Abstract
The section of the slowness surface of a monoclinic elastic material in the plane of symmetry consists of an ellipse and a quartic curve with two tested branches, the inner of which is convex. The elastic moduli governing the size and orientation of the ellipse have no influence on the other branches and whenever the outer member of the nested pair is non-convex (as is usually the case) a one-parameter family of these moduli can be found for which there appear on the section a transonic state of type 5 and its centrosymmetric equivalent. The construction of these states completes the proof that all six types of transonic states can occur in physically realizable anisotropic elastic materials.
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