THE CENTRAL-LIMIT-THEOREM IN TEXTURE COMPONENT FIT METHODS

This note is concerned with implications of spherical analogues of the central Limit theorem of probability in Euclidean space. In particula r, it is concerned with the presumption that the analogy holds in term s of interpreting a special spherical limiting distribution, the hyper spherical Brownian distribution, as the distribution of the resultant rotation composed by a sequence of successive random rotations under s imilarly mild assumptions as applied in the central limit theorem for Euclidean space. This interpretation has been stressed at several inst ances to indicate the superiority of the spherical Brownian distributi on for applications in texture component fit methods. Here it is shown , however, that this presumption is false. Thus, an explicit correspon dence of the Brownian form of texture components and processes causing preferred crystallographic orientations cannot be inferred from a cen tral limit type argument.