Abstract
A systematic study of the projective differential geometry of space curves was first made by Halphent in a memoir of 1880. Wilczynskil in 1905 and 1906 and Sannia? in 1926 made important additions to the subject. The projective differential theory of a curve involves many configurations associated covariantly with the curve. The purpose of this paper is to make some contributions to the theory of a space curve, which are based upon the study of configurations. The work follows the lines of a similar investigation made by Lane I for the case of a plane curve. We now make precise the meaning of the word consecutive as used in the present paper. Let us consider an analytic curve C in projective space of three dimensions. The equations of such a curve, in non-homogeneous projective coordinates x, y, z, can be written in the form of two power series expansions,
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