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



The values of velocity and resistance calculated in this way, are repre- 

 sented in Fig. 8 PI. VI by the faint curve (5). The curves (4) and (5) should 

 consequently coincide if the measurements, and the method of comparison 

 were exact. The agreement may be regarded as very good, and as far as 

 the maximum resistance is concerned, the difference lies within the limits of 

 experimental errors. The difference between the two curves at velocities 

 below the critical one, will be explained below, as due to the different width 

 of channel. The application of the experimental results to the case of 

 vessels on a different scale, may consequently be made according to the 

 scheme used in the Table p. 125. 



The agreement between Curves (4) and (5) in the case of the maximum-resistance, 

 does not exclude the possibility of appreciable errors, if the measurements be applied to 

 the case of full-sized ships. For the larger .Fram-model must have its dimensions 6"6 times 

 doubled in order to attain the size of the Fram herself (the power 6 - 6 of 2, is 100). Sup- 

 posing that the agreement between Curves (4) and (5) for the maximum dead-water resi- 

 stance, is trustworthy to within 5 per cent of the measured quantity, the experimental 

 result when applied to the case of the Fram herself, might then include an error of as 

 much as 38 per cent (the power 66 of 1*05 being 1'38). In any case the above comparison, 

 proves that Froude's rule gives results which are of the right order of magnitude; and 

 there is apparently no reason for supposing that it should not be practically exact. 



We may conclude also from experiments with salt-water of different spec, gravities, 

 that the friction had not so much influence in the experiments as to destroy their appli- 

 cability on a larger scale. For by using the artifice on p. 52 it follows from Equations (b) 

 and (c) p. 50, that the influence of the friction upon the motion, will be diminished just 

 as much when increasing the linear dimensions in the ratio r, as when increasing the 

 difference of spec, gravity 4q in the ratio r 3 . As the agreement between experiments 

 with differences of spec, gravity = 0-01, 0-02, 03, 0'07, and 016, is very good (see p. 116), 

 we may therefore expect the same agreement between for example, experiments on the 

 scales 1 : 100 and 1 : 50 with a difference of sp. gravity 0'02; and when the scale is further 

 increased, the agreement is likely to be so much the more certain. The same conclusion 

 could be drawn from the fact that the amplitude of the velocity-oscillations, was just as 

 great when the difference of spec, gravity was small, as when it was great; because the 

 velocity oscillations are more stifled by friction, the smaller the difference of spec, gravity. 



One more circumstance must be examined before applying the results of 

 the experiments. They were performed in a rather narrow channel, while 

 in cases actually interesting us, the vessel is moving on a more or less 

 open and extensive water-surface. The effect of this circumstance, upon the 

 frictional resistance and upon the sternward-pressure caused by it, has been 

 mentioned in section D of this chapter; and it was then pointed out that in 

 any case it would not appreciably influence the "dead-water resistance". On 

 the other hand, the wave-making resistance might be influenced, the waves 

 being to a greater extent transverse waves, when the vessel is moving in 

 a narrow channel. 



