PAPER BY PROF. OBERBECK. 141 



If v is a discontinuous function of x, then at such a locality the dif- 

 ferential quotient will be indefinitely large. Therefore two neighbor- 

 ing portions would exert an indefinitely great influence upon each other. 

 If therefore one of the fluid portions is at rest while a neighboring por- 

 tion that belongs to the jet flows by the first with a constant velocity 

 communicated to it by some exterior influence, then the first or quiet 

 particle must immediately begin to take part in the movement of the 

 second, but the second on the other hand must begin to lose a definite 

 fractional part of its velocity. The jet must therefore rapidly set the 

 surrounding quiet fluid in motion with it. It would according to this 

 appear to be doubtful whether sharply defined jets such as are de- 

 manded by the above-mentioned theory of Helmholtz could be formed 

 in a fluid subject to viscosity. 



The few experiments made hitherto upon this question appear to con- 

 firm this suspicion. Especially notable is an investigation by Magnus 

 (Poggeudovf£ Annalen, lxxx, pp. 1-40), who allowed pure water to flow 

 from a cylindrical opening into a weak solution of salt and, by means 

 of a glass tube drawn out into a fine point, led away a small quantity 

 of the inflowing water in the neighborhood of the opening. The liquid 

 thus caught was examined as to its salinity. From the latter one could 

 calculate to what extent the inflowing liquid had besome mixed with 

 that which was previously in the vessel. It resulted that pure water 

 could not be caught at any point of the inflowing liquid; that therefore 

 everywhere the original quiet liquid was carried along with the mov- 

 ing liquid. 



The analogous case of jets of air and of smoke, as also that of the 

 free jets of water in the air, demonstrates that in all these, we have to do 

 with phenonena of very slight stability. It is well known how sensi- 

 tive such jets frequently are with respect to the feeble periodic disturb- 

 ances produced by waves of sound.* 



It seemed to me therefore of interest to investigate more accurately 

 the formation of water jets in water and therein to utilize a method that 

 allows of following the course of the phenomena of motion better than 

 was possible in the experiments of Magnus. This object is most simply 

 attained in that we allow feebly tinted water to flow into colorless water. 

 Fuchsiu is used as coloring material. It is well known that with a very 

 small quantity of this material an intense red color is produced with no 

 fear lest hereby the specific gravity of the water be essentially changed. 

 In the first experiments performed with this it resulted that the jet of 

 colored liquid broke up at a very slight distance from the orifice into 

 reddish clouds and drops that mixed with the quiet liquid and carried 

 it along with them. By further investigation however, it became pos- 

 sible to determine conditions under which real jets of considerable 

 length and sharp boundaries were formed. Th ese were of gr eat sta- 



* See John Tyndall on Son^dTpp. 289-292 of the German edition edited by Helm- 

 holtz and Wiedemann, Brunswick, 18(59. 



