NO. 15-1 QUALITATIVE RESULTS. 61 



towing force is increased a little above the maximum resistance 0*29 grammes 1 , 

 the boat begins to be slowly accelerated ; it is accelerated faster and faster as 

 the velocity increases right up to 11 cm. per second, and continues to accelerate 

 as long as the resistance is below 029 grammes, i. e. up to 15 - 5 cm. per second. 

 Thus, if the towing-force be gradually increased, an almost sudden change 

 of velocity from 6 to nearly 16 cm. per second, will at a certain moment 

 occur. Similarly when the towing-force is again being gradually diminished, 

 a sudden decrease of velocity will take place, from 11 or 12 to about 4 cm. 

 per second. From this point of view the curve of resistance ought to consist 

 of two curves connected, by a horizontal straight line representing, in the case 

 of increasing towing-forces, 0.29 grammes 1 , and, in the case of decreasing 

 towing-forces, - 21 grammes. It may be here mentioned that the peculiar 

 shape of the curve (4) thus affords the explanation of the sudden decrease 

 or increase of velocity, which characterizes respectively the appearance and 

 the disappearance of the dead-water phenomenon. 



There is an apparent similarity between curve (4) and the curves in 

 Fig. 4, p. 38, representing the law of resistance in shallow water, discovered 

 by Scott Russell. 



A glance at curves (1) and (4) leaves the impression that the resi- 

 stance in salt-water covered with a layer of fresh-water, is made up of two 

 parts of different origins. One part is independent of the fresh surface-layer 

 and is identical with the resistance in homogenous deep water. The other 

 part, which must depend on the difference of density between the two water- 

 layers and may be called "dead-water resistance" , is practically restricted to 

 a certain range of velocities — below 12 or 14 cm. per second, say. We 

 shall see, that this latter part of the resistance mainly corresponds to the loss 

 of energy due to generation of waves in the boundary between salt and fresh 

 water. When calculated according to the formula (3) p. 43, the maximum velo- 

 city of the boundary-waves is, in the case eonsidered,7 - 3 cm. per second, which 

 velocity is indicated by a ? at the top of the figure. The "dead-water resistance" 

 is a maximum at about the same velocity (6 cm. per second), just as it 

 should be in accordance with the discussion in Chap. II, p. 47. It will be 



1 Owing to the way in which the experiments were made, this value does not indicate 

 the greatest resistance at constant speed. The maximum resistance in this simplest 

 meaning is somewhat higher than the value 0'29 gr., indicated by the curve (4). See later. 



