to a Travelling .Disturbance. 395 



Hence, in the case of a concentrated pressure travelling- 

 over the upper surface, 



-r _ 9_ (71) 



^-?{ P + (p'-p)e-^y ^ * 



^- p 2(c-U 2 ) 9 { p +Xp'-p)e-^} ' V } 



Next, suppose that an extraneous impulsive force cos kx 

 is applied downwards to an infinitely thin stratum at the 

 interface. The initial conditions are now 



0=0 (73) 



for ?/ = 0, and 



p'(j>' — pcj)= cos Lv (74) 



for y=—li. Thus 



Ai + A 2 =0, 

 and 



9 / 9 



(p'-p)e- kh A 1 -p( C oshkh-^sm\ik1i+ -/— /*^A 2 = 1. (75) 

 Hence 



AK*y=-v*)= p+(p r:" ) ,_ a t • • • ( 76 > 



The comparison with (70) shows, as we should expect, that 

 the second type of waves is now favoured relatively to the 

 first. 



In the case of a concentrated vertical force travelling 

 along the interface the two components of the resistance are 

 accordingly 



2 

 T> I _ P C ^2 (7R\ 



*-p<-p2(i-U,) ( j{p + { p'-p)e-^ s ■ ^' 0> 



It is to be remembered in these problems that R 2 an d IV 

 vanish when c>c . 



The formulae as they stand are open to the objection that 

 they make some part of the resistance increase indefinitely 

 as c is diminished. Thus (71) makes R^co for c = 0, 

 whilst (78) makes R 2 ' = co under the same condition. This 

 paradoxical result is easily understood if w T e remember that 

 we have imagined a finite force to be concentrated on an 



