The theory of ship waves, when the sea is considered to be of infinite depth, has been the subject of many researches. When the sea is of finite depth the integrals involved are more complicated, but in this case also the theory has been worked out in considerable detail. The main object of the present communication is to add to the number of cases which have been solved, or, to be more precise, which have been exactly formulated, a certain series in which the depth is variable. Of subsidiary interest, but coming under the title of the paper, are some considerations relating to the wave disturbance when the depth is finite. These are dealt with briefly in section 5.
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E. T. Hanson (1926) studied this question.