This paper gives a generalized statement of the Bremmer theory in the case that the medium and the incident wave are of general form (it is called the local principle of the process of wave motion) and proves it schematically. The Bremmer serieses of three concrete cases are deduced in a way similar to that used by Bremmer. These are:1) Planely stratified medium, obliquely incident plane wave;2) Cylindrically stratified medium with a line source coincident with the axis of the cylinder;3) Spherically stratified medium with a point source at its centre.Finally the author has attempted to give a mathematical form for the condition that the process of wave propagation can be described rigorously by rays, and points out the unstrictness in a paper of Bellman and Kalaba.
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