X. The differential covariants of twisted curves, with some illustrations of the application to quartic curves

Abstract

The object of the earlier parts of this paper is to obtain relations connecting what Halphen calls the canonical invariants of the curve, without the intervention of what are called by him the fundamental invariants. In any geometrical investigation it is the canonical in­variants which present themselves, and the relations between the con­secutive canonical invariants, and the values of their differential coefficients must, if the method of investigation is to be used, be expressed, in terms of canonical invariants only, without the inter­vention of the other series of invariants which Halphen treats as fundamental.