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As the a's approach certain limiting values, one or more of which is infinite, Ta may have a definite finite transformation T as a limit. The transformation T may be regarded as a transformation of the family, and, if equivalent to a transformation Tb with finite parameters, can be generated by an infinitesimal transformation of the family (namely, bxXx + •" + brXr), but not otherwise.* Let it be assumed that

On the singular transformations of groups generated by infinitesimal transformations