124 EKMAN. ON DEAD-WATER. [norw. pol. exp. 



merits than in the case of two sharply separated layers, apparently hecause 

 of the small difference of spec, gravity between each two adjacent water-layers. 



The resistance in the "mixed" water-layers is represented by the heavy 

 curves 1 and 2. For the sake of comparison, faint curves representing the 

 resistance in the corresponding unmixed water-layers (fresh-water layers, 

 3 and 5 cm. deep respectively; saltwater of specific gravity 1"030) are also 

 given. The velocities seem to be upon the whole, a little more reduced in the 

 case of the mixed water-layers than in the case of the corresponding pure 

 fresh-water layer; and the reason is obvious, because in the former case a 

 smaller velocity is sufficient to disturb the equilibrium of the water-layers, 

 and consequently to cause wave-motion. But this difference is of no prac- 

 tical importance. On the other hand, the maximum resistance is some- 

 what reduced by the mixing. The reduction is however, not very conside- 

 rable; the maximum dead-water resistance being only diminished by 11 per 

 cent — and the entire maximum resistance by 14 per cent — in Case (1), 

 in which the mixing extended uniformly right up to the surface. 



The fact that in the sea, the lighter surface-layer is in general not sharply 

 defined from the bottom-water, will therefore not invalidate the applicability 

 of the experimental results. In any case it will be possible to make a sui- 

 table correction by help of the curves Fig. 2 PI. XI. Fresh-water layers as 

 sharply defined from the salt-water below, as in diagram (2) — or even 

 sharper — are not unrare near the coasts. 



Application of the experimental results to the case of full-sized ships. 



Froude's rule (p. 51) was proved to hold exactly for wave-making resi- 

 stance in frictionless water, and reasons were given (p. 53) that it should 

 hold approximately for the frictional resistance. It may therefore be expec- 

 ted to hold very nearly true for the entire dead-water resistance, since the 

 greatest part of this is caused by wave-making. In other words: if the 

 dimensions of the vessel, the depth of the water-layers, and other linear 

 dimensions are increased in the proportion I, and if the vessel's velocity 

 is increased in the proportion ^X, the dead-water resistance will increase 

 as P. 



For a rough verification of this rule, we may compare two series of 

 experiments, one with the small Fraw-model, and one with the large one 



