  In 1982, in his classical work, L. Rayleigh considered the instability of a
cylinder of viscous liquid under capillary force, the so-called
Plateau-Rayleigh instability. In this work, in linear approximation, he
obtained a dispersion equation describing the increment of this instability as
a function of wavelength, the radius of cylinder, the mass density, surface
tension, and viscosity of the liquid. Hundreds of authors referred to this
work, but none of them used his dispersion equation in its complete form; they
used only the asymptotic solutions of his equation for zero and infinitely
large viscousities. A reason for this is, probably, that Rayleigh's writing is
very difficult and his dispersion equation is quite complex. Then, in 1961, S
Chandrasekhar, in his monograph, also considered the stability of a viscous
cylindrical jet and obtained his dispersion equation which is also quite
complex and differs from the one obtained by Rayleigh. As in the case of
Rayleigh's dispersion equation, other works use only the asymptotic solution of
Chandrasekhar's equation that corresponds to the case where the viscosity is
very large in comparison to inertia. In this paper, I demonstrate that
Chandrasekhar's dispersion equation is equivalent to Rayleigh's and then
simplify their dispersion equations to a form which can be easily solved
numerically for arbitrary values of viscosity. I also present Mathematica code
to calculate the maximum increment of the Plateau-Rayleigh instability for
given parameters of the jet. To illustrate how the code works, I apply it to a
cylindrical jet to estimate its breakup.
