Starting from the fundamental equations of hydrodynamics, the theory of sound rays in an inhomogeneous moving medium is developed. A system of first-order ordinary differential equations which determine the ray paths is derived. It is shown that the ray paths can be found by evaluating some definite integrals. The integrals may be evaluated numerically, but in some important cases the integrations can be done in closed form. Much of the emphasis in the paper is on deriving properties which are useful in computing ray paths or in understanding the qualitative effects of inhomogeneities in the medium. It is shown, for example, how rays which are ducted can be distinguished from those which are not. Finally, it is noted that the literature contains what amounts to two conflicting theories for sound rays in a moving medium. The differences are discussed, and it is pointed out that one of the theories is inconsistent.
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Robert J. Thompson (1972) studied this question.