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Extension of the Notion of Wave-surface to Space of n Dimensions

Published online by Cambridge University Press:  20 January 2009

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The following two modes of generation of the wave-surface are pretty generally known.

(a) A given ellipsoid (surface of elasticity) is cut by any central plane π along an ellipse of semiaxes λ1 and λ2. If π varies, the two pairs of planes π∲ parallel to π at distances k21, k22 (k = constant) from it envelope the wave-surface W1 represented by the tangential equation

if the tangential coordinates u1 depend on Σux +1 = 0.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1897