It is shown that in the magnetohydrodynamic approximation, neglecting pressure terms, the transverse wave fields in a uniform medium with a uniform magnetic field can be derived from linear combinations of scalar protentials of the form ϕ¿(x, y, z,¿VAt), where VA is the Alfv¿n speed; guidance by the magnetic field is thus perfect. It is further shown that in the ray approximation, strong guidance still exists even if the medium and the magnetic field are not quite uniform provided that the component perpendicular to the magnetic field of the propagation vector is much greater than the parallel component. If the reciprocal of the parallel component is not much greater than the spatial scale on which the medium and the magnetic field vary, then the ray approximation is only valid in the perpendicular direction. The differential equations of wave propagation along the magnetic field are derived under these conditions directly from Maxwell's equations. An alternative derivation, using an analogy to transmission lines, is also given. These equations must then be applied to each perpendicular Fourier component of a source; differently oriented Fourier components propagate differently. The resulting imperfections in guiding will be investigated elsewhere in detail.