Murthy 



$ and <f> are the potentials due to the forced 



oscillation of the side hulls and the air cushion 

 respectively in calm water, 



4> is the potential of the incident wave, 



and $ and 4> nin , are the potentials denoting the interfe- 



rence between the side hulls and the incident wave 

 (the diffracted wave) and between the air cushion 

 and the incident wave (the disturbed wave) respec- 

 tively. 



We shall only derive the lower order potentials 



*iooo ' ^oioo' ^ioio and ^0110 



in this study as these will be sufficient to evaluate the forces and 

 moment of low order. The method of derivation of the interference 

 potential 4> i ioo w ^^ also be briefly indicated without actually 

 carrying out the solution. 



The potential of the incident wave is readily written down. 

 The diffracted wave potential and that of the wave of disturbance 

 are only required in the higher order theory. 



Boundary Conditions. 



The boundary conditions satisfied by the potential are : 



(i) v 2 $ - 



This applies to potentials of all orders. 



(ii) On the EFS (z = 0) the condition (4. 6) is 



2 

 <j> - 2V<I> + V <J> - g* + 2V<l>.y (<J> - V4> ) + 

 tt xt xx ° z t x 



+ ($ - V* ) -3 — (<1> - 2V4> + V <t> - g$ ) = 



g t x oz tt xt xx ° z 



which reduces to the following conditions : 



2 

 0(8 ) V * - gd, =0 



K ' 1000 sq ^1000 



XX z 



214 



