92 



I = HBl'^(y) = HBJ j ^e'^^^^ cosy^d^df [l4 



J = HBJ^(y) = HBJ J ^ e'^^^'^^slny^dldf [15] 







+1 +1 







ai 



Mn 



>7 ,7? denote the symmetrical and asymmetrical parts of the hull with respect 

 to the midship section. The resistance R can be written 



This form has some slight advantage compared with the original one from the 

 point of view of computation. For rectangular contours integrations with re- 

 spect to ^ and t, can be handled independently; the discussion is based on 

 quadratures of the type: 



\^{y) = l^'^sin ^d^ ^ 



•(y) = f'^^cos |d^ [17]* 



■'0 



E (y) =f'e-''^^'"df ^= 2f^ 



Especially simple expressions are obtained for the elementary ship: The inte- 

 gral J (y) can be written in the form 



/(y) = Z[y) *(y) [l8] 



where S(y) depends only on the longitudinal and *(y) only on the vertical 

 distributions of the displacement. Examples are discussed in the main text. 



A rigorous proof of Michell's integral based on potential theory is 

 due to Sretensky.^* 



Three further methods of calculating wave resistance are mainly due 

 to Havelock. Explicit results so far have only been obtained in those cases 

 where a ship form can be represented by images. 



Using an approximate connection between the normal velcoity and a 

 plane surface distribution 



27ra = vg [19] 



*In the paper by the author JSTG (1930) there is an obvious misprint on page Ul8 as the double value 

 of the integral is defined as Af„(y). 



