Kelvin’s method of stationary phase?

The method of stationary phase is a standard technique for estimating the value of an oscillatory integral when a certain parameter in the integrand becomes large. The basic method was sketched in 1887 by Sir William Thomson (before he became Lord Kelvin) in a short paper, and applied by him to problems in the theory of linear water waves. The contents, context and consequences of his paper are discussed. Inevitably, earlier authors (such as Stokes and Riemann) could stake claims on the method, but we leave it to the reader to decide, based on the evidence presented. • Kelvin’s method is reviewed in its historical context. • Contributions of Stokes, Riemann, Lamb and Watson are discussed. • Applications of Kelvin’s method are discussed