putting for abbreviation 



17 



h 4 

 ^C 2 npg ^- = const = C ( 



(y/yj 3 



= f(r) 



yTyJ: 



-i 



[2k] 



J r. u L '.j J - 1 



+ JT(2r+1)(2s+1)a, a, _,.M' M' Idy [21] 

 with i , j , s , r integers . R can be built up of terms of the type 



r e ^[-^0 (r ^-i (r,M .i*i (y,dr "^-i.«-i [22] 



for the symmetrical part of the sectional -area curve 



and 



rexp[-^-^lf(y)M' (y)M' (r)&y =W o [23] 



J y L L y J 2r 2s 2r > 2s 



for the skew part. The final result is therefore obtained as a quadratic 

 form in the parameters a or, better, na 



R = ci X 21 2J a a TH + X(2r+1 ) (2s+1 )a a 7J7 1 I 



°|i^ 2i 2j 2i-l,2j-l 7^ 2r + l 2s + 1 2r,2s J 



with the tabulated integral values TV ,jyi f as main parts of the 



Si "I, 2j -1 2r, 2s 



coefficients 2i 2j #7 , etc. 



2i-l,2j-l 



We mention again the fortunate circumstance that the contributions 

 to the wave resistance due to the symmetrical and antisymmetrical parts can 

 be calculated independently and added. 



Returning now to a family of distribution curves given by Equation 

 [l+c] but generalized by one additional term a g £ 8 : 



* " 1' " iV n+ S '"•# " " ^ V" 1 + 8 V 7 [4i] 

 The wave resistance can be calculated by the functions 



^11 ^13 ^15 ^17 K, ^02 ^4 



^33 ^35 ^37 ^22 *?* 



^55 ^57 -»\L 



'24 



