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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. 1915 Excerpt: ...the integral expressions forll, nxi n2in these equations and equating to zero the coefficients of functions of type Jn(Xp) in the resulting integral equation, we obtain the system of equations IV THE SPREADING OF WAVES OVER AN INFINITE PLANE 75 where the last equation has been simplified with the aid of the relations / = g = 0 (n0) which are a consequence of the previous equations. Solving these equations we eventually find that if iWQ o, Qt), n, -(j?., o, n, ), + IB cos oS Jx (p) eTMla---5-r. Jo (I + m) (hH + km) The "directed effect" depends on the presence of the terms involving cos oS in the expressions for Qz and Rz. Now when r = oo for the second medium, h = cc, and these terms vanish altogether; hence the possibility of directing the energy of the radiation sent out from the bent antenna is due to the imperfect conductivity of the earth. Von Hoerschlemann has given a numerical discussion of the above formulae but the investigation is too long to be inserted here. 28. Propagation of electromagnetic waves along a straight wire of circular cross-section. Let us consider the symmetrical case when the electric force at any point is in a plane through the axis of the wire H. Hertz, Electric Waves; J. J. Thomson, Proc. London Math. Soc. Vol. 17 (1886), p. 310; Recent Researches, 259; A. Sommerfeld, Ann. d. Physik, Bd. 67 (1899), p. 233; Gray and Mathews, Bessel Functions, Ch. 13; M. Abraham, Encykl. d. Math. Wiss. Band V. 2, Heft 3 (1910), p. 526; J. Larmor, Proc. of the 5th Int. Congress of Mathematicians, Vol. 1 (1912), p. 206. The problem considered in this last paper is chiefly that of alternating currents, viz. the forced alternations of flow produced by a uniform periodic electric force. and the magnetic force is ...

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