48 EKMAN. ON DEAD-WATER. [norw. POL. EXP. 



water, and will give rise to wave-making resistance. In the present case, the 

 vessel may be followed, not only by transverse waves but also by diverging 

 waves, and as these move with a smaller velocity than the vessel herself, the 

 wave-making resistance will not completely disappear at the before mentioned 

 critical velocity. But the influence of the stratification of the water, on the 

 fridional resistance, may be expected to diminish and disappear at these high 

 velocities, for the same reason as was mentioned in the former case (p. 47). 

 Figs. 2—5, PI. V, illustrate the different forms of the wave-systems corre- 

 sponding to different ratios between the vessel's velocity and the maximum 

 wave-velocity 1 . The lines represent the wave-ridges seen from above, and the 

 vessel must be imagined to be at the point at the left end of the figure. In 

 Fig. 3 the vessel is moving at a considerably slower velocity than the maxi- 

 mum velocity of the waves (slower than at half this velocity). In Fig. 4 the 

 velocity of the vessel is nearly as great as (l - 2 times smaller than) the maxi- 

 mum wave-velocity ; in this case the wave-length of the transverse and diverg- 

 ing waves, is greater, and the waves stretch farther out to the sides, than at 

 a slower speed. In Fig. 5 the vessel moves at twice the maximum wave- 

 velocity, in this case the transverse waves cannot exist and have en- 

 tirely disappeared, but the diverging waves still exist and form a certain 

 angle with the course of the vessel. Fig. 2 gives on a larger scale, and for 

 several different velocities, the wave which is nearest to the vessel. In this 

 figure, d denotes the ratio of the maximum wave-velocity to the velocity of 

 the vessel, the latter velocity being the same in the case of all the curves. 

 The dotted curve inside the curve for d = 2, corresponds to d = <x>. If the 

 heights of the waves be known, the resistance caused by them may be cal- 

 culated in a similar way as on pp. 36—37, except that the "ratio of trans- 

 mission of the wave-energy" is not the same in both cases. 



The curves are drawn according to calculations, quite similar to those found in Lamb's 

 Hydrodynamics, p. 402, for ordinary ship-wares. 



