‎"DARWIN, G. H.‎
‎Periodic Orbits [Acta Mathematica] (+) Periodic orbits [Mathematische Annalen]. - [PERIODIC ORBITS]‎

‎Stockholm, Beijer, 1897 (+) Leipzig, B. G. Teubner, 1899. [Acta Mathematica] 4to. As extracted from ""Acta Mathematica, 21. Band]. No backstrip. Fine and clean. Pp. 99-242 + 4 plates. [Mathematische Annalen] 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 51. Band. 4. Heft."" Entire issue offered. A fine and clean copy. [Darwin:] Pp. 523-583. [Entire issue: Pp. 481-607 + 4 plates.].‎

Reference : 45786

‎First printing of Darwin's famous paper (including the abridgement published two years later) which contained the first systematic search for periodic orbits and work on the three body problem. ""The paper, which had taken him three years to complete, contained the numerical calculations of periodic solutions of the restricted three body problem, together with a discussion of their stability. It provided not only extensive details of the numerical results but also a full description of the mathematical methods used to obtain them."" (Barrow-Green, Poincaré and the three body problem, P. 194). Darwin was introduced to the three body problem through the works of Poincare. Following his accession to the Plumian chair Darwin delved even more deeply into the problems of the origin and evolution of the solar system, making numerous investigations of the figures of equilibrium of rotating masses of fluid and, later, making extensive studies of periodic orbits in the restricted problem of three bodies, carried out with special reference to cases obtaining for the particular values of the mass ratio of the two finite bodies of 1:10 and 1:1048 (the latter approximating the mass ratio of Jupiter to that of the sun). (DSB)‎