70 MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



resistance derived from them, and it will also appear that the new arrangement 

 of the particles of the displaced fluid renders the wave an element of diminished 

 resistance. By how much, in fact, the wave was at a lower velocity, a + ele- 

 ment of resistance will it now act as a — element of resistance. 



Let it now be supposed that the vessel had created by its motion an anterior 

 wave, and let it be supposed possible to lift the vessel entirely out of the water, 

 and place its centre on the top of the Avave, the stem being anterior to the wave, 

 and the stern behind it, and suppose the vessel to be of such a form as to remain 

 in a position of stable equilibrium on the surface of a fluid having the form of the 

 wave, and suppose such a velocity to be given to the vessel as to keep it in the 

 same relative position to the wave, then the following results would be obtained. 



(1.) The vessel would be permitted to recover the horizontal position, and would 

 present the minimum transverse section of resistance. 



(2.) The immersion of the vessel being . increased by the height of the crest 

 of the wave around its centre of gi-avity, the anterior and stern displacements 

 would be diminished, the total immersion being a constant quantity, by the amount 

 of excessive central displacement. 



(3.) The velocity of the vessel being now increased beyond that of the wave, 

 the waves of displaced fluid falUng continually behind the points where they were 

 raised, would fonn a continued series of great central waves, bearing the vessel 

 up upon then- summit. 



Such are precisely the circumstances of a vessel moving with a velocity greater 

 than that of the wave, as shewn in section in the following illustration. 



Fig. 7. — Behind the Wave. 



Fig. 8. — Upon Ihe Wave. 



But it wiU be inquired, how is a vessel to be placed in such circumstances ? 

 How is the extreme resistance of the anterior wave to be vanquished, and the 

 vessel planted on its summit ? This is admitted to be a practical problem, often of 

 extreme difficulty ; sometimes it is impracticable. There are some forms of vessel 

 that do not admit of a position of stable equilibrium on the top of a wave. Still, 



