(58 MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



Section V. — On the Nature of the Increased Resistance experienced at Velocities 



less than that of the Warn. 



From the great change that is effected on the form of the fluid by the mo- 

 tion of a floating body with a velocity less than that of the wave, it is now 

 very obvious that a vessel placed behind the wave, is in circumstances exceed- 

 ingly different from the hypothetical condition of being drawn in a horizontal 

 position along the surface of a level quiescent fluid. The prow of the vessel 

 is pressed into the anterior wave, the stem is depressed into the hollow of the 

 wave, the keel is inclined upwards in the direction of motion, at an angle 

 amounting in some cases to 20°, an additional surface of horizontal displace- 

 ment is presented, which increases as the sine of the angle of elevation of the 

 keel. On attemp i g s ill farther to accelerate the velocity of the vessel in the 

 vicinity of that of the wave, the variations which are thus produced in the condi- 

 tion of the vessel increase still further the causes of these variations, the increased 

 immersion of the bow in the wave, augments the anterior wave formed by the 

 displacement of the fluid, and the enlarged oblique surface now presented in the 

 bottom of the vessel presses forward with increased velocity the wave on the 

 slope of which it is elevated, and increases the elevation of that slope, becoming 

 more depressed also at the stem, and giving rise to more rapid currents, and a 

 higher stern surge. In short, it appears, that increased force applied gradually 

 to the vessel for the purpose of rendering the velocity of the body equal to, or 

 greater than that of the wave, has the effect at the same time of increasing at a 

 more rapid rate the retarding forces, and a limit is soon reached, which it has in 

 many cases been found impossible to pass. It is the circumstance of the very rapid 

 increase of the resistance in approximating to the velocity of the wave, that has led 

 to the false idea that there is a final and low limit to velocity on shallow water. 

 There are circumstances in which this limit is final, the channel being very shal- 

 low, and the boat very bluff in its formation, I have seen in such an extreme case, 

 when the depth of the channel was about five feet, the channel laid bare in the 

 stern hollow behind the wave, so that the stern of the vessel no longer floated but 

 rested on the bottom, while the bow was elevated and buried in a large anterior 

 wave, rising more than two feet above the level, and overflowing the banks, and 

 the posterior wave rushed on furiously behind, roaring and foaming, tearing up 

 the banks of the channel, and threatening the destruction of the vessel, which, in- 

 deed, on stopping, it nearly accomplished. In such a case the persons in the 

 vessel were not visible fi*om the shore, being sunk in the hollow between the 

 great anterior and posterior waves. 



