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Bean Harvey Brooks. He not only initially suggested the research problem discussed in this report, but guided the author's efforts throughout this investigation of the properties of alloys. In particular,, his knowledge of physical effects in real metals was an invaluable aid to the author. The author also acknowledges the help and encouragement of Professor Arthur Bienenstock. His continued interes c in the problem and willingness to discuss difficulties in the formalism were extremely significant at several stages in the research.