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



Fig. 2 PI. VI. The maximum wave-velocity v»> is, according to the data in 

 Scott Russell's paper, assumed to have been 8 miles an hour. The faint 

 curve in the same figure represents on the same scale the quantity subtracted. 



The two full-drawn curves in Fig. 3 PL VI represent the dead-water 

 resistance according to Fig. 1 PI. X — the heavy curve in the case of a 

 5 cm. fresh-water layer, and the faint curve in the case of a 9 cm. surface- 

 layer. Strictly speaking, the wave-making resistance and not the dead-water 

 resistance, should be compared with the calculated wave-making resistance. 

 The difference between these two quantities could, however, be determined 

 only for very small velocities and not for velocities at which the wave-motion 

 is considerable. In any case, the difference is not very great. 



It is obvious that the agreement between the calculated and the experi- 

 mental resistance-curves could not be complete: because in the experiments 

 the boat also created diverging waves, which persisted and caused resi- 

 stance, even at velocities higher than the maximum wave-velocity; and part 

 of the dead-water resistance was also due to friction. Finally, owing to the 

 oscillations in the velocity, (see pp. 67 seq.) the resistance measured, was not 

 the resistance at steady speed. The agreement between the experimental and 

 theoretical curves in Figs. 2 and 3 PI. VI may under these circumstances be 

 regarded as surprisingly good. The peculiar shapes of the theoretical resistance- 

 curves in homogeneous shallow water and in "dead-water" are, indeed, easily 

 recognized on the experimental curves, without any explanation. It is worthy 

 of special notice that the ratio between the velocity at which the dead-water 

 resistance was a maximum, and the maximum wave-velocity, should according 

 to theory be about 077 while the experiments gave practically the same value 

 namely 073 (see p. 123). 



The case in which the vessel moves in open water instead of in a narrow 

 channel has also been investigated in the same way and the waves affecting the 

 resistance evaluated in finite functions. In this calculation the vessel has been 

 replaced by a small reversed cupola put in the water-surface ; the wave-height 

 was found to decrease inversely as the square root of the distance from the 

 vessel. As the numerical calculations particularly of the diverging waves, have 

 at present not been completely worked out, I must here confine myself, to 

 one point of interest concerning the transverse boundary-waves. An approxi- 

 mate calculation of the resistance due to these latter was made, and the result- 



