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 the (vector) displacement of the particle whose undisturbed position is (x, y, z), and if p denote the density of the medium, the equation of motion is

where n denotes a constant which measures the rigidity, or power of resisting distortion, of the mediun, All such elastic properties of the body as the velocity of propagation of waves in it must evidently depend on the ratio n/ρ.

Among the referees of one of Navier's papers was Augustine Louis Cauchy (b. 1789, d. 1857), one of the greatest analysts of the nineteenth century, who, becoming interested in the question, published in 1828 a discussion of it from an entirely different point of view. Instead of assuming, as Navier had done, that the medium is an aggregate of point-centres of force, and thus involving himself in doubtful molecular hypotheses, he devised a method of directly studying the elastic properties of matter in bulk, and by its means showed that the vibrations of an isotropic solid are determined by the equation

here n denotes, as before, the constant of rigidity, and the constant k, which is called the modulus of compression, denotes the ratio of a pressure to the cubical compression produced by it. Cauchy's equation evidently differs from Navier's in that