Raymond Arthur Lyttleton (1911-95) was a British astronomer who won the Royal Society Royal Medal in 1965 for significant contributions to his field. In this book, which was first published in 1953, Lyttleton presents an account of advances in relation to a classical problem of mathematical astronomy. The text is mainly concerned with those parts of the theory most directly involved in determining the evolution of gravitating liquid masses. The important conclusion is reached that the dynamical evidence is against the so-called 'fission process' of binary system formation. This book will be of value to anyone with an interest in astronomy and the history of science.