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1. I N the study of a surface F in £4, one of the problems is the determination of the genus IT' of the double curve of a projection of F. Severif has shown that a general Fm in $4 has four fundamental projective characters, viz., the order m, the class n, the rank a of a hyperplane section, and the number t of trisecants through an arbitrary point 0 . He also gives an expression for the rank of the double curve in question, from which, knowing the number of pinch points J of F'm in projection of Fm, we can obtain T'. I t is not uninteresting

Double curves of surfaces projected from space of four dimensions