The velocity potential distribution of a circular emitter vibrating in an infinite wall is calculated by the King method for the points immediately before the wall. It is showed on the close connection between the Rayleigh formula and the expression for the velocity potential which follows from the King method. The equation for the space distribution of the velocity potential expanded in spherical wave functions is transcribed into an abstract form by means of the Dirac bra-vector, ket-vector, and linear operator represented by the corresponding matrices. The space distribution of the velocity potential is then computed from the known values in the plane immediately before the emitter by the well-known method of undetermined coefficients written in its matrix form. Thereafter the space distribution of the velocity potential is determined by another, new method due to H. Stenzel. In both methods explicit expressions are given for the case of a vibrating rigid disk, membrane, and plate.