only by a more profound analysis. Such an analysis apparently cannot rest on 

 Haskind's earlier approach [16] where diffraction effects have not been considered. 



Under these circumstances the experimental method is appropriate. Haskind 

 and Riemann [28] have proposed a method by use of which one is enabled to evaluate 

 coupling coefficients from test data under plausible assumptions. 



Experimental information on the damping coefficient N 35 has been obtained 

 by Golovato [34], using a TMB vertical oscillator. In a rather important range of 



\B~ 

 frequencv parameter id b - : — w 4/ — which, however, in general lies below synchronism 



T S 

 of pitch and heave, there is a striking coincidence with Havelock's findings, and outside 

 of it a strong departure. Special effects in the low frequency range are determined 



U 

 at the critical speed ratio — = ^W* = Va. At its peak value, the moment N 35 z m is 



c 

 not negligible as compared with the exciting pitching moment M tJ — Q m pgI v E^. The 



same applies in still higher degree to the term m 35 z m ; but such low frequencies can be 

 reached under exceptional conditions only. 



We expect still more difficulties for unsymmetric motions. For example, 

 Chadwick [17] showed that the so-called yaw-heel effect is essentially due to the rate 

 of sway (drift angle) and not to the centripetal acceleration of the ship moving on 

 a curved path as earlier thought [47]. 



It is reasonable to assume that the couplings of roll back into sway or yaw are 

 negligible. 



The papers reviewed represent important steps forward in some directions. 

 However, complete solutions are still lacking even in the calm water case, at least in 

 the official literature, and the general problem of arbitrary motions of a ship in a regu- 

 lar seaway is quite open. 



What difficulties must be expected when proceeding to the seaway problem can 

 be estimated from the author's tentative treatment on directional stability [48] which 

 unfortunately, is mutilated by misprints. Especially the computation of resistance 

 presents a rather formidable task. 



The establishment of equations of motion requires a thorough investigation on 

 the geometry as well as on the mechanics of the problem. Already Krylov has indicated 

 the difficulties arising from the fact that angular displacements of roll cannot be con- 

 sidered small. Further, Ursell has shown that the concept of a permanent axis of roll 

 breaks down in certain cases. Szebehely has discussed the problem of the apparent 

 pitching axis. 



One could further follow lines suggested by Haskind [16] which already led to 

 success in the case of heave and pitch. Useful if not general results may be expected, 

 however, in a rather cumbersome form. 



A scheme for linearized equations can be established using procedures familiar 

 in flight mechanics. Leaving aside the motion in the direction of the axis and assuming 

 that the symmetric oscillations of heave and pitch are described by Equations (12) and 

 (13), the following expressions can be given for the asymmetric group: 



m'ozij + N221J + mMd + 7V 26 + m 24 <£ + N 2 i<j> = Y, (14) 



where, probably, the terms with <p or <p can be neglected; and 



m\4 + Ni4 + 44 </> + m i2 y + N 42 y + m i( + N i5 d = M x , (15) 

 and 



ra' 66 + iV 66 + ?n 64 + iV 64 4> + m^ij + N 6i y = M z . (16) 



In [16] the terms with <p or <p may again be small. These equations do not represent 

 much more than a skeleton for research. 



75 



