474 Prof. T. H. Havelock on the 
showed a periodic movement of the wave crest position, backwards and 
forwards along the hull.” The diagram given in the paper shows the 
mean positions. From this diagram, it seems that we may assume there 
was no measureable phase lag for the ship moored, with zero speed, in 
490 ft. waves. Hence, from (16), the corresponding mean force is 
negligible, and this agrees with the observations. For the same wave- 
length when the ship had a speed of 8 knots, a rough estimate of the 
phase lag from the diagram is about 12-5°, and we take that value for 
B’ in (16). As the free periods of heave and pitch are nearly equal, and 
the damping probably of the same order, we take the same value for f 
in (16). From the measurements given in the paper for 5 ft. waves, we 
have ¢,=2-1 ft., 6) =1-6°. With these values in (16) we get the extra 
resistance for the ship in tons; expressing the result for the model, 
16 ft. long, we obtain from (16) a mean resistance of 0-63 lb. The 
measured value was 0:37 lb. 
It is not worth while pursuing these tentative calculations further at 
present, but at least it seems that one can obtain results of the right 
order of magnitude ; in fact, the calculated results are generally too high, 
especially at the peak values under resonance conditions, but that might 
have been anticipated. On the theoretical side, the various limitations 
and assumptions have already been sufficiently indicated in the course 
of the work. On the experimental side, there is a lack of suitable data 
obtained under conditions sufficiently approximating to the simplifica- 
tions which have to be made before any calculations are possible. 
6. In the present work, with the ship head-on to the waves, heaving 
and pitching have been considered together ; for if the argument is valid 
for one kind of dispiacement it should also apply to the other. Moreover, 
the natural periods of heave and pitch are usually nearly equal and so 
resonance effects for the forced vibrations overlap. Reference has been 
made to Watanabé’s work on the drifting force when rolling, that is, 
when the ship is broadside-on to the waves ; in that work, as in Suyehiro’s, 
the effect of heaving was entirely neglected. The expression (16) given 
here for the drifting force in heaving and pitching may also be used for 
heaving and rolling when the waves are broadside on, with the quantities 
in (16) having the appropriate values for those conditions. However, 
the natural periods of heave and roll usually differ considerably, and 
therefore the resonance effects are separated. The data for Suyehiro’s 
model are not sufficient for these calculations to be made, otherwise one 
might compare the drifting forces due to heaving and rolling ; it would 
be of interest if experiments could be devised to test whether these 
separate effects are observable, and to have experiments made under 
conditions suitable for comparison with theory. 
490 
