In Volume II it was intended to include chapters on the kinetics of a particle and of solid and fluid bodies, on the vibrations of solid bodies, and on wave-motion in general. It was expected also to contain a chapter much referred to in Volume I, on "Properties of Matter." That the work was not completed is a matter of keen regret to all physicists, regret, however, now tempered by the fact that many of the subjects of the unfulfilled programme are represented by such works as Lord Rayleigh's _Theory of Sound_, Lamb's Hydrodynamics, and Routh's _Dynamics of a System of Rigid Bodies_. But all deeply lament the loss of the "Properties of Matter." No one can ever write it as Thomson would have written it. His students obtained in his lectures glimpses of the things it might have contained, and it was most eagerly looked for. If that chapter only had been given, the loss caused by the discontinuance of the book would not have been so irreparable. The first edition of the book was published by the Clarendon Press, Oxford. It was printed by Messrs. Constable, of Edinburgh, and is a beautiful specimen of mathematical typography. In some ways the first edition is exceedingly interesting, for it is not too much to say that its issue had an influence on dynamical science, and its exposition in this country, only second to that due to Newton's Principia. Three other works, perhaps, have had the same degree and kind of influence on mathematical thought--Laplace's _Mécanique Céleste_, Lagrange's _Mécanique Analytique_, and Fourier's _Théorie Analytique de la Chaleur_. The second edition was issued by the Cambridge University Press as Parts I and II in 1878 and 1883. Various younger mathematicians now of eminence--Professor Chrystal, of Edinburgh, and Professor Burnside, of Greenwich, may be mentioned--read the proofs, and it is on the whole remarkably free from typographical and other errors. With the issue of Part II, the continuation was definitely abandoned. In the second edition many topics are more fully discussed, and the contents include a very valuable account of cycloidal motion (or oscillatory motion, as it is more usually called), and of a revised version of the chapter on Statics which forms the concluding portion of the book, and which discusses some of the great problems of terrestrial and cosmical physics.