A useful method is described for determining the orientations of crystal grains in polycrystalline specimens having cubic lattice structure from the observation of angles between the surface markings such as slip lines or twins which are developed in {111} planes. From the computation of relations between the angular co-odinates (ξ,η) of the crystal orientation and the relative angles (α,β,γ,δ) in four directions of {111} traces a chart of isogonic lines of α and γ is plotted with the intervals of two degrees. The orientation of a given crystal grain in the specimen can be determined immediately from the above chart if the angles α and γ are measured, and its accuracy is also shown obviously. The case of {111} traces in only three direction is discussed and the relation between the angles of the three traces and the number of possible orientations corresponding to the same traces are explained.
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Takeuchi et al. (1958) studied this question.