go MR RUSSELL'S RESEARCHES IN HYDRODYNAMICS. 



fluid itself by the motion of the floating body. At this part of the inquiry I dis- 

 covered phenomena of a most singular character, by means of which the resolu- 

 tion of the anomalies in resistance has been most successfully effected, and which 

 gives to many of the facts of practical experience a satisfactory explanation, and 

 points the way to many important improvements in the construction of vessels, 

 the navigation of rivers and shallows, inland navigation, and other departments 

 of hydrodynamical engineering. These phenomena arise from the generation and 

 propagation of Waves of the fluid b}^ the motion of the floating body. 



It has appeared, in the course of these investigations, that the restoration of 

 equilibrium among the particles of the fluid when it has been deranged by the 

 motion of a floating body, is effected, not so much by means of the generation of 

 currents in the fluid, as has hitherto been generally assumed, as by means of 

 the generation of waves of the fluid, in which form the elevations of the fluid 

 raised on the front of the moving body are propagated with an ascertained velo- 

 city in the direction of the motion of the disturbing body. It appears that these 

 waves move with a velocity that is nearly uniform, — that they travel to very 

 great distances, — ^that then* velocity is not in any degree connected Avith the form 

 of the vessel, — that their velocity is not at all dependent on the velocity of the 

 body which generates them, — that their velocity is due alone to the depth of the 

 fluid, being equal to the velocity acquired by a body falling in vacuo through a 

 space equal to half the depth of the given fluid, — and that the height of the wave 

 itself above the fluid will only increase its velocity by so much as it increases the 

 depth of the fluid at that point, reckoning from the summit of the wave. 



I next proceeded to examine the nature of the interference of such waves, so 

 as to determine their effect in modifying the resistance of the fluid to the motion 

 of the body giving rise to them. I found immediately that the point of first 

 maximum of resistance coincides accurately with the point at which the velocity 

 of the motion of the floating body becomes equal to the velocity of the motion of 

 the propagated waves. It appeared further, that the effect of the formation of 

 these waves, when the velocity of the solid was less than the velocity of the waves, 

 was to send forward towards the anterior part of the solid an accumulation of 

 successive waves (to which accumulation I have given the name of the anterior 

 wave), and to create a posterior depression in that part of the fluid from which 

 these waves had been sent out, and thus to change the form of the surface of the 

 fluid in such a manner that the axis of the floating body, formerly horizontal, 

 no longer remained so, but was elevated anteriorly and depressed posteriorly, so 

 as to form a considerable angle of inclination, and greatly increase the anterior 

 section of displacement of the solid, whereby, at velocities less than the velocity 

 of the wave, a very rapid increase of resistance was experienced in approximating 

 to that velocity. It appeared, on the other hand, that at velocities greater than 



