Damoiseau and Pontécoulant had neither of them attached sufficient importance to the actual ellipse described by the comet in 1759. As 1759 was the starting-point from which to determine the probabilities of 1835, it was important to obtain the most accurate knowledge possible of the condition of things in 1759. Rosenberger thought that he ought to go much further back than either Damoiseau or Pontécoulant had done, and that it would be impossible to make a trust- worthy prediction for 1835 unless he began as far back as 1682, and computed the perturbations between 1682 and 1759, and so led up to 1835.
In performing his task Rosenberger took account not only of the influence of the great planets Jupiter, Saturn, and Uranus, but also of the smaller influence exerted by Venus, the Earth, and Mars, with some allowance also for Encke's supposed Resisting Medium as affecting his (Encke's) Comet. Omitting in the first instance any allowance for a Resisting Medium Rosenberger named Nov. 11, at 0h Paris M.T., for the comet's perihelion passage. If an allowance supposed to be appropriate were made for a Resisting Medium the perihelion would fall about a week earlier or on Nov. 3 at 19h Paris M.T. The actual effects on the comet's motion ascribed to the smaller planets were as follows:—the Earth 1523 days, Venus about 513 days, and Mercury and Mars together nearly 1 day. By these periods of time (namely, about 22 days) added together, Rosenberger considered that the comet's return would be hastened. "Professor Rosenberger's investigation is remarkable for its extraordinary completeness, for the pains taken to include every possible source of perturbation, without regard to the numerical labour, and for the masterly manner in which the whole of the vast work was conducted."
Rosenberger, however, had a competitor in his own country. Lehmann thought there was room for another discussion of the elements and disturbances of the orbit of Halley's Comet, and though his labours were not in some respects as meritorious as Rosenberger's they have a merit of their own, inasmuch that Lehmann took the year 1607 as his starting-point. On this basis he fixed Nov. 26 for the perihelion passage, which
