52 



Using Equation [30], various changes in S can be easily estimated 

 within the range of validity of the formula. For instance, the influence of 

 an asymmetric term can be discussed as follows: 



H t = H s + H a 



*s = J" < H s + V< H s + H a^ = J s + I" W^ + £ Wa ^ 



[32] 



where I refers to the even part following [30]. When the meridian 

 curve has vertical tangents at the bow and stern (or bow or stern) the pre- 

 ceding reasoning can be applied in principle to a range 1 - e„ > £>-(! - e. ), 

 and the remainder is calculated as the surface area of a segment of the 

 sphere generated by the radius of curvature at the nose or stern. Such an 

 approach is, however, only useful when the integrals involved are of simple 

 type. 



