The method of Helmholtz has been recently employed by Hook to obtain uncoupled equations of motion from the vector wave equations governing the propagation of elastic waves in certain types of nonhomogeneous media. The work reported on in this paper casts the method of Helmholtz in terms of matrices and extends the work of Hook to media with variable Poisson's ratio. It is found that the constitutive parameters must satisfy a pair of nonlinear ordinary differential equations. These differential equations are integrated in a special case and a useful and interesting example of a nonhomogeneous medium is given.

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