The present volume covers those parts of the theory of the stability of rotating gravitating liquids that seem to be of primary importance in determining the evolution of such systems. Apart from the intrinsic mathematical and dynamical interest of the subject, the problem is also of considerable interest from a cosmogonical standpoint, as its solution is the sole source of theoretical information on the question of how an isolated unstable rotating mass will develop. The important conclusion is reached, contrary to Jeans's views and to those still largely current amongst astronomers, that the dynamical evidence is entirely adverse to the so-called fission process of formation of binary systems. The work accordingly removes theoretical foundation from this process as playing any role in the evolution of binary systems. In this way the study indirectly assumes astrophysical value in that in disposing of the fission hypothesis it lifts what seems to the writer to have been one of the major obstacles to progress with the greater problem of stellar evolution.

My own interest in the subject of rotating gravitating liquids, as best I can remember, began twenty years ago with Professor H. F. Baker's lectures at Cambridge, when he used to conclude his course on celestial mechanics with a rapid survey of those parts of the present subject that could be dealt with by elementary methods. The astronomical importance of the problem became clear to me from studies of the origin of the solar system, and in particular it was from the problem of the origin of satellites that I was first led to suspect the validity of the fission process—this, incidentally, going to show how even conjectural studies can at times contribute suggestively to more precise matters. Investigation of the details of Jeans's researches soon disclosed numerous places where he had fallen into error, and I accordingly resolved to see if after rectifying these the subject could be brought into some more coherent form, not in conflict with the strong indications already available from other related fields.