NO. 16.] EMPIRICAL LAWS OF RESISTANCE. 1 1 7 



from 103 to 1'18, it is clear that for variations actually occurring on the sea, 

 the rule will hold almost exactly. 



The curves in Fig. 1 PI. XI, show the remarkable fact, that within a 

 certain range of velocities, the resistance may be increased by diminishing 

 the difference of spec gravity between the two water-layers, and vice versa. 

 For instance, at a velocity of 7 cm. per second, a difference of spec. g. of 

 O030 gives a resistance of 1*8 gr., and a difference of spec. g. of 0160, 0'6 

 gr. only. The reason is evidently that in the latter case, the difference of 

 spec. g. was too great for the vessel to give rise to any appreciable waves 

 at that velocity; indeed in this case it was not possible from the side of the 

 tank, to detect the least disturbance in the boundary 1 , while at the same 

 velocity, and with a difference of spec. g. of 0"032, the waves were very 

 considerable (see PI. XVI Figs. 2 and 3) 2 . If the bottom-layer were mercury 

 instead of salt-water, the boat would generate practically no waves within 

 the range of velocities used in the experiments, and would move with just the 

 same resistance as if the boundary were replaced by a rigid bottom (the depth 

 of the surface-layer being more than the vessel's draught). When the spec, 

 g. of the salt-water is sufficiently increased, the resistance at a given velocity 

 will diminish towards this limit. The resistance-curve in 5 cm. of homogeneous 

 water should consequently be something like the dotted curve in Fig. 1 PI. XI 

 — or perhaps it should approximate somewhat more nearly, to the curve for 

 salt-water P160 — *. e. the resistance should be somewhat more than twice 

 the resistance in deep homogeneous water. 



In conclusion, the resistance in "dead-water" may be subdivided in 

 various ways. The difference between the resistance in "dead-water" and in 

 homogeneous deep water, is the above mentioned "dead-water resistance". 



1 In experiment 155, only very slight diverging waves could be seen through the clear 

 fresh-water from above. In experiment 157 they were very beautiful, and very low 

 transverse waves could also be detected although with difficulty. Only when the 

 velocity was at least 12 cm. per second (experiment 159), were the waves large enough 

 to be seen from the side of the tank. 



2 The wave-making resistance might of course, increase, with the difference of spec, 

 gravity although the wave-height decreases; because the wave-energy is proportional 

 to the difference of spec gravity. The latter circumstance is however, insufficient to 

 balance the effect of the largely decreased wave-height. It follows from the rule p. 

 52 that the wave-making resistance (or the dead-water resistance) will increase with 

 decreasing difference of spec, gravity, if it increases according to some higher power 

 than the square, of the velocity; the curves in Fig. 1 PI. XI, show an actual increase 

 even equal to the sixth power of the velocity. 



