repeated here. The resistance integral for the case of an infinite ocean of finite depth 

 h is given by 



R = 



2pgc f" I ti 



7!" J MA I M — V 



where 



tanh yh 

 cosh n(y + h) 



[P 2 + Q 2 1, 



P = j j dxdy £ x (x,y) 



s cosh nh 



cos xWvy tanh /x/i 



(89) 



(90) 



and Q is a similar function where sine replaces cosine; here ^ is the nonzero solution 

 of p. — v tanh ph. if such exists, otherwise zero. The latter case occurs if c 2 /gh ^1. 

 As h -> oo, tanh yh —> 1, ^ . — > v, and ft approaches Michell's integral in the form it 

 takes if one makes the substitution /x = vA 2 . 



Accelerated Motion. The velocity potential for a submerged source moving 

 with velocity c{t) has been given Sretenskii [3], and by a different method by Have- 

 lock [e.g., 11]. From this one can find the wave resistance of a thin ship as before. A 

 detailed exposition is given in Sretenskii [3] and Lunde [1]. The result is: 



(91) 

 pc'it) 

 R = jj dxdy // d&r, Ux,V)US,i)\[(x - £) 2 + (v - v)T' A 



TT S S 



2pg 

 -l(x-ty+(y + v)T % ] + — SS dxdy Jf d& v Ux,y)US,v) 



IT S S 



• J" dk ke^+^j 1 dr c{t) cosVgk (t - r)J (k(x - £) + kj* dr' c{t')). 



129 



