Postface

In early 1944, I got a job in the Columbia University Divi sion of War Research, to work on sonar. My boss, Henry Primakoff, asked me to help him analyze the scattering of sound by a dome. This is a thin, streamlined aluminum shell, which surrounds a projector. The projector emits a pulse of sound waves, and then acts as a hydrophone to detect any waves reflected by a submarine. We obtained a Kirchhoff-like integral for the waves scattered by the dome, and evaluated it asymptotically for ka large. Here, k = 2π/λ, where λ is the acoustic wavelength, and a is any lateral dimension of the dome.