NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 109 



resistance does not decrease correspondingly with the velocity of the vessel 

 since it is chiefly due to wave-making and only to a very small extent to 

 friction. The wave-making resistance depends on the size of the boun- 

 dary-waves and their position relative to the vessel (see p. 74); and as the 

 vessel stops very quickly, the boundary-waves, owing to their great length 

 and slow speed, do not alter their position relative to the vessel, very 

 much during this time: The resistance might consequently, in a particular 

 case, persist even after the velocity is completely lost, and this explains the 

 observation made on the Fram, that the ship was sucked back again. 

 This result, namely that the Fram when in dead-water, should lose her speed 

 after going a distance of about 18 m., agrees remarkably well with the 

 observations at Taimur and at Bergen. 



If the vessel moves in dead-water in a narrow channel, she will, as shown 

 by the experiments, be followed by a long train of transverse boundary-waves. 

 When she has stopped, she will be overtaken by these waves and will swing 

 to and fro under their action, just as was observed by Mr. G. A. Larsen. 

 It is here of interest to notice, that Mr. Larsen's experience is derived princip- 

 ally from working on rivers, where the conditions are more favourable for 

 the formation of transverse waves. In open water, the transverse waves, by 

 spreading to the sides, diminish more rapidly in size at a distance from the 

 vessel; and this is probably the reason why similar swingings were not 

 observed in the case of the Fram. 



The varying ways in which the boat moved in the different experiments, 

 obviously depend upon the velocity-oscillations, described on pp. 67 seq. The 

 velocity of the boat and the height and the position of the waves relative to 

 the vessel, continually change from one instance to another. As the experi- 

 ments were not all made in exactly the same way, the values of these 

 quantities — and consequently of the resistance — at the instant at which 

 the towing force was annulled, may therefore have been different in different 

 cases. It is obvious that this accounts for the differences mentioned. I have 

 given reasons for supposing that the velocity-oscillations are on the open 

 sea, always very small; the effect of the dead-water on a vessel, when 

 her engine, is stopped, should therefore be less variable than in the 

 experiments. 



