2,35) (BechjS) (tanh/S) ' K 1 The quantity y is reduced to so that A3 = csecy, and the equation of the system of ellipsoids is K + 7rA-2 = c (36) (secy)-(tany)2 v' Ellipsoids of this kind, which are figures of revolution about their conjugate axes, are called planetary ellipsoids. The quantity of electricity on a planetary ellipsoid maintained at potential V in an infinite field, is Q = CrZ_, (37) where c sec y is the equatorial radius, and c tan y is the polar radius. If y = 0, the figure is a circular disk of radius c, and V r =, (38) Q = c. (39) 152. Second Case. Let b = c, then k = 1 and k'= 0, It-I-2 0 a = log tan-----, whence Xj = c tanh a, (40) and the equation of the hyperboloids of revolution of two sheets becomes a? y2 + 2? __ 2, . (tanhp (Bechp ' (' The quantity 0 becomes reduced to j, and each of the hyperboloids of...show more

Product details

  • Paperback | 158 pages
  • 189 x 246 x 9mm | 295g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236813960
  • 9781236813961