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.

Preface vii

I. Introduction 1

II. Stability 6

III. The spherical form 31

VI. The spheroidal and ellipsoidal forms 35

V. Ellipsoidal harmonic analysis 51

VI. Further properties of lamé functions and application to gravitation 77

VII. The secular stability of the Maclaurin spheroids 91

VIII. The secular stability of the Jacobi ellipsoids 102

IX. The ordinary stability of the Jacobian ellipsoids 114

X. Cosmogonical implications 133

Appendix: references 145

Index 149

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