NO. 15.] EMPIRICAL LAWS OF RESISTANCE. 137 



While in dead-water on Aug. 30th and Sept. 2nd— 3rd, it is possible that 

 the difference of spec, gravity between the water-layers never fell below - 019, 



19 



and the maximum-resistance might then have been as much as^ X 1'25 = 15 



ton. On Aug. 29th and 30th, the boiler required cleaning, and consequently 

 the force of propulsion was somewhat reduced. These circumstances might 

 perhaps be counter-balanced by the fact that the force of the propeller is 

 greater at the low speeds considered, than at full speed; although I am not 

 able to say how much influence the speed may have had on the force of 

 propulsion. 



The velocity, at which the resistance was a maximum, should according 

 to the above calculation have been 1*2 or 1*3 knots, and this should conse- 

 quently be an upper limit for the actual velocity. This calculation is based 

 upon experiments in the comparatively narrow tank, while in open water the 

 velocities become somewhat greater (see Fig. 9, PI. VI). It is, however, 

 highly improbable, that the vessel had the velocity corresponding to the maxi- 

 mum resistance, because then she might at a favourable moment have got 

 rid of the dead-water. From a comparison of Curves 2 and 3 in Fig. 9 

 PI. VI, it follows, that the Fram's speed when in dead-water, was very 

 probably between 1'2 and 1'5 knots; which agrees remarkably well with 

 the speeds alleged by Prof. Nansen. 



The above calculations prove that under suppositions consistent with 

 the actual measurements of the water-layers, the observed effects of dead- 

 water may be explained from the experimental results, even as far as abso- 

 lute quantities are concerned. But they also show another point of interest. 

 The excess of the maximum-resistance above the force of propulsion, is 

 rather moderate, even assuming the former to have been the greatest possible 

 allowed by the observations made at the time; probably this excess has been 

 very small. When the Fram was steadily struggling and steaming ahead, 

 the power of the dead-water may have grown considerable; but it is very 

 possible that if she had stopped and after a while, had suddenly made full 

 speed, she would after a few such spurts, have succeeded in getting entirely 

 free (see p. 110). The Fram had a triple-engine, which could be shifted into 



compound; and then for a short time, it was possible with great waste of 



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