On Kelvin's ship-wave pattern

When a concentrated pressure travels with constant velocity over the free surface of water, it carries with it a familiar pattern of ship waves. Let viscosity and surface tension be neglected, let the free-surface condition be linearized, let the depth of water be assumed infinite, and let initial transient effects be ignored. Then, as is well known, the wave motion everywhere can be found by standard methods in the form of a double integral. The wave pattern at a great distance behind the disturbance can be found by an application of the ordinary method of stationary phase, which shows that the wave amplitude is considerable inside an angle bounded by the two horizontal rays c from the disturbance, where $\theta_c = \rm {sin}^{-1} {\frac{1}{3} \eDot 19{\frac{1}{2}\deg$. But the method fails in two regions, near the track = ±θc.