Prof. Helmlioltz on Discontinuous Movements of Fluids, 339 



become negative, and the fluid must be torn apart. At such a 

 place the accelerating force which is proportional to the differ- 

 ential coefficient of the pressure becomes, of course, discontinuous, 

 and consequently the condition is fulfilled which is necessary to 

 bring about a discontinuous motion in the fluid. The motion 

 of the fluid in passing by such a place must be of such a nature 

 that a surface of separation is there formed. 



The velocity necessary to bring about the rupture of the fluid 

 is that which the fluid would assume if it were to flow into 

 vacuum under the pressure which the fluid would have at the 

 same place when at rest. This is certainly a comparatively con- 

 siderable velocity ; but we must bear in mind that if fluids are 

 to flow continuously like electricity, the velocity at every sharp 

 edge around which the current turns must be infinitely great*. 

 It consequently follows that every perfect geometrically sharp edge 

 by which a fluid flows must tear it asunder and establish a surface 

 of separation, however slowly the rest of the liquid may move. 

 When the edges are imperfectly formed, and rounded, such a 

 separation requires a certain increased velocity. Pointed projec- 

 tions on the side of the orifice must act in the same manner. 



In regard to gases, the same condition obtains with them as 

 with liquids, with the exception that the vis viva of the motion 

 of a particle is not directly proportional to the diminution of the 

 pressure^, but to the quantity p m , where, taking into account 



the cooling of the air by expansion, m = l , 7 being the ratio 



between the specific heat with constant pressure and that with con- 

 stant volume. For atmospheric air, the exponent m has the value 

 0*291. Since this is positive and real, p m and p can only decrease 

 to nothing, and not become negative as the velocity becomes high. 

 It would be otherwise if gases simply followed Mariotte's law, 

 and. did not suffer any change of temperature. The value logjo 

 would then enter instead of p m ; and this value may become in- 

 finite and negative without p becoming negative. Under this 

 condition, a tearing asunder of the mass of air would not be 

 necessary. 



We may satisfy ourselves of the actual existence of such dis- 

 continuities by allowing a stream of air impregnated with smoke 

 to flow through a round hole or cylindrical tube with mode- 

 rate velocity so that no hissing ensues. Under favourable cir- 

 cumstances thin streams may in this way be obtained of a line 

 in diameter and several feet long. Within the cylindrical 



* At the very small distance £ from a sharp edge the faces of which are 



inclined at an angle a, the velocity becomes infinite with g~ m , where 



or — x 

 m=z - . 



Z7T — CC 



Z2 



