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At Lord Kelvin’s suggestion I reproduce, with additions and extensions, a paper I published eleven years ago in the ‘Transactions’ of the Seismological Society of Japan. This Society ceased to exist some years ago; a fact which may serve as a further reason for reproducing a paper, in which the problem of the behaviour of an elastic wave incident on the interface of rock and water was for the first time fully worked out. In that paper also, I believe, the sound method of treating the general problem when the two media are elastic solids was first explicitly stated (see below, pp. 71, 92).

For convenience I have divided the present communication into three parts.

Part I. is a reproduction of my seismological paper of 1888 with a few verbal corrections. Footnotes added now are enclosed in square brackets.

Part II. contains detailed numerical calculations for rock-rock interface and for rock-air interface, similar to the calculations for rock-water interface in Part I.

Part III. gives the mathematical investigation and the various sets of formulæ on which these calculations are based.

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