Steady and of Periodic Fluid Motion. 463 



ing it always in the direction of its motion. It will not 

 thus be brought into a state of increasing oscillation, bat the 

 work done upon it will be spent in augmenting the energy of 

 the fluid motion : so that if, after a great number of to-and- 

 fro motions of the piston with some work done on it during 

 each of them, the piston is once more brought to rest, the 

 energy of the fluid motion will be greater than in the begin- 

 ning, when it was rotating homogeneously like a solid. It 

 has still exactly the same moment of momentum and the same 

 vorticity * in every part ; and the motion is symmetrical 

 round the axis of the cylinder. Hence it is easily seen that 

 the greater energy implies the axial region of the fluid being 

 stretched axially, and so acquiring angular velocity greater 

 than the original angular velocity of the whole fluid mass. 



8. The accompanying diagram (fig. 3) represents an easily 

 performed experimental illustration, in which rotating water 

 is churned by quick up-and-down movement of a disk carried 

 on a vertical rod guided to move along the axis of the con- 

 taining-vessel which is attached to a rotating vertical shaft. 

 The kind of churning motion thus produced is very different 

 from that produced by the perforated diaphragm ; but the 

 ultimate result is so far similar, that the statement of § 7 is 

 equally applicable to the two cases. In the experiment, a 

 little air is left under the cork, in the neck of the containing- 

 vessel, to allow something to be seen of the motions of the 

 water. When the vessel has been kept rotating steadily for 

 some time with the churn-disk resting on the bottom, the sur- 

 face of the water is seen in the paraboloidal form indicated 

 (ideally) by the upper dotted curve (but of course greatly 

 distorted by the refraction of the glass) . ISTow, by finger and 

 thumb applied to the top of the rod, move smartly up and down 

 several times the churn-disk. A hollow vortex (or column of 



Motion," and now in the press for republication along with other lectures 

 and addresses in a volume of the i Nature Series.' il A little wooden 

 ball, which when thrust down under still water jumped up again in a 

 moment, remained down as if imbedded in jelly when the water was caused 

 to rotate rapidly, and sprang back as if the water had elasticity like that 

 of jelly when it was struck by a stiff wire pushed down through the 

 centre of the cork by which the glass vessel containing the water was 

 filled.'' 



* The vorticity of an infinitesimal volume dv of fluid is the value of 

 dv . Tjj/e, where -or is its molecular rotation, and e the ratio of the distance 

 between two of its particles in the axis of rotation at the time considered, 

 to the distance between the same two particles at a particular time of 

 reference. The amount of the vorticity thus defined for any part of a 

 moving fluid depends on the time of reference chosen. Helmholtz's fun- 

 damental theorem of vortex motion proves it to be constant throughout 

 all time for every small portion of an inviscid fluid. 



