558 XL HYDRODYNAMICS. 



which is infinite when t = 0, - = = 0, as we supposed, but which 



immediately drops to a finite value, and, no matter what the value 

 of y, immediately acquires values different from zero. Thus the 



Fig. 172. 



vorticity, originally confined within the infinitely thin sheet of dis- 

 continuity, is instantaneously distributed throughout the liquid, as 



shown in Fig. 172, for the times -^9 > > 1, 4 times Thus we 



see how discontinuities of the sort shown in Fig. 166 are impossible 

 in nature, being replaced by the formation of eddies. 



