NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 95 



surface- waves, and also disappear at a much slower velocity than these latter; 

 and this is the reason why the velocity is so considerably reduced by the 

 dead-water, whenever it is upon the whole, influenced by it. 



The physical reason why the waves in the boundary are created, and 

 the way in which they are able to exert resistance upon the vessel, have 

 been explained above, from different points of view (see particularly pp. 66 — 67). 

 Here it may be sufficient to keep to the two facts that the vessel generates 

 waves in the boundary, and that they (owing to the energy required for 

 their maintenance) cause resistance. As far as other details are concerned, 

 the explanation may be based upon the resistance-curves and other experi- 

 mental results. 



As was mentioned on pp. 60 — 61, curve (4) in Fig. 8, PL VI, shows that 

 the change of the boat's velocity from below to above the maximum wave- 

 velocity (and vice versa) must always take place suddenly. And as the ne- 

 cessary condition for the generation of large boundary-waves, and ipse facto 

 for all the effects of the dead-water, is, that the vessel move at below the 

 maximum wave-velocity, the same resistance-curve involves the explanation of 

 the fact that the dead-water always appears and disappears suddenly. This 

 matter may hre more explicitly slated; and for that purpose it is convenient 

 to alter the units of velocity and resistance in Fig. 8, PI. VI, to refer to a case 

 more similar to that of full-sized ships. If we e. g., imagine the velocities 

 to be given in decimetres per second and the resistances in tons, instead of 

 in cm. per second and grammes respectively, it follows from Froude's rule 

 (pp. 51 and 53) that the curves in Fig. 8, PI. VI, refer to a vessel of one 

 hundred times the size of the model used in the experiments, i. e. a vessel of 

 the same shape as the "Fram" but of half her size. The depths of the 

 water-layers must at the same time be imagined to be as many metres as 

 they were centimetres in the actual experiments. 



Suppose, for example, this vessel to sail — in open sea-water of ample 

 depth — before a fair breeze giving her a speed of 14 dm. per second (2"8 

 knots). According to curve (1), the propelling force should then be - 24 ton. 

 Now suppose that the vessel reaches a place where the sea-water (of spec, 

 gravity P03) is covered with a 2 m. thick, layer of fresh-water. Curve (4) 

 referring to this case, shows that the speed of the vessel will be hardly appre- 



