Abstract
A theorem due to Brinkman states that, given a solution of the vacuum general relativistic field equations, it is never possible to generate a further solution by means of a nontrivial conformal transformation. It is pointed out here that there are exceptions to this result. The discussion is then extended to the nonsymmetric unified field theory, and the circumstances under which this theory admits a rigidly valid analog of Brinkman's theorem are investigated.
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