As mentioned in footnote 2 in the previous paper, in private correspondence, Élie Cartan made certain observations on the manuscript that DDK had sent him. There seems to have been a lively exchange of letters and ideas between Kosambi and Cartan, as the next paper also testifies. The previous paper, this note, and a later paper, by S. S. Chern in the Bulletin des Sciences Mathématiques, 63, 206 (1939) form the basis of the Kosambi–Cartan–Chern or KCC theory. Kosambi’s contribution here is the short explanatory paragraph in English at the end. Although the paper is in French, it seems more appropriate to include it here, given the close relationship it bears to the preceding paper, rather than in Sect. III.