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The pair of equations ± v a = log2 ρ/D, v = ϕ {v ± a) t—q}, which constitute Poisson’s solution of the accurate equations applying to the transmission of sound through a cylindrical tube derived by La Grange method, have long attracted the attention of mathematicians. For La Grange’s equations we may substitute the following, viz.— dv/dt + a2/D dρ/dx=0, dv/dx + D/ρ2 dρ/dt=0. } . . . . . . (A) The first of these is obtained from the equation of the Encyc. Met. (Art. “Sound”), by putting v for dy/dt and D/ρ for dy/dx.

proceedings of the royal society of london

I. On Poisson’s solution of the accurate equations applicable to the transmission of sound through a cylindrical tube; and on the general solution of partial differential equations