Paper, 'On instability of periodic motion' by William Thomson A printed proof of Thomson's paper. Thomson writes: 'Let ψ, φ, χ, ϑ be generalised coordinates of a system; and let A (ψ, φ, . . . . , ψ', φ', . . . . ) be the action in a path (2 above) from the configuration (ψ', φ',. . . .) to the configuration (ψ, φ, . . . .) with kinetic energy (E—V) with any given constant value for E, the total energy; V being the potential energy, of which the value is given for every possible configuration of the system.' Includes a postscript, dated 10 November 1891, in which Thomson discusses Henri Poincaré's 'Sur le problème des trois corps et les équations de la dynamique'. Annotations in pencil and ink. Subject: Physics / Mathematics Received 12 November 1891. Read 26 November 1891. A version of this paper was published in volume 50 of the Proceedings of the Royal Society as 'On instability of periodic motion'. 1891