118 EKMAN. ON DEAD-WATER. [NORW. POL. EXP. 



It is due to the wave-making as well as to the effect of shallowness. The 

 latter part of the resistance depends on the water's diminished passage past 

 the vessel; it is at the lowest velocities, approximately represented by the 

 vertical distance between the dotted curve and the lower continuous curve, in 

 Fig. 1 PI. XI. At higher velocities, it is smaller than this, and at velocities 

 greater than the maximum wave-velocity, it practically disappears altogether. 

 That it does so is obvious, because the entire dead-water resistance vanishes; 

 the physical reasons for it are indicated in Chap. II, p. 47. The resistance 

 represented by the dotted curve, may be called "shallow homogeneous-water 

 resistance". At below the critical velocity the resistance may be divided into 

 two parts, of which the one is approximately equal to the "shallow homoge- 

 neous-water resistance", and the other is the "wave-making resistance" due 

 to boundary-waves. According to the arguments brought forward in Chap. 

 II (p. 47), the resistance in homogeneous deep water, as well as the resistance 

 due to shallowness, depends partly on friction and partly on pressure, while 

 the wave-making resistance depends essentially only on the latter. 



The relationship between the different curves in Fig. 1, PL XI, shows 

 clearly and conclusively that the greatest part of the dead-water resistance, 

 is due to wave-making. From the measurements of surface-disturbance (see 

 p. 66 and the diagrams PI. IX) we are able to approximately calculate the 

 pressure at different points. The pressure-resultants against the boat-model, 

 calculated in this way are in complete agreement with the above estimation 

 of the different parts of the resistance and their causes; and although this 

 calculation cannot be more than a first approximation, it may therefore be of 

 interest to cite it here. 



The table on the next page contains the chief results of the measurements of surface- 

 disturbance. The experiments were made with the larger from-model. The numbers in 

 the 1st column, refer to the corresponding numbers of the diagrams in Fig. 3 PI. IX. The 

 2nd— 6th columns have the same signification as the 3rd— 7th columns in the tables p. 77. 

 The 7th column gives the final velocity, or if there were velocity-oscillations, the mean towards 

 which it approximated. The 8th column gives the greatest difference of level of the water- 

 surface, measured on the original drawings, which are copied in PI. IX. 



If the waves were moving freely, solely on account of gravity and the inertia of the 

 water, it should be possible to calculate the ratio between the wave-heights at the surface 

 and in the boundary, according to equation (1) p. 42; in this case the moving forces are 

 concentrated in the neighbourhood of the salt-water fresh-water boundary. Actually how- 

 ever, the waves nearest to the vessel, are forced ; and the moving forces are to a certain 

 extent distributed over the vessel's surface, i. e. in the middle of the surface-layer. In 

 this case it is obvious that the corresponding equation for long waves (2, p. 42) gives a 

 better approximation ; the 9th column gives the greatest difference of level in the boundary, 



