Prof. Helmkoltz on Discontinuous Movements of Fluids. 341 



established for gyratory motions, the lines, and with them the 

 surfaces of gyration, can neither originate nor disappear in the 

 interior of a fluid free from friction, but that, on the contrary, 

 every line of gyration must retain the same moment of rotation 

 constant. It is further clear that the lines of gyration upon a 

 gyration surface must advance with a velocity which is the mean 

 of the velocities existing on both sides of the surface. It hence 

 follows that a surface of separation can only be elongated in that 

 direction in which the stronger of the two contiguous currents 

 in it moves. 



I sought, in the first place, for examples of persistent sur- 

 faces of separation in stationary currents which would allow 

 of integration, in order to test whether the theory gives forms of 

 currents which correspond better with experiment than when the 

 discontinuity of the motion is neglected. If a surface of sepa- 

 ration which divides flowing from still water has to remain sta- 

 tionary, the pressure along the surface must be the same in the 

 moving layer as in the stationary one ; whence it follows that 

 the taugental velocity of the particles of water throughout the 

 whole extent of the surface must be constant. So also must be 

 the density of the fictitious lines of gyration. The beginning 

 and end of such a surface can only lie at the side of the vessel, 

 or at an infinite distance. In the first case they must be tan- 

 gental to the side of the vessel, provided that the latter be con- 

 tinuously bent, because the component of the velocity perpen- 

 dicular to the side of the vessel must be equal to nothing. 



The stationary forms of the surfaces of division are distin- 

 guished, as experiment and theory alike indicate, by a remark- 

 ably high degree of alterability when subjected to the least dis- 

 turbance, so that they comport themselves in some degree like 

 bodies in unstable equilibrium. The remarkable sensitiveness to 

 sound of a cylindrical current of air impregnated with smoke has 

 already been described by Dr. Tyndall. I have verified Dr. 

 TyndalFs experiments. This is clearly a property of the surfaces 

 of separation, which is of the greatest importance in sounding 

 musical pipes. 



Theory points out that, wherever an irregularity is formed on 

 the surface of an otherwise stationary current, this must give 

 rise to a progressive spiral unrolling of the corresponding part 

 of the surface; the corresponding portion, moreover, advances 

 along the current. This endeavour towards spiral unrolling at 

 every interruption is also easily recognizable on observing the 

 currents. According to theory, a prismatic or cylindrical cur- 

 rent could be infinitely long. But in practice such a current 

 cannot be formed, because in an element which is so easily moved 

 as air it is impossible entirely to avoid small disturbances. 



