90 Prof. C. G. Knott on Reflexion and Refraction of 



descent below the earth's surface in the value of the elastic 

 coefficient which determines the speed of transmission of the 

 preliminary tremors. 



But these preliminary tremors, from the moment they begin 

 to show themselves, continue until the large wave-motion sets 

 in ; and are probably continuous with the tremors which 

 survive after the large waves have died away. If we regard 

 the first recorded tremors as having passed from the earth- 

 quake origin to the station at which they are being recorded 

 by the path of shortest time through the earth, the subsequent 

 tremors may be regarded as having arisen in one of two ways. 

 They may be sent off as forerunners from the wave-front 

 of the Large Waves, especially when this wave-front is passing 

 across surfaces of discontinuity; or they may come by more 

 or less circuitous paths, after it may be several reflexions from 

 fissures or other surface barriers. A very distinct change 

 in the elastic constants or in the densities of the materials in 

 contact is sufficient to make the interface, for certain inci- 

 dences, a practical barrier to the transmission of waves. 

 Milne's recent discovery of reverberations, that is, the recur- 

 rence of the same groups of waves in the tremor record, seems 

 to demonstrate the existence of reflexion of waves within the 

 body of the earth. 



Part III. 



Theoretical Discussion of the Behaviour of Elastic 

 Waves at the Plane Interface of Solids and 

 Fluids. 



The equations of motion for plane waves in an elastic 

 solid are expressible in the form 



><v*f=P d ^ > (I.) 



n7 *"'5F J 



in which, the plane XY being taken perpendicular to 

 the wave-front, the displacements in directions X, Y, Z are 

 respectively 



