15 



Figure 3 - Ellipsoid 



with the moment 



H(x,z] 



= c^/rT 



a^ - b' 



- To" 



[8] 



where C is constant. The ellipsoid is a simple example of a "double" model. 



This somewhat lengthy reasoning on submerged bodies has been made 

 with the purpose of obtaining an approximation for surface ships. It is as- 

 sumed that the undervrater part of the ship is one half of the "doubled" sub- 

 merged body and is generated by half the corresponding singularity distribu- 

 tion, an assumption which is rigorous only when the wave making can be ne- 

 glected. The approximate relations between the body form and the image system 

 are also applicable to the ship under this condition. 



A closer approximation can be obtained by distributing singularities 

 over the surface. As no useful practical results have been obtained in this 

 way we shall not pursue this method at present. 



"Michell's ship" corresponds to an image system distributed over a 

 vertical plane. Actually ships with b = y > H should be approximated in an- 

 other way, which has been initiated by Havelock and used by Lunde.^-"- Never- 

 theless, our reasoning will be based on Michell's formula^^ which is valid 

 under the following conditions: 



, a. Ideal fluid. 



b. Small slopes of the surface. 



c. Small wave slopes. 



d. No change of model attitude. 



