is constantly dissipated by progressive waves. A "reversible" part of the 

 kinetic energy corresponds to local disturbances in the neighborhood of the 

 body and may presumably be used for the calculation of the added mass quanti- 

 ties. This manner of separation, however, has not been accomplished as yet; 

 on the other hand, a direct calculation of the applied forces leads in prin- 

 ciple to the goal, although it has been actually successful only in a few 

 cases. Independent of the steady or unsteady nature of the body motion, the 

 force and moment vectors are given by 



[ [pndA M = - [ j prndA [4, 



where n indicates the exterior normal and r the radius vector. The integra- 

 tion is performed over the surface of the body. 



The pressure p is determined by the instantaneously existing flow 

 field, the structure of the latter, however, is in general not only a function 

 of the instantaneous velocity and acceleration but is also a function of the 

 law according to which this acceleration dies out. In other words, the flow 

 field and therefore the pressure and the forces developed depend on t.ie 

 history of the motion of the body. 



This means that for a given speed and acceleration the added mass 

 of a body may vary with the kind of the motion, for instance, assume different 

 values for a translation, a free or a forced oscillation in the same direction. 



Under these circumstances, the question, whether and to what extent 

 the concept of hydrodynamic masses can still be maintained in the case of an 

 accelerated motion of the body on a free surface, appears justified. We shall 

 here anticipate the answer: the concept remains quite suitable, however, the 

 quantities in question can be functions of various variables so that they lose 

 their simple geometrical character. 



Some simple formal reflections now follow. 



2.2 If our body is moved on or in the neighborhood of the free surface, 

 then our velocity potential must satisfy, in addition to Laplace's equation 

 and the boundary condition on the body, the linearized boundary condition of 

 the free surface 



+ g ff-O *»«-<> 151 



We shall consider two important special cases: 



a. The ship undergoes a uniform translational motion U; then one 

 writes in place of [5] 



-0+-*|f=O for z = [6] 



