There are two separate but closely interwoven strands of argument in this paper; one mainly mathematical, and one mainly physical. The mathematical strand begins with a method of asymptotically evaluating Fourier integrals in many dimensions, for large values of their arguments. This is used to investigate partial differential equations in four variables, x, y, z and t , which are linear with constant coefficients, but which may be of any order and represent wave motions that are anisotropic or… CONTINUE READING
Figure 8 shows how the semi-angles, 8, and O,, of the cones within which lie the wave systems corresponding to S,and S,,vary with w l q . These graphs are obtained from the relationships W 2 tan 0,-- -. = sin 0,.