INTRODUCTION. 51 



that of the waves, the effect of their generation by the floating body was to dimi- 

 nish the resistance given by the fluid, because the elevations of those waves fall- 

 ing behind those points of the body by which they had been raised, constituted an 

 accumulated wave towards the middle of the body, upon the crest of which wave, 

 poised in a position of stable equilibrium, it was borne along in a horizontal posi- 

 tion, with a diminished section of immersion at the stem and stern, and conse- 

 quently with a diminished section of resistance. 



Besides the diminution of the resistance to the floating body experienced at 

 velocities greater than that of the wave, it is also rendered apparent why there 

 should be likewise experienced a great diminution of that commotion which takes 

 place in the fluid at velocities less than that of the wave, and how it is that the 

 phenomenon of stern surge, so destructive to the banks of the channel, and so 

 dangerous in the practical navigation of shallow water, is found to disappear 

 entirely at velocities greater than that of the wave in the given depth of fluid. 



The effect of the motion of the floating body in changing the form of the fluid 

 is least when the velocity is least and greatest ; its effect is greatest when its ve- 

 locity most nearly approximates to the velocity of the wave. 



From the investigations of 1834, a form of great resistance suggested itself 

 to me. A vessel, named in the tables " The Wave," was constructed of this form. 

 This vessel was made the subject of experiment in 1835. It appears from the 

 tables, that the resistance of this vessel was much less than that of other beauti- 

 fully shaped vessels with which it was compared ; and one phenomenon which I 

 observed seems to me to estabUsh as true, that the form of this vessel does not 

 deviate widely from the form of least resistance. This tentative phenomenon seems 

 to me to demonstrate, that the motion communicated to the particles of the fluid 

 is the smallest that is consistent with the translation of the moving body, and it 

 is this, — that at all velocities extending up to seventeen miles an hour, no spray, 

 no heaping up of water at the stem, no lateral currents extending beyond the pre- 

 cincts occupied by the body itself, were ever sensible, but the body entering the 

 water having a smooth and glassy surface, left it unchanged and unruffled. In 

 the motion of all the other forms it was observed, that the water was thrown 

 aside at the stem of the vessel in the form of a " head and feather" of spray, and 

 that "broken water" extended to a distance even among the particles considera- 

 bly removed from the line of the vessel's motion. The equation to the curve of 

 least resistance was found by supposing the lateral motion given to a particle of 

 the fluid, to receive equal increments in equal times from zero to a given maxi- 

 mum of velocity, after which, by equal decrements in equal times, it should again 

 be brought to rest at the required distance from its original position in the place 

 necessary to permit the transit of the greatest diameter of the immersed body. 

 The curve thus obtained is concave outwards at the stem, and becomes convex 



