and 



Bessho 



(2gVTr) log (8/7g) for HgCy) , (57a) 



for Hb(y) , (57b) 



8g/7T for H^(y) . (57c) 



Thus, H^ represents the elliptic loading of which resistance and minimum 

 character are found by Maruo. He explains that the wave resistance is similar 

 to the induced drag of a wing physically and theoretically (7). 



In this respect, H^, corresponds to the load distribution of a wing: 



H(y) = l/7l-y' • (58) 



Since the induced velocity of this distribution is zero, there might be no in- 

 duced drag for such a wing, if such a flow could be realized (16). For the plan- 

 ing surface, however, there may be a possibility to realize such a flow by adding 

 floats at both ends (17). 



On the other hand, the similarity of H^ (Fig. 5) to the wave -free distribu- 

 tion (Fig. 1), especially at low speed, is also to be remarked. 



Generally speaking, the situation with respect to the wave -free solution may 

 be similar to that of slender ship theory, in which case there also exist wave- 

 free distributions having a finite displacement, and they correspond to another 

 class of the distribution which has smaller resistance than the slender ship (2). 



CONCLUSION 



As explained above, there is a close similarity between the theory of the 

 thin ship and the pressure distribution. Thus, any pressure distribution is 

 composed of line wave sources and wave -free distributions which have no dis- 

 placement. 



A typical elementary wave source is the twin hull ship type, that is, the 

 longitudinal line distribution of the pressure on two parallel lines. Another is 

 the planing surface type, that is, the transversal line distribution of the pressure. 



Generally speaking, the minimum problem of the wave resistance has no 

 solution and the least wave resistance may be zero, because some elementary 

 wave sources could be summed up so as to cancel out their amplitude functions 

 with each other. However, there are special cases when the solutions exist. 



In this paper, the transversal line distribution of the pressure is treated, 

 and it is found that there exists a unique minimum solution except for the wave- 

 free distribution with a finite displacement. This wave -free distribution corre- 

 sponds to the inverse elliptic load distribution of a wing and seems difficult to 

 realize practically but suggests that distributions of another class may exist 

 which have smaller wave resistance than the one considered here. 



788 



