Elastic Waves, with Seismological Applications. 69 



that the paper deserves the special attention of members 

 of the Society I need but quote the two concluding 

 sentences : — " It is not improbable that the surface-waves 

 here investigated play an important part in earthquakes, and 

 in the collision of elastic solids. Diverging in two dimensions 

 only, they must acquire at a great distance a continually 

 increasing preponderance," — that is, I presume, as compared 

 to waves diverging in three dimensions. 



The purpose of the paper is " to investigate the behaviour 

 of waves upon the plane free surface of an infinite homo- 

 geneous isotropic elastic solid, their character being such that 

 a disturbance is confined to a superficial region of thickness 

 comparable with the wave-length. The case is thus ana- 

 logous to that of deep-water waves, only that the potential 

 energy here depends upon elastic resilience instead of upon 

 gravity/' 



Starting with the usual equations of motion of a vibrating 

 elastic solid, Lord Rayleigh obtains a general solution on the 

 assumptions that the displacements are harmonic functions of 

 the time and the two coordinates parallel to the plane free 

 surface, but are exponential functions of negative multiples of 

 the distance from this plane. The boundary equations are 

 then introduced ; and from the conditions for the equilibrium 

 of a surface-element the various constants of integration are 

 determined in terms of the circumstances of the assumed 

 motion. Two cases are discussed in detail — those, namely, 

 of an incompressible elastic solid, and of a solid for which the 

 Poisson ratio has the value one-fourth. For both cases the 

 results are very similar. Thus, if the displacements are sup- 

 posed to be confined to one plane, a particle at the surface 

 moves in an elliptic orbit whose major axis is perpendicular 

 to the plane surface of the solid. For the incompressible 

 solid the major axis is nearly twice as great as the minor 

 axis ; and for the other case it is about one and a half times 

 as great. The displacement parallel to the plane surface 

 penetrates but a short distance into the solid — to about one- 

 eighth of a wave-length for the incompressible substance, and 

 to about one-fifth for the other case. On the other hand, 

 there is no finite depth at which the motion perpendicular to 

 the plane vanishes. The surface-waves are propagated at 

 a slightly slower rate than a purely distortional plane wave 

 would be. 



It would appear then that vertical motion on a level surface 

 over which a disturbance is passing cannot exist alone. 

 Associated with it there must always be a distinctly smaller 

 horizontal motion, which vanishes completely at a short depth 



