Elastic Waves , with Seismological Applications. t>5 



by Hopkins in Lis tl Report ou the Theories of Elevation and 

 Earthquakes/' presented to the British Association in 1847. 

 During the forty years which have elapsed since then, our 

 knowledge of earthquake phenomena has steadily grown. 

 The labours of Mallet have been largely supplemented by the 

 observations and experiments of a small army of enthusiasts, 

 who have pitched their tents on the trembling soil of Italy 

 and Japan. Their energies have been mainly directed to 

 the perfecting of seismographs and seismometers, to the 

 registering of all kinds of earth-movements, to the study of 

 the effects of these on buildings, and, in a limited degree, to 

 the measurement of the velocities of propagation of dis- 

 turbances due to artificial earthquakes. With all this activity 

 on the experimental side, we have to confess that theoretic 

 views have hardly advanced beyond the stage in which 

 Hopkins left them in 1847. G. H. Darwin's discussion of 

 the strains due to continental areas, and Lord Rayleigh's 

 investigation into a special case of surface -waves on an elastic 

 solid, are perhaps the only mathematical pieces of work that 

 have any distinct bearing on seismic phenomena. The 

 former gives an obvious raison d'etre for the existence of 

 seismically sensitive regions within the earth's crust, but, 

 being an equilibrium problem, can throw no light on that 

 progress of the state of strain which constitutes earthquake 

 motion. Lord Rayleigh's results will be referred to here- 

 after in due course. Meanwhile, as it is my object to 

 discuss in a general way how far earthquakes and their 

 accompanying effects may be explained as disturbances in 

 an elastic or subelastic medium, it will be convenient to 

 reproduce here much that may be found in authoritative 

 earthquake literature, such as Hopkins'' and Mallet's ' Re- 

 ports/ Mallet's ' Neapolitan Earthquake/ Milne's ' Earth- 

 quakes,' and so on. 



From the general theory of the vibrations of homogeneous 

 elastic solids, we know that there are three types of wave 

 propagated with different velocities. If we confine our 

 attention to an isotropic elastic solid these types reduce 

 to two, which are kinematically easily distinguished by the 

 relation which the direction of vibration of any particle bears 

 to the direction of propagation of the wave. Thus, in the 

 one type the vibrations are normal to the wave-front ; in 

 the other they are transverse or tangential. Dynamically, 

 the types may be distinguished as the condensational and 

 distortional waves. The former is of essentially the same 

 character as ordinary sound-waves in air ; and the latter 

 Fhil Mag. S. 5. Vol. 48. No. 290. July 1899. F 



