u, = V x A - VQ , 

 1 (II-22) 



with V • A = , (II-23) 



so that V • 0, = - V 2 Q , (H-24) 



and 7x0, = - V 2 A . (II-25) 



Thus, equations 11-21 and 11-16 become 



p 0f c ( 2 V 2 O = -|£- (H-26) 



and 



Po, -|f(V x A) - n Sf V x (V 2 A) = - VP, - Z,V(WC1) + p 0f -^-(VO) . (H-27) 



If the curl of equation II-27 is taken, 



V x VP, = V x VO = V x V(V 2 0) = . (H-28) 



Thus, 



Po, -|y (V x A) - ris.V x (V 2 A) = , (M-29) 



or 



Therefore, 



n sf v 2 A- Po»|y = o 



(II-30) 



VP, + $V(V 2 G) - p 0f -| ? (VQ) = . ("- 31 ) 



Then substituting equation II-26 into 11-31 and taking the divergence yields: 



Equations 11-30 and 11-32 are the wave equations in the fish flesh. In water, where the viscosity is zero, the 

 wave equation is 



1 9 2 Pi 



(II-33) 



(11-34) 



(11-35) 

 and 



(11-36) 



Then equations 11-30, 11-32, and 11-33 are, after eliminating the numerical subscripts, 



10 



