....[*]
We can reproduce Equation (667) by realizing that $ \partial v_x/\partial x+ \partial v_z/\partial z = V^{\,-1}\,\partial V/\partial t$ , where $ V$ is the volume of a small co-moving volume element. Combining this expression with the definition of bulk modulus, $ K=\rho \partial p/\partial\rho=-V \partial p/\partial V$ , we obtain $ \partial p/\partial t = -K (\partial v_x/\partial x+\partial v_z/\partial z)$ .
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... gives[*]
Taking the finite compressibility of water into account, this equation generalizes to $ \partial^2\phi/\partial t^2 = c^2(\partial^2\phi/\partial x^2+\partial^2\phi/\partial z^2)$ , where $ c=\sqrt{K/\rho}$ is the velocity of sound. However, the left-hand side of the general equation is negligible for gravity waves, whose propagation velocities are much less than $ c$ .
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...quanta,[*]
Plural of quantum: Latin neuter of quantus: how much.
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