and 



5^£l _ _[ Qo{r ,} +Q ,{, (| _ 2) }_ 7(T L_ (QiW 



-Q 1 {y(?-l+p)} + Q 1 |v(^-l-p)j-Q 1 {Y(^-2)])] 



[7] 



where Z, is the surface elevation due to non-wave portion of disturbance caused by motion of 

 the form,* and Z is the surface elevation due to wave system. 



The non dimensional longitudinal distance £ is positive when measured in the astern 

 direction. The basic functions P and Q are defined as follows: 7, 8 



P {u) = 2 sin ( u sec (f>) dtp 

 •'o 



P _1 (w) = 1 + Pj (u) = 1 - 2 cos <j> cos (u sec <j> ) d <f> 

 K 



In the present calculations, the values of the P functions were obtained from a graph prepared 



by Professor Lunde. 7 



Q M = f \ U {H (t)-Y (t)jdt 



where H Q (t) is Struve's function and Y Jt) is the Bessel function of the second kind. The 

 values of Q (u) may be calculated for values of t < 16 using the tables of HJt) and Y Q (t) 

 given by Watson. 9 For values of t > 16 (for which the values of HJt) and Y Q (t) are not given), 

 the following method was used: 



When t is large (in this case for t > 16) 



tf (O=r (t)+^27 



Therefore 



Q (l)-Q„(16)-| 



=• '■(i-M')-" 



-u I 1 \ 



m r\m + n" J 



♦"The function Q„ does not oscillate but is monotonic, and the terms in Q n represent a symmetrical disturbance 

 of the surface in the neighborhood of the form which dies away quickly both fore and aft of the form. It absorbs 



no energy owing to its symmetry and therefore does not affect the resistance. 



,,6 



