222 KEPORT— 1875. 



fluid, would encounter no resistance whatever. By a perfect fluid, I mean a fluid 

 which is free from viscosity, or quasi-solidity, and in which no ixiction is caused 

 by the sliding of the particles ol the fluid past one another, or past the surface of 

 the body. 



The property which I describe as " quasi-solidity " must not be confused with 

 that which persons have in their minds when they use the term " solid water." 

 When people in this sense speak of water as being " solid," they refer to the sen- 

 mtion of solidity experienced on striking the water-surface with the hand, or to 

 the reaction encountered by an oar-blade or propeller. "What I mean by "quasi- 

 solidity," is the sort of stifl'ness which is conspicuous in tar or liquid mud ; and this 

 property undoubtedly exists in water, though in a very small degree. But the sen- 

 sation of solid reaction which is encountered by the hand or the oar-blade is not 

 in any way due to this property, but to the ineHia of the water : it is in eflect this 

 inertia which is erroneously termed solidity ; and this inertia is possessed by the 

 perfect fluid with which we are going to deal, as fully as by water. Nevertheless 

 it is true, as I am presently going to show you, that the perfect fluid would ofier 

 no resistance to a submerged body moving through it at a steady speed. It will be 

 seen that the apparent contradiction in terms which I have just advanced is cleared 

 up by the circumstance, that in the one case we are dealing with steady motion, 

 and in the other case with the initiation or gi-owth of motion. 



In the case of a completely submerged body in the midst of an ocean of perfect 

 fluid, unlimited in every direction, I need hardly argue that it is immaterial 

 whether we consider the body as moving imiformly through the ocean of fluid, or 

 the ocean of fluid as moving uniformly past the body. 



The proposition that the motion of a body through a perfect fluid is unresisted, 

 or, what is the same thing, that the motion of a perfect fluid past a body has 

 no tendency to push it in the direction in which the fluid is flowing, is a novel 

 one to many persons ; and to such it must seem exti-emely startling. It arises from 

 a general principle of fluid motion, which I shfill presently put before you in detail — 

 namely, that to cause a perfect fluid to change its condition of flow in any manner 

 whatever, and ultimately to return to its original condition of flow, does not require, 

 nay, does not admit of, the expenditure of any power, whether the fluid be caused 

 to flow in a cuin'ed path, as it must do in order to get round a stationary body 

 which stands in its way, or to flow with altered speed, as it must do in order 

 to get through the local contraction of channel which the presence of the sta- 

 tionary body practically creates. Power, it may indeed be said, is first expended, and 

 force exerted, to communicate certain motions to the fluid ; but that same power 

 will ultimately be given back, and the force counterbalanced, when the fluid yields 

 up the motion which has been communicated to it, and returns to its original con- 

 dition. 



I shall commence by illustrating the action on a small scale by fluid flowing 

 through variously shaped pipes ; and I must premise that in the greater part of 

 what I shall have to say, I shall not require to take account of absolute nydro- 

 static pressures. The flow of water through pipes is uninfluenced by the absolute 

 pressure of the water. 



I will begin with a very simple case, wliich I will treat in some detail, and 

 which will serve to show the nature of the argument I am about to submit to you. 



Suppose a rigid pipe of uniform sectional area, of the form shown in fig. 1 

 (Plate IX.), something like the form of the water-line of a vessel. 



The portions A B, B C, D, D E are supposed to be equal in length, and of 

 the same curvature, the pipe terminating at E in exactly the same straight line in 

 which it commenced at A, so that its figure is perfectly symmetric on either side 

 of C, the middle point of its length. 



Let us now assume that the pipe has a stream of perfect fluid running through 

 it from A towards E, and that the pipe is free to move bodily endways. 



It is not unnatural to assume at first sight that the tendency of the fluid would 

 be to push the pipe forward, in virtue of the opposing surfaces offered by the bends 

 in it — that both the divergence between A and C from the original line at A, and 

 the return between C and E to that line at E, would place parts of the interior 

 surface of the pipe in some manner in opposition to the stream or flow, and that the 



