146 Lord Rayleigh on the Instability of a Cylinder 



meme si le liquide etait exempt de toute viscosite"*. In the 

 case of jets composed of liquids such as water, the influence 

 of viscosity might be expected to be small, but it would be 

 erroneous to conclude that the limit ka = 1 would then corre- 

 spond to the mode of maximum instability. Inertia would 

 necessarily play a leading part, and from a complete investi- 

 gation t it appears that the mode of maximum instability 

 corresponds with X=4*51x2a, exceeding very considerably 

 the circumference of the cylinder. 



The importance attached by Plateau to viscosity suggested 

 an investigation in which this property should be included ; 

 and the results would at any rate find application to threads 

 of materials like glass and sealing-wax, in which viscosity 

 would predominate over inertia. Having in my mind some 

 old experiments upon the behaviour of fine threads of treacle 

 deposited upon paper, which slowly resolve themselves into 

 drops having a very similar appearance to those obtained 

 from a jet of water, I rather expected to find that under the 

 influence of viscosity alone the mode of resolution would be 

 nearly the same as under the influence of inertia alone. This 

 anticipation proved to be wide of the mark, the result showing 

 that under viscosity alone the value of X for maximum insta- 

 bility would be very great. And a little consideration shows 

 that the retarding forces exerted by the paper support may well 

 be of quite a different character from those due to mere fluid 

 viscosity. In the latter case the gathering together from con- 

 siderable distances is but little resisted, the motion not differing 

 greatly from that of a solid body, whereas such a mode of 

 resolution would be greatly impeded by the contact with 

 paper. In order better to represent such contact forces, 1 

 have considered the problem in the form which it assumes 

 when the resistances are proportional to the absolute velocities 

 of the parts. This admits of easy solution, and the result 

 illustrates the behaviour of the thread of treacle in contact 

 with paper, and shows that there is a marked difference between 

 this case and that of a thread whose disintegration is resisted 

 by true fluid viscosity. 



The introduction of resistances proportional to absolute 

 velocities does not interfere with the irrotational character of 

 the motion of otherwise frictionless fluid J. The radial and 

 axial velocities u, iv may thus, as usual, be regarded as derived 

 from a velocity-potential according to the equation 



* Statique e.rperimentale et theorique des liquides soumis aux seules 

 forces moleculaires, 1873, vol. ii. p. 231. 



t Proc. Math. Soc. November 1878. See also below. 

 % < Theory of Sound,' vol. ii. § 239 (1878). 



