Theory of Stability of Laminar Flow 459 
Y,,(@,B) P(a) = - #| E(x) ee dx. (4.4) 
Combining these equations we obtain for the surface compliances 
Y, (2,8), =——________ (4.5) 
Yo % 2) = TP eq aaamOG sous ww vat (4.6) 
So far these are purely formal relationships which, for example, would allow us to determine 
the surface compliance experimentally from the reaction of the surface to a pressure. This 
is useful in that equipment can be designed and has been designed to use this relation for 
the determination of the surface compliance of arbitrary surfaces. However, we must put it 
in more manageable shape for the determination of experimental quantities, and we will show 
how it can be used to relate the surface compliance to the propagation constant of Rayleigh 
waves at a given frequency. Let us suppose that the pressure is applied over a very small 
length which is allowed then to go to zero. Experimentally, this could be achieved by the 
use of a very narrow knife edge as a driving unit. We will have for the pressure 
P(x) = = when =e <x < ¢ 
(4.7) 
PCx) = 0 when xX <-€ or X> &. 
Using these in Eq. (4.4) to obtain the Fourier integral of the pressure, we have 
Bee, 8) 1 p Sin Qe ties 
VJ 27 de : 
Taking the limit as € > 0 we finally obtain 
1 sin de 1 
P(a@,8) = ——F lim — = ——F, (4.9) 
p Vv 27 630 Qe J 2r 
