10 



thus 



,* = | + V 3 - (l+b a )«- 



[4g] 



The only arbitrary parameter b can be fixed by one additional condition; as 

 such we choose the tangent value t* at the bow (at the stern the correspond- 

 ing value is -t*) 



t I=" 



d r,*(l 

 8* 



= + 4 + 2b 



hence 



b = - 2 + t*/2 

 3 a 



[4h] 



the corresponding tangent value t of ri a , Equation [4e], is obviously 



t„ = a t* 



a i a 



The table below shows some examples of skew forms. The parameter 

 <j>* = J 77* df is an area coefficient referred to the unit square. Plots of 

 | _ £3 > | _ ^5 and some ther "skew" forms used in the TMB Series are shown on 

 Figure 5. The actual skew part 77 contains additionally the "strength para- 

 meter" a ; see Equation [4e]. 



*s 







i 



2 



4 



"a* 



§(1 - S 2 ) 2 



§ - 1.5? 3 + 0.5* 5 



* -* 3 



« -* 5 



877 */3* 



1 - 6? 2 + 5I 4 



i - 4.5? 2 + 2.51 4 



l - 3I 2 



l - 5* 4 



<** 

 *a 



1/6 = o.i 66. .. 



5/24 = 0.2083... 



lA 



1/3 



Our numeric evaluations are primarily based on Equations [4c] and 

 [5]— which are stated below — but the theoretical treatment will be carried 

 out along more general lines. 



Extended investigations have been made by Landweber and Gertler 2 

 on the influence of an additional term ajx 7 on the form of the body when the 

 geometric parameters are kept constant. 



Using our system of axes it is easy to perform similar investiga- 

 tions for the symmetric and asymmetric part of [4c] 



»»„ = V o + n = 1 - y aJ n +a (5 +b^ 3 +b{ 5 ). 

 'o 's 'a / - n ' 1 * 3' 5 

 2,4,6 



