Murthy 



5 side hulls perturbation parameter denoting the small 

 order of the semi-width of the side hulls on either side of 

 the longitudinal plane. 



e incident wave perturbation parameter denoting the small 



order of the wave slope (ratio of the amplitude to the length 

 of the wave). 



£,*?,$" dummy co-ordinate system having the same disposition as the 

 (x, y,z) system -source point co-ordinates. 



angular co-ordinate ; variable of integration. 



6 pitch displacement. 



X wave length of the incident wave. 



p fluid density. 



2_, control surface (comprising 2^ 2*> 2~i and 2-j ) 



2-j 2-i 2-/ 2-i as defined in Appendix V. 

 O 1 2 3 ™ 



a frequency of incident wave relative to space. 



0" e encountered frequency of incident wave ( = a + kV ) 



<$> velocity potential of water in frame of reference fixed in 



space. 



$ velocity potential of water in frame of reference moving 



in space with velocity V . 



* time -independent part of velocity potential. 



f elevation of water surface. 



w angular velocity of ACV about a vertical axis. 



A dot denotes differentiation with respect to time. 



Derivatives are noted by subscripts when not written in 

 explicit form. 



Special Note . 



In the case of terms containing e l<rt as a factor, it is 

 naturally understood that the real part of the complex quantity is to 

 be taken. This exponential factor denoting harmonic variation with 

 respect to time occurs both in the case of the oscillatory displace- 

 ments and in the case of the unsteady potential. When a factor of 



252 



