Of recent years there have appeared in the literature several attempts to apply to the subject matter of chemistry mathematical theories which had not thitherto found any use in that field. With the spirit and purpose of such attempts, the author of this paper is thoroughly in sympathy. But some of the investigators who have undertaken this kind of pioneer work in applied mathematics have apparently entered upon their tasks without appreciating the difficulties involved, and have hence produced results more likely to obscure than to clarify their subjects.