TREMORS OVER THE SURFACE OF AN ELASTIC SOLID. 41 



give us a convenient view of the progress of q () as a function of t. The difficulty is 

 due to the peculiarities of annular propagation to which reference has already been 

 made. 



In fig. 10 an attempt, based on the former method, is made to represent (very 

 roughly) the whole progress of the horizontal and vertical displacements due to a 

 single impulse of the type (165) at a distance large compared with T/C. 



SUMMARY. 



We may now briefly review the principal results of the foregoing investigation, so 

 far as they may be expected to throw light on the propagation of seismic tremors 

 over the surface of the earth. 



It has been necessary to idealize this problem in various ways in order to render it 

 amenable to calculation. In the first place, the material is taken to be compact and 

 homogeneous, to have, in fact, the properties of the " isotropic elastic solid" of 

 theory. Moreover, the curvature of the surface is neglected. Again, instead of a 

 disturbance originating at an internal point, we study chiefly the case of an impulse 

 applied vertically to the surface. Under these conditions the disturbance spreads 

 over the surface in the form of a symmetrical annular wave-system. The initial form 

 of this system will depend on the history of the primitive impulse, but if this be of 

 limited duration, the system gradually develops a characteristic form, marked by 

 three salient features travelling with the velocities proper to irrotational, equi- 

 voluminal, and Rayleigh waves, respectively. As the wave-system, thus established, 

 passes any point of the surface, the Jwrizontal displacement shows first of all a single 

 well-marked oscillation followed by a period of comparative quiescence, and then 

 another oscillation corresponding to the epoch of arrival of equivoluminal waves. 

 The whole of this stage constitutes what we have called the "minor tremor" ; it is, 

 of course, more and more protracted the greater the distance from the source, and 

 its amplitude continually diminishes, not only absolutely but also relatively to that 

 of the " main shock," which we identify with the arrival of the Rayleigh wave. It may 

 be remarked that the history of the minor tremor depends chiefly on the time- 

 integral of the primitive impulse ; the main shock, on the other hand, follows the 

 time-scale of the primitive impulse, and is affected by every feature of the latter.* 



Similar statements apply to the vertical displacement, except that the minor 

 tremor leads up more gradually to the main shock, being interrupted, however, by a 

 sort of jerk at the epoch of arrival of equivoluminal waves. 



The history of the horizontal and vertical displacements, about the epoch of the 

 main shock, in the case of a typical impulse of the type (165), is shown in fig. 8 ; 



* Observational evidence in favour of the existence of the three critical epochs in an earthquake 

 disturbance has been collected and discussed by R. D. OLDHAM, "On the Propagation of Earthquake 

 Motion to Great Distances," 'Phil. Trans.,' A, 1900, vol. 194, p. 135. 



VOL. CCIII. A. G 



