THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



AUGUST 1892, 



XVI. On the Instability of a Cylinder of Viscous Liquid under 

 Capillary Force. By Lord Rayleigh, Sec. U.S.* 



THE main outline of the theory of the instability of a long 

 cylinder of liquid is due to Plateau, who showed that if 

 the equilibrium surface r — a be slightly deformed so as to 

 become 



r = a + <x cos kz, (1) 



in which z is measured parallel to the axis, the deformation is 

 stable or unstable according as ha is greater or less than unity; 

 that is, according as the wave-length \ of the varicosity is less 

 or greater than 27ra, the circumference of the cylinder. The 

 solution of the merely statical question is, however, insufficient 

 for the application to the important problem of the disin- 

 tegration of a jet of liquid. A deformation of any wave- 

 length exceeding 2ira increases exponentially with the time 

 (e gt ) ; and what we require to know is the relation between q 

 and X. A value of X, if any, for which q is a maximum, 

 determines the mode of maximum instability; and this in 

 general tends more and more to be the actual mode of disin- 

 tegration as the initial disturbances are reduced without limit. 

 As resisting the capillary force, Plateau seems to have had 

 in view only viscosity. " Par suite des viscosites interiaure 

 et superncielle, le rapport entre la longueur normale des 

 divisions et le diametre du cylindre surpasse toujours la 

 limite de la stabilite. II se reduirait sans doute a cette limite 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 34. No. 207. Aug. 1892. L 



