In choosing axes for a crystal often the first selection is later found to be unsatisfactory and a new set must be chosen. For example, the first chosen cell may turn out to be larger than necessary and simplification will follow adoption of the smaller cell. In dealing with the most general crystal system—the triclinic—it becomes obvious that the crystal axes a b c are not the axes of immediate reference. X-ray measurements determine d001 for example, not c, and the relation between d001 and c is not simple. An optical goniometer measures the angle between normals to the faces (001) and (100) which is not β nor related simply to β Both these types of measurements are related simply to a set of axes which are perpendicular to the cell faces—the so called reciprocal cell axes. We find that, in dealing with triclinic crystals we must have two systems of axes, the direct system and the reciprocal system. This dual axial system is a great convenience in computations for all crystal systems. Hence we seek ways of converting information gathered and expressed in one system into its proper expression in another system.