87 



Finer variations of form such as changes of the curvature may be 

 performed by polynomials of the type (n^ngngn ; 0; 0) for instance 



{2,3A.e; 0; 0) = ^2 - ^e + ^^ -^^ [37] 



(2,4,6,8; 0; 0) = ^^ - 5^ + 7|' " 3|' [38] 



complying with the conditions 



and 



|( )| =0 [39] 



( = 1 



(Cf. Reference 102). The presence of the square ^^ is obviously essential 

 when investigating the curvature of the midship section. 



Additional even functions are introduced by using odd powers of abso- 

 lute values. Especially the cube |f|° is important for various purposes. We 

 normally omit the symbol | | . 



When different equations are used for the forebody jjp and afterbody 

 Tj. the symmetrical part of the resulting body is given by l/2{r}„ + 77.), the 

 asymmetrical by 



The system of curves representing water lines and sectional area curves dif- 

 fers from Taylor's system** by: 



A. The choice of axes of reference. The origin is located at the mid- 

 ship section; the fore and afterbodies can be dealt with simultaneously even 

 if expressed by different equations. 



B. A greater variety of forms. 



C. The final purpose of obtaining explicit equations of the surface, 

 not of sets of lines. 



D. Parallel middlebodies may be introduced. However, when using equa- 

 tions of surfaces for resistance calculations it is generally simpler to ap- 

 proximate a cylindrical part by high powers of ^ . 



