88 EKMAN. ON DEAD-WATER. [norw. poL. exp. 



aft of the boat, the surface-film might have a tendency to be ruptured, and the surface- 

 tension takes its maximum value or in any case becomes increased 1 , whereas no such effect 

 takes place ahead of the boat. Not much attention was paid to this circumstance, before 

 the completion of the experiments, and it would in any case have been difficult to avoid 

 the error caused by it. 



The greatest possible variation of the surface-tension being from 0'0755 to 0"0407 or 

 00348 gr. per cm. 1 , and the .FVawi-model being 11 cm. broad, the resistance caused by 

 surface-tension could theoretically amount to 0034-8 X H = 038 gr. The surface- 

 tension has not, however, its minimum value in its equilibrium state (see F. Nansen 1. c. 

 pp. 38 and 43) but takes a mean value. In our case, it might rather have been nearer to the 

 maximum value, because the surface was repeatedly cleaned by expansion. The effect of 

 the blotting paper in reducing the surface-tension (F. Nansen 1. c. p. 63 seq.) cannot have 

 been very considerable, because the area of it in contact with the cleaned surface was al- 

 most nil. Further, as the breadth of the boat-model decreases very evenly towards its 

 stern, the maximum surface-tension could hardly act in any case upon more than a small 

 part of the whole breadth of the boat. For these reasons it is probable that the resistance 

 due to the surface-tension effects, has not been more than 01 gr. for the highest velocities, 

 and much smaller for the smaller velocities at which "dead-water" occured. In a few cases, 

 exactly similar experiments were made before and immediately after the surface was cleaned; 

 the results agreed with the above supposition, that the surface-tension effects was of very 

 little importance. They might possibly have been somewhat greater in the case of dead- 

 water than in homogenous water, because in the former case the motion of the water aft 

 of the boat, is more turbulent. 



6) Owing to the boat moving in a rather narrow channel, the frictional resistance 

 and the pressure-resultant caused by it, may have been too high, for the same reason given at 

 the top of p. 47. The experiments made, do not allow the value of this error being de- 

 termined with any certainty; this would require a greater accuracy in the determination of 

 the resistance especially in the case of the small boat-model, than was actually obtained. 

 A comparison between the curves (1) in Figs. 8 and 9, PI. VI, shows however, that the 

 resistance to the small .Fram-model was practically the same in the small and in the 

 large tank. (The model used in the former case, had a rougher surface than that used 

 in the latter case, see p. 59). This error cannot therefore have been very great, and has 

 probably been quite inappreciable; its influence on the determination of the "dead-water 

 resistance" has certainly been of no importance whatever. 



On the other hand, the narrowness of the tank may have influenced the dead-water 

 resistance, by altering the wave-motion. This circumstance will be examined below in 

 section F of this chapter. 



7) When the boat had not time to acquire a steady speed, the towing force must be 

 diminished by the force accelerating her, in order to give the resistance to uniform motion 

 (see columns 7, 8, 9, of the tables). This correction which in the case of the actual mea- 

 surements, was always comparatively small, is equal to the product of the boat's acceler- 

 ation and her inertia. The inertia which comes into account is, however, somewhat more 

 than the mass of the boat itself; for the surrounding water must be accelerated as well as 

 the boat. It was therefore determined experimentally in the following way. In experiments 

 46_47 the towing force was O'l gr., and the velocity 4 cm. per second. According to 

 the diagrams on PI. VII, the acceleration was practically nil, and O'l gr. is consequently 

 the resistance at 4 cm. per second. In experiment 35 the towing force was 0'8 gr.; and 

 the diagram on PI. VII shows that the velocity increased from 2'5 to 5"5, that is by 3 cm. 

 per second, in 4 intervals of time. The mean velocity during the interval being 4 cm. 

 per second, the resistance to uniform motion was as before, O'l gr.; and the accelerating 



1 Compare the treatise "On hydrometers and the surface-tension of liquids", by Fridtjof 

 Nansen. No. 10 of this report, p. 21. 



2 L. c. p. 27. Lord Rayi.eigh, Phil. Mag., 5 Ser., v. XXX, p. 386. 



