no. 15.] EMPIRICAL LAWS OF RESISTANCE. 121 



45 per cent of the rest, or approximately, to the whole resistance less 55 per cent of the 

 shallow homogeneous-water resistance. The whole resistance may be assumed equal to the 

 towing force found in the 6th column of the table p. 119. The "shallow homogeneous-water 

 resistance" is, in experiments 3—6, easily found by means of the velocity given in the 

 table, and the dotted curve in Fig. 1 PI. XI. For experiments 8 and 9 it may be found 

 in the same way, if a curve corresponding to the dotted curve Fig. 1 PI. XI be drawn by 

 using the experiment 126—132. In that way, the pressure-resultants found in the 13th 

 column of the table p. 119 were calculated. They agree, as well as could be expected, with 

 the values in the 12th column, found from the observations of surface-disturbances. (It 

 may be pointed out here, that if in [he calculation of the former values the entire 

 resistance be not assumed equal to the towing force but be determined according to the 

 resistance-curves in Fig. 1 PI. XI and Fig. 1 PI. X, from the velocity, the agreement with 

 the values in the 12th column will be found almost exact). In this agreement we have a 

 sort of control upon the correctness of the explanation of the dead-water resistance. 



The influence of the depth of the fresh-water layer. 



Owing to the simple connection between the difference of spec, gravity 

 of the water-layers and the dead-water resistance, it was not necessary in 

 what follows to vary the specific gravity of the salt-water. This was therefore 

 the same in most of the experiments, namely l - 030. 



Fig. 1 PI. X shows the resistance-curves for the larger -FVaw-model in a 

 fresh-water layer of 1, 3, 5, 7, 9, and 13 centimetres' depth, as well as in 

 homogeneous water. The velocities are plotted horizontally in cm./second, 

 and the resistances vertically in grammes. The influence of the fresh-water layer 

 upon the resistance, decreases, as might a priori be expected, when its depth 

 becomes either very small or very great. It is (at most velocities) greatest, 

 when the fresh-water is 4 or 5 cm. deep ' , i. e. about the same as the draught 

 of the boat; a smaller as well as a deeper fresh-water layer causes a smaller 

 resistance. It is easy to find a plausible explanation of this latter fact. On 

 the one hand, the wave-making power of the boat, is smaller, the farther the 

 latter is from the boundary where the waves are generated, and on the other 

 hand, its wave-making power will be diminished, if it reaches into the salt- 

 water, since that part which is below the boundary and that above it, coun- 

 teract oneanother. Furthermore, if the depth of the surface-layer is small, it 

 will put a limit to the height of the waves which can be generated, and con- 

 sequently to the wave-making resistance. 



To keep the figure clear, the curve for fresh-water 40 cm., is omitted. It may easily 

 be drawn from the numbers in the table (p. 79). The maximum resistance is found 

 to be 2'2 grammes. 



16 



