73] DISCONTINUOUS MOTIONS. 101 



Everything being at rest to begin with, let a slowly increasing 

 velocity be communicated to the plug P, so that (for simplicity) 

 the motion at any instant may be regarded as approximately 



steady. At first, provided a sufficient force be applied to Q, a 

 continuous motion of the kind indicated in the diagram on p. 83 

 will be produced in the fluid, there being in fact only one type of 

 motion consistent with the conditions of the question. As the 

 acceleration of the piston P proceeds, the pressure on Q may 

 become enormous, even with very moderate velocities of P, and if 

 Q be allowed to yield, an annular cavity will be formed at each end 

 of the tube. 



The further course of the motion in such a case has not 

 yet been worked out from a theoretical stand-point. In actual 

 liquids the problem is modified by viscosity, which prevents any 

 slipping of the fluid immediately in contact with the tube, and 

 must further exercise a considerable influence on such rapid 

 differential motions of the fluid as are here in question. 



As a matter of fact, the observed motions of fluids are often 

 found to deviate very widely from the types shewn in our dia 

 grams. In such a case as we have just described, the fluid issuing 

 from the mouth of the tube does not immediately spread out in 

 all directions, but forms, at all events for some distance, a more or 

 sb compact stream, bounded on all sides by fluid nearly at rest. 



