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1. The existence of relations between the coaxial minors of a determinant was first discovered by MacMahon in 1893. The whole literature of the subject is comprised in three papers, viz.:—MacMahon,Phil. Trans., clxxxv. pp. 111–160.Muir,Phil. Mag., 5th series, xli. pp. 537–541.Nanson,Phil. Mag., 5th series, xliv. pp. 362–367.My present object is to continue the investigation of the relations in question, and more particularly to draw attention to anexplicitexpression for a determinant of the 4thdoi:10.1017/s0080456800034104 fatcat:6fj56tt46fcl5kvgggv4mseqai