This paper describes recent work on magnetohydrodynamics by M. H. Rogers and myself. It has seemed to us that the large-scale dynamics of cosmical gas clouds must take into account the fact that a gas is a compressible material, so that the hypothesis of a constant density must be avoided. Secondly, there must be present a pressure-gradient force. Thirdly, self-gravitation cannot be omitted. Fourthly, the motion should be adiabatic, in the first instance at least. To these conditions we have now also added the effects of the presence of magnetic fields, but have assumed that the conductivity of the material is infinite and that it is of constant permeability. We have neglected the effects of turbulence, of viscosity, and of heat conduction.