79 93 



where p^^ is the hydrostatic pressure on that face. 



The second release pressure p^g ^^ automatically allowed for in the 

 quantities <p and * as originally defined. Hence, if desired, all of the pre- 

 ceding formulas, Equations [100] to [l4l], will still hold provided p and c 

 in those formulas are replaced by p, and c,. 



As an alternative, 4> may be defined as 



^ = ^-P.2= ^0-^/7 ■^-^'^S [143] 



where 4>^ denotes the difference between hydrostatic pressure on the front and 

 on the back, plus the net force on the plate per unit area due to stresses. 

 Then by [113b] and the transformation leading to [11 6] 



D 



= <P^- p^jz^{t-f-)vis)ds [144] 



' 2 



where 



<1>^= j<l>J(x,y)dS [145] 



If this is done, it is readily seen that, besides the substitution 

 of 0n for <i> in all equations, every term containing an integral with z ,_± or 

 z{t - s/c) in the Integrand is replaced by the sum of two similar terms with 

 p and c changed to p, and c, or to Pj and Cg, respectively; furthermore, in 

 such equations for M, as [127], [128a, b] and [132], p is replaced by pj + Pg, 

 and where the acoustic impedance pc occurs, as in [107], [108], [109], and 

 [140], it is replaced by the sum of the two impedances, PjCj + P2'^2- 



In particular, for a uniform plane plate between two fluids, with 

 plane waves incident normally upon it on one side, [107] becomes 



TOz + (pjCj 4- P2 Cg^z =2p, + (/>p [l46] 



CAVITATION AT A PLATE OR DIAPHRAGM 



The analytical theory of cavitation at the interface between a 

 plate and a liquid will be developed here on the two assumptions that cavita- 

 tion occurs whenever the pressure sinks to a fixed breaking-pressure p^, and 

 that the pressure in the cavitated region has a definite value p^, not less 

 than pj. The assumptions hitherto made concerning the plate will be retained. 



On these assumptions, cavitation will begin in an area on the plate 

 in which the pressure is decreasing and at a point at which a local minimum 



