DIPOLE-SHEET TRANSFORM.

A new integral transform, derived from the three-dimensional Radon transform, is introduced. The basis functions for this transform, which may be physically interpreted as sheets of dipoles, are shown to be orthonormal and complete. The inverse transform is derived, and an expression for the Fourier transform of the basis functions is found. It is demonstrated that all spherically symmetric functions retain the same functional form under this transform and that it can be used to reduce certain differential equations, such as the Helmholtz equation, to a spherically symmetric form, even if the original problem has no symmetry at all.