Propagation of plane electromagnetic waves in a homogeneous ionized gas in a uniform magnetic field is compared with the propagation of light in an optically inactive birefringent crystal. It is well known that propagation in a crystal may be described by using a system of real orthogonal axes for which the dielectric constant is given by a diagonal matrix. This paper shows that propagation of plane waves in the ionosphere may be described in a similar manner, the medium having an effective dielectric constant given by a diagonal matrix, provided that a system of "complex" orthogonal axes is used for the description of the components of the field vectors. This set of component axes (which is quite different from and not to be confused with coordinate axes) is equivalent to resolving the field vectors into components parallel to the magnetic field and two contrarotating circular components in a plane perpendicular to the magnetic field. An expression giving the velocity of each of the two modes of propagation in a given direction and expressions for the amplitude of each component of the field vectors are obtained (equations 43 and 44). Provided that one accepts the concept of a complex velocity of propagation, the results hold when electron collisions are included. When electron collisions are neglected, it is possible to form a double-sheeted surface, called the normal velocity surface, which is of some assistance in visualizing the manner in which the velocity of propagation of the plane waves in each mode changes with direction.