George Green

XI.—On Waves in a Dispersive Medium resulting from a Limited Initial Disturbance

§ 1. In a former paper “On Group-Velocity and on the Propagation of Waves in a Dispersive Medium” ( Proc. R.S.E. , xxix. pp. 445–470, 1909), it was shown that group-velocity, or the principle of “ stationary phase ,” provides us with a satisfactory explanation of the modus operandi of dispersion; and the principle was applied to obtain an expression for the effect of a single impulse confined to the neighbourhood of a point of the medium. The present paper is intended to fulfil a promise given in § 29 of that paper, to show that by means of this principle we can arrive at the general features of the wave-system in a dispersive medium resulting from any limited initial disturbance.