Le& 



where the bar si^n means the complex conjugate e.g. 



^5.= 9.,^- 3<P 



2x ^2cx J^2sx* 



If we let 



6j = tan"' (Rej Pi/lrrij pj) for 1=1, 2,. ..,6, 



we can express these pressures in the form 



Pi = JlPi |e 



for 1=1, 2,. ..,6 



or, in association with the time harmonics, 



where 



-jU)jt I I 



Pje = |p. I sin (oijt + 6i) for 1 = 1 ,2,. . , ,6 



O): = < 



(61) 



5. 2 Vertical Hydrodynajnic Force on the Body 



The vertical hydrodynamic force acting upon the body is given 



by 



F = - 2 



pi(t) 



\ P cos (n,y) di. 



'V») 



Here igCt) is the instantaneous position of the point of intersection 

 between the bottom of the body and the y-axis , i(t) the instantaneous 

 position of the point of contact of the body with the free surface, and 

 cos (n,y) the direction cosine of the unit normal vector on the body 

 surface in the y-direction. The positiye direction of the unit normal 

 vector is into the fluid, and the integral is taken along the cylinder 

 contour. Eq. (54) enables us to show that for the family of cylinders 



924 



