A Method of Calculating the Solid Angle Subtended by a Circular Aperture

Practical formulae in terms of elliptic integrals have been obtained which are useful for calculating the solid angle subtended by a circular aperture at a point which is not on the axis of the aperture. Like the familiar formulae in terms of zonal harmonics, these formulae can be used not only to calculate the solid angle with an accuracy of 4 significant figures, but are also applicable to cases in which the former formulae cannot be employed owing to their slow rate of convergence. The results of some preliminary calculations are shown in tables.