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The early history of hollow tube waveguides is described. Conceived by Lord Rayleigh in 1897, they were little used and the idea forgotten. Almost 40 years later, G. C. Southworth and W. L. Barrow rediscovered the concept, each working independently for almost five years with no knowledge of the other. This work culminated in almost simultaneous public presentations in 1936. The significance of these events for gaining insight into the interactions of science, mathematics, and engineering is discussed.
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