A = Z 



2**X 



and the absolute density of the source is given by 



(293) 



l(x) | = 8A|V| = B(x)|v| 



(294) . 



The coefficients A n and B are determined by the standard calculation of the 



two-dimensional problem of a heaving cylinder. The density and phase of 



dipoles which represent lateral oscillations can be determined in a similar 



way. Since the function U £ 3<J> n /3z does not include the source term nor 



w U 



horizontal dipole, the density of sources and dipoles of <j>' is identical 

 with that of <j>. . It is not easy to give a general formulation for the 

 effect of the second term of Equation (282), but it can be expressed by a 

 form of a correction term to the vertical velocity in the case of semi- 

 circular cross section, since the hull boundary condition in this case is 

 given by the form 



+U-5-I {B(x)(z -xijJ-C )} (295) 



3n' B(x) V 3t 3x 



If we assume the above relation in arbitrary cross section, we can put the 

 vertical velocity of each section in the form 



V = iW ( ia * U h) {B(x)(z g -x^S w )} (296) 



A similar approximation can be applied to the lateral oscillation. 



Numerical Examples for Added Resistance 



In the previous sections, formulae for calculating the added resistance 

 and steady side drift force are presented. The formula, which is originally 



100 



