TREMORS OVER THE SURFACE OF AN ELASTIC SOLID. 



39 



Fig. 9. 



Fig. 8. 



The method applied in that Article to obtain a general view of the whole progress 

 of the vertical displacement at any point might be employed again here, the upper and 

 lower curves in fig. 4 being combined with auxiliary movable graphs of 



Or" 3 r 



- R (t #arcosh u) <ln and 6 R (t 6ts cosh ) du, 



CIS Jo ot . a 



considered as functions of 6. In the case of a primary impulse of the type (105), both 

 graphs would have somewhat the form of the lower curve in fig. 8, the functions being 

 practically (except for a constant factor) of the type 



n 



v 



- sin (477 |x) cos ! " x , wliere x ^ an 



_, t ^ra- 



in the more important part of the range. Both graphs, if drawn to the scale of 

 fig. 4 or 5, would be excessively contracted horizontally when we are concerned with 

 values of is large compared with T/C O . Owing to the compensation between positive 

 and negative ordinates in the auxiliary graphs, it is plain that the disturbance 

 expressed by the ^-integrals in (109) and (170) will be relatively very small except 

 when t/zs has values for which the gradient of U (0) or V (0) is considerable. As 



