Note on the Relationship between Imai's and Tomotika-Tamada's Formulae in the Theory of Two-dimensional Subsonic Flow of a Compressible Fluid

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Complex variables and conformal transformations are successfully employed in the theory two-dimensional subsonic flow of a compressible fluid past an obstacle, and so far various formulae have been proposed for calculating the first-order effect of compressibility upon the complex velocity potential for the flow or similar other quantities. In this paper a discussion is first made on the relationship between Imai's and Tomotika-Tamada's formulae, and it is shown that the latter formula can be derived from the former by a suitable choice of complementary functions contained in the former. The relationship between Tomotika-Tamada's formula and another formula due to Kaplan is also discussed and it is shown that the letter formula can be derived from the former.

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