In his anniversary address on 30 November 1935, the President of the Royal Society paid a tribute to the work of HECTOR MUNRO MACDONALD. In the course of his address he made particular reference to MACDONALD’s solution of the difficult, and analytically very attractive, problem of diffraction by a prism, perhaps better known as the Wedge Problem. A few years ago the author of the present paper, who was much impressed by the work of MACDONALD and had the privilege of corresponding with him, made some notes upon this problem and upon an associated problem of particular interest. Arising from these notes, which were recalled upon reading the President’s address, certain ideas, which would appear to be of a fundamental nature, have been developed to form the subject of the following communication. The problem of the half-plane had been previously treated by two distinguished mathematicians, but the first complete solution of the wedge problem was given by MACDONALD. The two mathematicians were POINCARE and SOMMERFELD. Subsequently to the publication of MACDONALD’s work, BROMWICH published a paper which gives a slightly more general treatment of the problem. References are given at the end of the paper.