Consideration is given to the steady flow of a micropolar liquid near a rigid boundary. It is shown that while micro-inertia itself is not important, nevertheless, some properties of the microstructure do play a vital rôle in determining the structure of the boundary layer. The Kármán—Polhausen method is used to provide an estimate of the shear stress at the boundary, and detailed calculations are given for flow near stagnation. The important significance of the standard length of the micropolar liquid is demonstrated for this flow, as for other flows in this medium.

In a recent paper (1), Paria has discussed the propagation through a solid of a certain type of magneto-thermo-elastic plane wave. The analysis is essentially a reconciliation of the equations governing three fields: the electromagnetic field, the thermal field and the elastic field, which interact one with another. The principal result which was obtained was the dispersion equation connecting the frequency and the wavelength of waves of this type.

The propagation of magneto-elastic plane waves is a topic which has recently aroused much interest. Thus Paria ((l)), for example, and the present author ((2)), have studied in some detail the interaction between the magneto-elastic field and the thermal field. Analyses published so far, however, have neglected the effects due to the passage of the wave upon the magnetic permeability of the medium. It is the object of the present paper to consider these effects and it will be shown that although the elastic strains induced cause but a small change in the numerical values of the permeability, nevertheless the effects upon wave propagation may be very considerable. The principal result is the demonstration that the effects considered are equivalent so far as the dispersion equation is concerned, to an anisotropic rescaling of the primary magnetic field, the direction of propagation of the wave being a preferred direction. For simplicity, thermal effects are not considered here.

With the neglect of collisions, a relativistic form of Boltzmann's transport equation is derived and its invariance under a Lorentz transformation is established.

The dispersion equation describing the character of the equilibrium of two viscous incompressible superposed fluids under the action of gravity is considered in detail. Approximations for extreme wave-numbers are obtained and exact numerical results for particular cases are given. The existence of certain secondary modes is also considered.