ox THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 171 



between two media different in tlieir elasticity, either a condensational or 

 a.distortional wave is broken up into reflected and refracted distortional 

 waves as well as reflected and refracted condensational waves, and thei'e- 

 fore as a disturbance travels through the heterogeneous mass of materials 

 constituting the earth's crust there is, in every probability, a continual 

 change in the cliaracter of the motion. 



Not only does tliis consideration make it appear unlikely that the 

 tremors which have been observed at stations far removed from an origin 

 if they were propagated on or near to the surface of the earth are due to 

 condensational waves, while the more pronounced movements which 

 succeed them represent the distortional waves, but it also indicates that 

 at a given station there should be no definite relationship between the 

 motion of an earth particle and the direction of propagation of an earth- 

 quake. For feeble earthquakes, and for those recorded at points outside a 

 megistoseismic area, this latter conclusion is remarkably concordant with 

 observation. 



On the other hand, however, if preliminary tremors are movements 

 which have been transmitted at great depths through a medium where 

 "^ e/p is constant or changes gradually, it is likely that they have a con- 

 densational character. 



Next we may consider the probable nature of surface waves. Lord 

 Rayleigh, in a paper on waves propagated along the plane surface of an 

 Elastic Solid, ^ investigates 'the behaviour of waves upon the plane free 

 surface of an infinite homogeneous isotropic elastic solid, their character 

 being such that a disturbance is confined to a superficial region of thick- 

 ness comparable with the wave-length. The case is thus analogous to 

 that of deep water waves, only that the potential energy here depends 

 upon elastic resilience instead of upon gra'S'ity.' 



Two cases are discussed, but the results are very similar. A particle 

 at the surface moves in an elliptic orbit with its major axis perpendicular. 

 The displacement parallel to the plane surface penetrates into the solid 

 for an incompi-essible solid about the eighth of a wave-length, and to 

 about the fifth into the solid when the Poisson ratio has a value of one- 

 fourth. The surface waves aie propagated at a slightly slower rate than 

 a purely distortional wave is propagated. 



From observations made upon earthquakes near to their origin, it 

 seems that when vertical motion appears it is accompanied by horizontal 

 displacements greater than that required by the formula given by Lord 

 Rayleigh, but the question arises whether the accepted horizontal move- 

 ments are not more apparent than real, being displacements due to tilting 

 of the recoi'ding instruments. That at the time of a strong earthquake 

 surface waves have an existence, because they have been seen, been felt, 

 and been recorded by instruments, is a fact not to be disputed. As they 

 spread the distance between crest and crest apparently increases, and 

 calculations have been made to detei^mine their height and length. About 

 the path described by a constituent particle nothing has yet been experi- 

 mentally determined. The decided movements which have been recorded 

 at great distances from their origin, which have been referred to as possibly 

 being distortional waves, because tlaey slowly tilt pendulums from side to 

 side, are not unlikely to be long flat undulations ivJiich near to the origin 

 were decided surface waves. If this is the case, the phenomenon to be 



' Froc. Lond. Math. Soc, vol. xvii. 1883-G. 



