Such families have been called "basic forms" by the present writer 13 and 

 designated by (2,4,6;0;t) since the arbitrary parameters a a can be de- 



rl 2 4 



termined by the prismatic coefficient </> = J 77 d£ and by Taylor's tangent 

 value t - -dufl )/d|. 



It is thought that the Landweber Series [1 ] meets almost all 

 reasonable requirements as to wave -resistance properties presented by prac- 

 tice although only two arbitrary parameters <£,t are at our disposal for the 

 main symmetric part. The reason for this assumption is that from investi- 

 gations on surface ships it is well known that area curves of fine ships, 

 based on the basic family equation (2,4,6;<£;t) are advantageous in the range 

 of high and medium Proude numbers. At low Proude numbers other polynomials 

 are preferable but there the wave resistance of submerged bodies becomes 

 rather negligible. 



We have, however, introduced an additional term a g £ 8 for which 

 auxiliary wave -resistance functions are also tabulated in this report; thus 

 more elaborate investigations can be performed using the polynomial 



Z v 1 



2,4,6,8 

 The asymmetric (skew) part is the function 



>s = 1 



2,4,6,8 



T7 = a £ + a £ 3 + a ? 5 [4d] 



a i* 3' 5 



factoring out a , we write 



n = an* = a U + b J 3 + b J 5 ) [He] 



a 1 <4 1 3 5 



Obviously the resultant curve 77 = 77 + n can have its maximum section out- 

 side of l = and the area of this section will generally differ from one. 

 This slight complication does not involve any difficulties in actual work. 

 Let us investigate 



"* = £ + b £ 3 + b £ 5 [4f] 



a * 3 5 



This trinomial has to comply with the conditions 



77*(o) = 



U*(+1) = i?*(-f) = 



whence 



b = -(1 + b ) 

 5 3 



