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*Presented to the Society in the form of two papers February 22, 1902, and (San Francisco) May 3, 1902. Received for publication March 14, 1902. t To facilitate references to my previous papers on this subject, I shall quote them in the text by the initial words of their titles, viz.: Invariants, Geometry, Reciprocal Systems They have all been published in these T ra n sacti o n s: Invariants, vol. 2, p. 1 ; Geometry, vol. 2, p. 343; Reciprocal Systems, vol. 3, p. 60. 423

Covariants of systems of linear differential equations and applications to the theory of ruled surfaces