This site contains the only complete exposition of the so called "screening-, shadow-, lesage- or kinetic theory of gravitation" by Nicolas Fatio de Duillier. This version is based on a copy of his manuscripts which was made by Jakob Bernoulli in 1701.
On pp. 19-22 there is an introduction by Bopp (in German).
Fatio's paper begins at the end of p. 22 (in French).
Fatio also made a copy of some remarks of Isaac Newton from 1692 (beginning at the middle of p. 64, in Latin). Newton wrote that Fatio's theory is the only one, which might explain gravity by mechanical means. (However, Newton changed his mind afterwards).
For further details see:
Fatio de Duillier, Nicolas (1701), Die wiederaufgefundene Abhandlung von Fatio de Duillier: De la cause de la Pesanteur, in Bopp, Karl: "Drei Untersuchungen zur Geschichte der Mathematik", Schriften der Straßburger Wissenschaftlichen Gesellschaft in Heidelberg 10: 19-66, Berlin & Leipzig, 1929
Zehe, Horst (1980), Die Gravitationstheorie des Nicolas Fatio de Duillier, Hildesheim: Gerstenberg Verlag