Discovery of the identity of the comets of 1682, 1607, and 1531; Halley announces the next return for the year 1758 – Clairaut undertakes the calculation of the disturbing influence exercised by Jupiter and Saturn upon the comet of 1682; collaboration of Lalande and Mdlle. Hortense Lepaute – The return of the comet to its perihelion is fixed for the middle of April 1759; the comet returns on the 13th of March – Return of Halley's comet in 1835; calculation of the perturbations by Damoiseau and Pontécoulant; progress of theory – The comet will return to its perihelion in May 1910

Let us recal the memorable words of Seneca in his Quœstiones Naturales: ‘ Why should we be surprised that comets, phenomena so seldom presented to the world, are for us not yet submitted to fixed laws, and that it is still unknown from whence come and where remain these bodies, whose return takes place only at immense intervals? … An age will come when that which is mysterious for us will have been made clear by time and by the accumulated studies of centuries… Some day there will arise a man who will demonstrate in what region of the heavens the comets take their way, why they journey so far apart from other planets, what their size, their nature.’ Eighteen centuries have elapsed, and not one man, but the accumulated efforts of many men have raised a corner of the veil spoken of by Seneca.