16 



Here for brevity the designation y = y sec 9 has been introduced, [l6]. 

 For the symmetrical (even) part 



q* = f a*(£) cos(y n * sec0)dM - X(2mfl)a o M'(ysec0) [17] 



Jn t> <J .«=— 2m+l 2m O 



with 



M' (y rt sec 9) = M' (y) = M' = f £ 2m cos(y # sec 9 )d£ = (" £ 2m cos y d| 



2m 2to 2m J„ O J ' 



J ° ° [18] 



inserting [15] and [16] into [12] one obtains 



R = 4C 2 nPg £ y Q j^exp [-4 £ y Q sec 2 ,] {(^2k a^ M^J 2 + 



+ (^(2^)a 2TO+i M-J 2 } .eo«M9 [1 9 ] 



This formula is suitable for numerical computations above in special cases, 

 since tables of the funct. 

 published in a TMB Report. 



since tables of the functions M (y) , M 1 (y) are available and will be 



2k~l 2m 



3.2. TABULATION OP RESISTANCE INTEGRALS FOR A 

 FIVE-PARAMETER CLASS OF BODIES 



As mentioned before, auxiliary integrals have been prepared for the 

 three -parameter symmetric distributions of Equation [5], /u*($) (asymmetric 



ina*U: 



"£(*) = T "27 a n*" and a I U) = ~Z na n^ _1 

 2,4,6,8 2,4,6,8 



and the one-parameter skew distribution Aq(£) (symmetric in<rj(£)) 



**U) = * + b a * 3 - (1+b a )* 5 and o*(t) = 1 + 3b^ 2 - 5(1+b g )| 4 



The computations are based on a slightly different form of R (see Appendix 

 II). Substituting 



r = r sec 9 sec 9 = y/y Q tg 9 = |/(y/y Q ) 2 -1 



one obtains 



(y/yJ 2 dy 

 dy = y sec 2 0sln0d0; y Q sec 3 0d0 = 



)/(y/y ) 2 -1 



" 6 a J^ ^ L yj ^^Tj^T U * 2/c 2fc-1 ' 



(27 (2m+1 )a 2m+i M 2m (r)) 2 ] dy [20] 



hence fc * r- r -*^i (y/yJ 2 



R = 4C 2 



