1879.] 



the Capillary Phenomena of Jets. 



83 



operative in these experiments was somewhat less than that deter- 

 mined by Quincke for distilled water. 



When the pressures are small, the wave-lengths are no longer con- 

 siderable in comparison with the diameter of the jet, and the vibra- 

 tions cannot be supposed to take place sensibly in two dimensions. 

 The frequency of vibration then becomes itself a function of the 

 wave-length. This question is investigated mathematically in 

 Appendix I. For the case of w=4, it is proved that approximately 



r= M 1+ w> 



Hence for the aperture of Table VII, 



\ocV7z (1--088X" 2 ), 



X being: expressed in centimetres. The numbers in the fourth column 

 of the table are calculated according to this formula. 



On the other hand at high pressures the frequency becomes a 

 function of the pressure. Since frequency is always an even function 

 of amplitude, and in the present application, the square of the 

 amplitude varies as h, the wave-length is given approximately by an 

 expression of the form s/h (M+N&), where M and N are constants. 

 It appears from experiment, and might, I think, have been expected, 

 that frequency diminishes as amplitude increases, so that N" is positive. 



When the aperture has the form of an exact circle, and when the 

 flow of fluid in its neighbourhood is unimpeded by obstacles, there is 

 a perfect balance of lateral motions and pressures, and consequently 

 nothing to render the jet in its future course unsymmetrical. Even in 

 this case, however, the phenomena are profoundly modified by the 

 operation of the capillary force. Far from retaining the cylindrical 

 form unimpaired, the jet rapidly resolves itself in a more or less 

 regnlar manner into detached masses. It has, in fact, been shown by 

 Plateau,* both from theory and experiment, that in consequence of 

 surface-tension the cylinder is an unstable form of equilibrium, when 

 its length exceeds its circumference. 



The circumstances attending the resolution of a cylindrical jet into 

 drops have been admirably examined and described by Savart,f and 

 for the most part explained with great sagacity by Plateau. There 

 are, however, a few points which appear not to have been adequately 

 treated hitherto ; and in order to explain myself more effectually 



* " Statique Experimentale et Theorique des Liquides soumis aux seules Forces 

 Moleculaires." Paris, 1873. 



t " Memoire sur la Constitution des Yeines Liquides lancges par des Orifices 

 Circulaires en mince paroi." Ann. d. Chini., t, liii, 1S33. 



G2 



