On deep-sea water waves caused by a local disturbance on or beneath the surface

The classical problem of waves produced in deep-sea water by a local disturbance of the free surface has been investigated by Prof. H. Lamb in a very able manner. He completed the theory of wave propagation in one dimension and in two horizontal dimensions when the initial disturbance is concentrated in the immediate neighbourhood of a line or a point, assuming that Fourier's double integral theorem can be applied in such a case. In this paper I venture to disturbance, followong Prof. Lamb's method, in cases where the initial disturbance is spread over a certain extent of the free surface; and, as an application of the general solution, I propose to treat the case in which the initial disturbing source is situated at a finite depth from the surface, i.e. where the surface wave is produced by an explosion like that of a mine under water.