4G4 Stability of Steady and of Periodic Fluid Motion. 



air bounded by water) , ending irregularly a little above the disk, 

 is seen to dart down from the neck of the vessel. If, now, the 



Fig. 3. 



churn-disk is held at rest in any position, the ragged lower 

 end of the air-tube becomes rounded and drawn up, the free 

 surface of the water taking a succession of shapes, like that 

 indicated by the lower dotted curve, until after a few seconds 

 (or about a quarter of a minute) it becomes steady in the 

 paraboloidal shape indicated by the upper dotted curve. 



9. We have supposed the piston brought to rest after having 

 done work upon the fluid during a vast but finite number of 

 to-and-fro motions. But if left to itself it will not remain at 

 rest ; it will get into a state of irregular oscillation, due to 

 superposition of oscillations of the fluid according to an infi- 

 nite number of fundamental modes, of the kind investigated 

 in my article " Vibrations of a Columnar Vortex," Proc. Roy. 

 Soc. Edinb., March 1, 1880, but not, as there, limited to being 

 infinitesimal ! If the motion of the piston be viscously resisted 

 these vibrations will be gradually calmed down ; and if time 

 enough is allowed, the whole energy that has been imparted 

 to the liquid by the work done on the pistons will be lost, and 

 it will again be rotating uniformly like a solid, as it was in 

 the beginning. 



[To be continued.] 





