Muvthy 



1 « 4 pV 



&£/stti£l a, dz //M|^ 



6 hulls 5* 



'* 2 1 ° r Sl ° l 



■k (z' + f')sec 9 cos k (x'-{) secfl 



/• : 



ll + cos 2 k b sec sin sec 0d0 (6-27) 



If we use the expansions 



cos k (x 1 - £' ) sec = cos (k x'sec 0) cos (k £' sec0) + 

 o J o o 



+ sin (k x' sec0) sin (k £' sec0) 

 o o 



and 



2 2 2 



1 + cos (2 k b sec sin ) = 2 cos (k b sec sin0) 

 o o 



and write ? 



"V sec i 



P (0) = cos (k b sec sin0)J J — . \ — -e 



cos (k x' (sec 0) dx'dz 1 1 o 

 o 



if- 



and 



S' 



i « Y i i\ ~k z sec 

 Q(0) = cos (k b sec sin0) // ■ i' * e 



sin (k x' sec0) dx'dz' 'o , . 



we have for the absolute value of the wave resistance 



tt/ 2 



I^r = ±£g / (P 2 +Q 2 ) sec 3 d0 (6-29) 



5 W hulls ttV 7 q 



When the quantity b representing one half of the separation 

 between the two hulls is set equal to zero we get the result for two 

 superimposed hulls which is the limiting condition of two contiguous 

 hulls with the width doubled and as the resistance can be seen from 

 (6-28) and (6-2 9) to be proportional to the square of the width of the 

 hull, we will have to take one quarter of the above value for a single 



152 



