fluid. This nonessential assumption, which practically speaking is generally 

 justified in our case, simplifies the presentation. 



As long as the fluid is assumed to extend infinitely in all direc- 

 tions, we shall avoid in definitions the expression "ship," although we are 

 primarily interested in applications to the ship. 



1 .2 With regard to methods for calculating the hydrodynamic mass quan- 

 tities or their coefficients, refer to, for example, the textbook of Lamb 1 

 and the dissertation of Wendel. 2 They are based on knowledge of the velocity 

 potential <f> , with whose help the expression for the kinetic energy or the 

 components of the force and of the moment can be ascertained. For a "regular" 

 body (without a hole) one obtains, as is well known, fifteen hydrodynamic 

 inertia quantities, which number is reduced to six if the body has three 

 planes of symmetry. Inasmuch as the hydrodynamic mass represents a tensor 

 quantity, the notation becomes important. For example, a useful symbolism is 

 obtained if one puts the kinetic energy 



6 6 

 c t=l J = l X J ± <J 



where the components of the velocity of translation are u = u , etc., and 



1 x 



the components of the velocity of rotation are u = w , etc. We cannot 



aspire to completeness here, however; on the contrary, we must frequently be 



satisfied with the implications only. 



Therefore, we shall confine ourselves to body forms whose kinetic 



energy is determined by six hydrodynamic masses which we shall designate in 



the usual way by m , m , m_ for the translational motions and by J , J , 

 x y z m yy 



and J for the rotational motions. The corresponding inertia coefficients 

 are then defined, although not entirely fortuitously, by 



m m 



k = ™ > K = m - etc • . 



x m Q ' y m o 



k =4^. k =iz, etc. 



M J ox yy V 



Here, as previously indicated, m is the mass of the displaced 



fluid. 



J , J , J are the moments of inertia of the displaced fluid or 

 ox oy oz 



of the homogeneous body having the density of water p. Naturally, J ox » etc., 

 differ in general from the moment of inertia of. the body J , etc., although 

 the mass of the body, as assumed here, is equal to the mass of the fluid. 

 For completeness, we note, in addition, that the symmetry of the 



