66 EKMAN. ON DEAD-WATER. [NORW. POL. EXP. 



the water — a slight depression just over each elevation in the boundary, and 

 vice versa. This was verified by a few experiments described above (p. 59). 

 Fig. 3, PI. IX, shows some of the wave-profiles in the water-surface, drawn 

 in these experiments. The numbers 1 — 9 to the left of the figure, denote 9 

 separate experiments. The horizontal line which is on a level with each of the 

 numbers, indicates the undisturbed water-surface in the corresponding experi- 

 ment; the boat-model is drawn black, on a scale of 1 : 20, in its due position 

 relative to this line. The disturbance of surface-level in the neighbourhood of 

 the boat is represented by the curved line: the vertical distances between it 

 and the line of undisturbed surface-level, are 25 times as great as the disturb- 

 ances of level observed in the experiments; the horizontal scale of the wave- 

 profile is the same as that of the boat itself, and the scale of heights is con- 

 sequently 500 times the scale of length. 



A comparison of these profiles, with photographs of the boundary-waves 

 in similar cases, shows quite clearly the above mentioned connection between 

 the wave-motions in the surface and in the boundary. Compare, for instance, 

 the profile 6, PI. IX, and the photograph Fig. 2, PI. XVI -- both taken in 

 the case of a 5 cm. deep surface-layer, in which the boat moves at somewhat 

 below the critical velocity. Similarly, compare the profile 7, PL IX, and Fig. 4, 

 PL XVI (the water-layers the same as before, but the velocity of the boat 

 above the critical velocity). In both cases the shape of the surface is — when 

 leaving out of account the scale of heights — a reversed image of the shape 

 of the boundary. By calculation it can be shown that the ratio of the height 

 of the surface-disturbances to that of the boundary-waves, is of the same order 

 of magnitude as it should be according to the theoretical formula (1) p. 42. A 

 more rigorous testing of the agreement between theory and experiment in 

 this respect, is impossible, because the latter were not made with towing-forces 

 corresponding to oneanother. 



The disturbance of the surface-level gives a very simple explanation of 

 the increase of resistance which is caused by the boundary-waves. Figs. 1 

 and 2, PL IX. are intended to illustrate this; they show the same surface- 

 disturbances as the profiles 6 and 7, Fig. 3, but on less exaggerated vertical 

 scale (50 times the horizontal scale). The boat is sketched in her true position 

 relative to the actual (disturbed) water-surface, and the illustrations then be- 

 come more realistic. In both cases illustrated, the towing force is 3 grammes, 



