This is the concluding part of a modernized rendition of Poincaré's Rendiconti paper on relativity, of which the first two parts appeared in the November 1971 and June 1972 issues of this Journal. It covers the last section of that paper, in which Poincaré develops in masterful, even if incomplete, fashion, a generalization of Newtonian gravitational theory, involving retarded action-at-a-distance interaction that is covariant under the Lorentz group. As the first such attempt it is of obvious historical significance. In addition, just as the first two parts, so this part, too, contains material of independent interest to the historian of the genesis of special relativity.