A general theorem concerning the stability of a particular non-Newtonian fluid

It is the intention of the present paper to prove a theorem concerning the stability of a particular non-Newtonian fluid suggested to the author by Professor R. S. Rivlin of Brown University. The method used in proving this theorem is similar to that employed by H. Schlichting in his proof of a similar theorem for an inviscid fluid which was originally established by Lord Rayleigh. The acceleration gradients introduced by the non-Newtonian fluid model into the constitutive equations are found to alter the stability criterion set forth by Rayleigh for an inviscid fluid.