1879.] 



the Capillary Phenomena of Jets. 



73 



of thin sheets, whose planes are perpendicular to the sides of the 

 polygon. 



Bidone explains the formation of these sheets, in the main (as it 

 appears to me), satisfactorily, by reference to simpler cases of meeting- 

 streams. Tims equal jets, moving in the same straight line, with equal 

 and opposite velocities, flatten themselves into a disk, situated in the 

 perpendicular plane. If the axes of the jets intersect obliquely, a 

 sheet is formed symmetrically in the plane perpendicular to that of the 

 impinging jets. Those portions of a jet which proceed from the out- 

 lying parts of an unsymmetrical orifice are considered to behave, in 

 some degree, like independent meeting streams.. 



In many cases, more especially when the orifices are small and the 

 heads of water low, the extension of the sheets in directions perpen- 

 dicular to the jet reaches a limit. Sections taken at greater distances 

 from the orifice show a gradual shortening of the sheets, until a com- 

 pact form is attained, similar to that at the first contraction. Beyond 

 this point, if the jet retains its coherence,, sheets are gradually thrown 

 out again, but in directions bisecting the angles between the directions 

 of the former sheets. These sheets may, in their turn, reach a limit 

 of development,, again contract, and so on. The forms assumed in 

 the case of orifices of various shapes, including the rectangle, the 

 equilateral triangle, and the square, have* been carefully investigated 

 and figured by Magnus.* Phenomena of this kind are of every- day 

 occurrence, and may generally be observed whenever liquid falls from 

 the lip of a moderately elevated vessel. 



Admitting the substantial accuracy of Bidone's explanation of the 

 formation and primary expansion of the sheets or excrescences, we 

 have to inquire into the cause of the subsequent contraction. Bidone 

 attributes it to the viscosity of the fluid, which may certainly be put 

 out of the question. In Magnus's view the cause is " cohesion ;" but 

 he does not explain what is to be understood under this designation, 

 and it is doubtful whether he had a clear idea upon the subject. The 

 true explanation appears to have been first given by Buff,f who refers 

 the phenomenon distinctly to the capillary force. Under the operation 

 of this force the fluid behaves as if enclosed in an envelope of constant 

 tension, and the recurrent form of the jet is due to vibrations of the 

 fluid column about the circular figure of equilibrium, superposed upon 

 the general progressive motion. Since the phase of vibration depends 

 upon the time elapsed, it is always the same at the same point in space, 

 and thus the motion is steady in the hydro-dynamical sense, and the 

 boundary of the jet is a fixed surface. 



In so far as the vibrations may be considered to be isochronous, the 



* " Hydraulische UntersucTxungen." " Pogg. Ann.," xcv, 1855. 

 f " Pogg. Ann.," Bd. c, 1857. 



