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. 1889 edition. Excerpt: ...Electromagnetic Disturbance, Spherical Waves of Light, and the Dynamical Theory of Refraction." Prof. J. J. Thomson has also considered spherical waves in a dielectric in his paper "On Electrical Oscillations and Effects produced by the Motion of an Electrified Sphere," Proc. London Math. Soc. vol. xv., April 3,1884. The conjugate property of U and W is UW'-U'W=-2?, (112) which is continually useful. We have next to combine U and W so as to produce functions suitable for use inside spheres, right up to the centre, and finite there. Let = i(U + W), w = i(U-W).-.. (113) It will be found that when m is even, w/r is zero and u/r infinite at the origin; but that when m is odd, it is u/r that is zero at the origin and w infinite. The conjugate property of u and w is uw'--u'w = q, (114) corresponding to (112). 19. Construction of the Differential Equations connected with a Spherical Sheet of Vorticity of Impressed Force.--Now let there be two media--one extending from r = 0 to r=a, in which we must therefore use the u function or w function, according as m is odd or even, and an outer medium, or at least one in which q has a different form in general. Then, within the sphere of radius a, we have R=Ar (115)-k1E = Ar-1u', (116) where 1 = 47rA+ cp, and we suppose m odd. It follows that S-i? (U7) In the outer medium use W, if the medium extends to infinity, or both U and W if there be barriers or change of medium. First, let it be an infinitely extended medium. Then, in it, R = Br-u-w), (118)-jfc2E = Br-1(M'-/), (119) where ks = iirk + cp in the outer medium. From these 5--r--(120) a. /c2 u--w v' (117) and (120) show the forms of the resistance-operators on the two sides. Some rather important considerations are presented...
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