60 EKMAN. ON DEAD-WATER. [norw. pol. EXP. 



B. QUALITATIVE RESULTS. 

 Tlie connection between resistance and velocity. 



The influence of the fresh-water layer upon the speed of the vessel ap- 

 peared distinctly even in the first preliminary experiments in the small tank. 

 The results of some of these are represented graphically in Fig. 8, PI. VI. 

 The velocities of the boat-model in cm. per second, are plotted as abscissae 

 and the corresponding resistances in grammes, as ordinates. 



The curve (1) relates to the case in which the boat moves in homogenous 

 water (salt or fresh) of the full depth of the tank. The resistance varies 

 approximately as the square of the velocity. The dotted curves (2) and (3) 

 relate to the cases of homogenous water of smaller depths, 5 and 2 - 5 cm. 

 respectively. As might be expected, the resistance is greater in the cases in 

 which the depth is small; but it seems to increase with the velocity according 

 to an exactly similar law as when the water is deep 1 . 



When there is a layer of fresh water on the top of the salt-water, the 

 result is quite different. Curve (4) is characteristic for such a case, the spec, 

 gravity of the salt water being l - 030 and the depth of the fresh water 2 cm. 

 In this case the resistance is, at velocities below 6 cm. per second, more than 

 twice as great as in homogenous water of 2"5 cm. depth. At about this velo- 

 city, however, the resistance becomes a maximum, and when]' the velocity 

 is further increased, the resistance decreases and becomes smaller than in 

 homogenous shallow water. At great velocities the resistance seems to be 

 approximately the same as in homogenous deep water. 



There is, of course, no stable motion possible, corresponding to a point 

 on that part of the curve (4) which slopes to the right (at velocities between 

 7 and 11 cm. per second); for if the velocity be increased a little, the resi- 

 stance decreases, and the velocity continues to accelerate still faster. If the 



' The actual velocities in these experiments were too small (below 16 cm. per second) 

 for the peculiar phenomena discovered by Scott Russell (see pp. 38—39) to take place. 

 Indeed, the maximum resistance discovered by him, should appear at a velocity of 

 50 cm. per second, when the water is 2"5 cm. deep ; at half this velocity, i. e. 25 cm. 

 per second, the shallowness has no sensible influence upon the waves and wave-making 

 resistance (see p. 44). 



