Murthy 



which reduces to 



0(M 



d<t> 



1000 



a n 



= V 



"air* 



0(0) 



0(6« ) 

 O(0a) 



0(6/3) 



a<J> 



0100 



a n 

 ^4) 



1010 



= Condition does not apply. 



l 



a^ 



a n 



ooi ax' 



+ (ior* A1 + V 6 nn .) 



ooi oor ^z 1 " 



a* 



0110 



an 



a$ 



1100 



= no condition 



ah 



an 



= V 



1 



oio az» 



(V.7) 



These conditions relate to the outer hull surfaces. In the case of the 

 inner surfaces the hull function h should be replaced by h . 



The first four conditions may be represented in the form 



a* 



Tn _= 8 



ah 



ah 



+ aiia r 



+ V ^m) 



ooi oor dz 1 



(V.8) 



(v) 



Radiation and Boundedness Conditions. 



We may assume that the potentials of all orders satisfy the 

 conditions 



* — *0 , i. e. ty — »0 



and 



a_^ 

 a-z 



-0 , i. e. 



a^ 



as z — > oo at the bottom of the ocean. We may also assume that the 

 potentials and their derivatives satisfy suitable radiation conditions 



as 



218 



