A theoretical analysis of the cubic to orthorhombic transformation is presented which predicts for a partly transformed crystal, the interface plane, orientation relationships, and macroscopic distortions from a knowledge only of the lattice parameters of the initial and final phases. Arguments are advanced to show that in order to minimize the strain energy associated with the transformation, the interface plane must be one of zero average distortion. This leads directly to considerations of an inhomogeneous product phase. Experimental studies on an AuCd alloy are described and the observed crystallographic features of the transformation compared with values calculated using the theory. The agreement between calculated and observed results for this alloy system as well as others is strong evidence for the theory of diffusionless phase transformations presented.