PAPER BY PROF. OBERBECK. 



143 



a small excess of pressure into the quiescent liquid. I therefore begin 

 with a description of the experiments relative to this. 



If we allow the stop-cock to be opened for only a short time, then 

 even with the smallest differences of pressure of two or three milli- 

 metres, a sharply defined mass of liquid penetrates into the quiescent 

 liquid. The original form of this mass is soon modified by viscosity 

 and by the participation of the hitherto quiet liquid in its motion, in a 

 peculiar manner, and finally it rolls itself into a ring. The colored mass 

 of liquid goes through the series of forms presented in Figs. 10, 11, 

 12. and 13. Of these drawings, as of most of the following ones, it is to 

 be noted that they represent a section of the mass of liquid by a plane 

 that passes through the axis of symmetry of the formation. In order 

 to find the true form therefore, one must imagine the figure revolved 

 about this axis. 



Q 



Fin-. 12. 



Fis- 10. Fig. 11. 



With the form of Fig. 13, the ring formation is completed. More- 

 over in general even for differences of pressure of 10 to 20 millimetres, 

 the living force of the liquid was consumed so that this figure long- 

 floated motionless in the colorless liquid. 



If we use somewhat larger differences of pressure we observe that 

 the liquid within the ring continues rotating for a longer time. The 

 original progressive movement has therefore been transformed into a 

 vortex movement. The vortex movements have been theoretically 

 treated by Helmholtz* and he has in the introduction to his memoir 

 referrtd to the necessity of the transformation of any current or move- 

 ment that has a velocity potential into a vortex movement in conse- 

 quence of viscosity. 



Many other consequences drawn by Helmholtz in his memoir just 

 referred to can be easily observed by the help of the apparatus used 

 by the present writer. 



*Crelle's Journal lv. pp. '25-56, [and No. II of this collection of Translations. ] 



