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Abstract

This paper deals with radiation (scalar, electromagnetic, or gravitational) produced by an extended source. The object is to construct a model source the radiation from which is concentrated in a jet of small angle with an assigned target direction. This is done by taking for the source an infinite train of high-frequency plane waves travelling in the target direction with the basic speed of propagation, the amplitude falling off exponentially with distance. The critical number, to be made large in this model, is the ratio a/A, where a is a typical radius of the source and X the wave length. However, it is also shown that a jet of scalar radiation may be obtained from a source which possesses no frequency but consists of a single shock wave. □ p = Pt.t ,(2.2) where P, is a body-force per unit volume constituting the source. This differs from (2.1) only in that the right-hand side is the divergence of a vector field. We shall proceed with (2.1) and return to (2.2) later.The retarded potential solution of (2.1), observed at the event X, iŝReceived June 2, 1967.