XVII. On the curvature of the Indian arc

This communication completes the series of the author’s papers on the subject of the Indian Arc. He commences by recapitulating the chief results of his former calculations, and adverting to the attempt which he made in his former papers to explain the difficulty which those calculations brought to light, namely, that the amplitudes of the arcs from Kaliana to Kalianpur and from Kalianpur to Damargida, determined geodetically, were so little in excess as they proved to be of the same amplitudes determined astronomically,—a difficulty which he endeavoured to get over by attributing to the Indian Arc a curvature different from that corresponding to the mean meridian of the earth. In the present communication, introducing the condition that the length of the chord of the arc must be the same in both the ellipses, the local and the mean, drawn through the stations at the extremities of the arc, he demonstrates that no change in the curvature of the arc, within reasonable and indeed within wide limits, can have any appreciable effect on the calculated amplitude.