Steady and of Periodic Fluid Motion. 



461 



rotation in each part will change in direction so as to keep 

 along the changing direction of the same line of fluid par- 

 ticles ; and its magnitude will change in inverse simple pro- 

 portion to the distance between two particles in the line of the 

 axis. 



5. But, now, to simplify subsequent operations to the utmost, 

 suppose that anyhow, by quick motion or by slow motion, the 

 containing-vessel be changed to a circular cylinder with per- 

 forated diaphragm and two pistons, as shown in fig. 1. In 

 the present circumstances the motion of the liquid may be 

 supposed to have any degree of complexity of molecular rota- 

 tion throughout. It might chance to have no moment of 

 momentum round the axis of the cylinder, but we shall sup- 

 pose this not to be the case. If it did chance to be the case 

 (which could be discovered by external tests), a motion of the 

 cylinder, round a diameter, to a fresh position of rest would 

 leave it with moment of momentum of the internal fluid round 

 the axis of the cylinder. Without further preface, however, 

 we shall suppose the cylinder to be given, with the pistons as 

 in fig. 1, containing fluid in an exceedingly irregular state of 

 motion, but with a given moment of momentum M round the 

 axis of the cylinder. The cylinder itself is to be held absolutely 

 fixed, and therefore whatever we do to the pistons we cannot 

 alter the whole moment of momentum of the fluid round the 

 axis of the cylinder. 



6. Suppose, now, the piston A to be temporarily fixed in 

 its middle position C C, and the 

 whole containing-vessel of cylinder 

 and pistons to be mounted on a 

 frictionless pivot, so as to be free to 

 turn round AA / the axis of the 

 cylinder. If the vessel be of ideally 

 rigid material, and if its inner sur- 

 face be an exact figure of revolu- 

 tion, it will, though left free to turn, 

 remain at rest, because the pressure 

 of the fluid on it is everywhere in 

 plane with the axis. But now, in- 

 stead of being ideally rigid, let the 

 vessel be of natural viscous-elastic 

 solid material. The unsteadiness 

 of the internal fluid motion will cause deformations of the 

 containing-solid with loss of energy, and the result finally 

 approximated to more and more nearly as time advances is 

 necessarily the one determinate condition of minimum energy 

 with the given moment of momentum ; which, as is well 



Fig. 1. 



