81 95 



The high values of the acceleration associated with the passage of 

 the edge travel along with it. Hence, if x is the coordinate of any point on 

 the plate measured from P perpendicularly to the edge and in its direction of 

 motion, and if z,{f) is the special, high acceleration due to the edge at P 

 at a certain time (, the simultaneous value of this acceleration at any other 

 point will be the same as the value that was at P at the earlier time ( - x/U, 

 or 'i^(t - x/U). Thus the total contribution of the edge to the integral in 

 [103] can be written 



4^-jf-N'-f-F) 



Just after the edge has passed P, the integrand in the last integral is eas- 

 ily seen to differ from zero only for elements dS lying near a small ellipse 

 surrounding P. 



Let polars r, ^ be introduced such that s = r, x - r cos 0. Then 

 dS = ZnrdrdO and the last equation becomes 



dS C ,^ C-- I . I" 'f cos6) 



r.. dis c j„ r.. I r r cose\ . 



— r J .> r c d ■ t ^ ^ r cosB\ , 



where 4z is the Jump in the velocity z at the edge taken in the direction of 

 decreasing r. 



Thus, according to [103], 



_£_ 

 2n 



2,rc(4i)(l - -^) 'J = -4p= -(p,-p,) [148] 



.2^1 



- - 'ir'i^ - i^y M.91 



Az 



p 



Or, since according to [101] the pressure Just before the edge arrived was 

 connected with conditions in the plate by the equation 



p = T)^^ = m'z - ^ + Po 



2 i 



Ai =-^[l-jj^)Hv,-mz + <i>-p,) [150] 



