70 EKMA N. ON DEAD-WATER. [norw. pol. EXP. 



The photographs PI. XIV, which were taken in the small tank, do not 

 represent very well, the waves behind the vessel, which are on the other hand, 

 better seen in PI. XV— XVII. Fig. 3, PI. XVI, shows the moment when the 

 waves begin to break; the velocity is just a minimum, and has dropped from 

 its maximum 9 - 4 cm. per second to 4-6 cm. per second (see diagram 81, PI. VII). 

 A few seconds after the photograph was taken, the boat had its speed acceler- 

 ated again ; and if the length of the tank had allowed it, the same phenomena 

 should have taken place once more. 



The whole process took place in just the same way, whether the boat reached 

 down into the salt-water or not. Even if the fresh-water reached so much as 

 2 cm. below the keel of the boat-model, the oscillations in the velocity were 

 rather great (see diagrams 103—106, PL VIII). Figs. 1—3, PI. XVII, show 

 that the waves were, at the same time, very considerable. (The three last- 

 mentioned figures show the situation of the waves just after the velocity had 

 been a minimum: before the minimum was attained, the elevation of the 

 boundary, which is now seen under the keel of the boat, had a position more 

 astern). 



If different velocity-diagrams be compared, it will be seen that the oscill- 

 ations take place more slowly, the smaller is the difference of spec, gravity 

 between the two water-layers. Compare, for instance, the diagrams 134 and 141 

 (difference of spec, gravity 0"01 and - 02, respectively), 77 — 81 (difference of 

 spec, gravity 0-032), 148—150 (difference of spec, gravity 0-07), and 160—162 

 (difference of spec, gravity 0*16). Indeed, according to the rule, p. 52, the 

 period of the oscillations should alter inversely as the square root of the dif- 

 ference of spec, gravity, if, at the same time, the towing force were altered in 

 the same ratio as this latter. This rule is approximately verified by experi- 

 ments 141, 79, 149, and 161, in which the towing-forces stand to each other 

 approximately as the differences of spec, gravity. 



The amplitude of the oscillations, relative to the mean velocity, seems 

 on the whole to be just as great when the difference of spec, gravity is 0"032, 

 as when it is 0'16 (see diagrams 77—81 and 160—162). This fact will be 

 made use of, later. 



Some important conclusions regarding wave-making resistance may be 

 drawn from the above-described phenomena. They show that the corre- 

 sponding changes of the waves and the resistance, do not take place simid- 



