THE PHYSICAL SOCIETY LONDON. REPORT OK THE RELATIVITY THEOEY OF
GRAVITATION. A. S. EDDINOTON, M. A., M. Sc., F. E. S. M Plumtan
Professor of Astronomy and Experimental Philosophy, Cambridge.
Price to Non-Fellows, 6 8. net, post free 6s. 3d, Bound in doth,
8s. 6d., post ree 8s 9d LONDON. FLEET WAY PRESS, LTX, 1, 2 AND 3,
SALISBURY COUBT, FLEET STBEET 1920. CONTENTS. CHAPTEE L PAGE THE
KESTRICTED PRINCIPLE or EELATIVITY 1 1-3. The Michelson-Morley
experiment and its significance. 4. The transformation of
co-ordinates for a moving observer. 5. Reciprocity of the
transformation. 6. Standpoint ot the Principle of Relativity. 7,
Transformation of velocity, of den sity and of mass. 8. Scope of
the Principle. CHAPTER II. THE KELATIONS OF SPACE, TIME, AND FORCE
14 9-10. Minkowskis transformation. 11. Invanance of 8. 12.
Irrelevance of co-ordinate systems to the phenomena, 13-14. The
Principle of Equivalence. 15-16. Definition of a field of force by
g v . 17. Purpose of the theory of tensors. 18, Nature of space and
time in the gravitational field. CHAPTEE III. THE THEORY OF TENSORS
30 19. Notation, definition and elementary properties of tensors.
20. The fundamental tensors associated tensors. 21. Auxili ary
formula for the second derivatives of the co-ordinates. 22.
Covariant differentiation. 23-24. The Riemann-Ghristoffel ten sor.
26. Summary. CHAPTEE IV. EINSTEINS LAW OF GRAVITATION 41 26. The
contracted Eiemann-Christoffel tensor. 27. Limitation of the
Principle of Equivalence. 28. The gravitational field of a Dartiole
IV. CONTENTS. CHAPTER V. PAGB THE CRUCIAL PHENOMENA 48 29-30. The
Equations of Motion. 31. Motion of the Perihelion of Mercury.
32-33. Deflection of a ray of hght 34. Displacement of spectra
lines. CHAPTER VL THE GRAVITATION OF A CONTINUOUS DISTRIBUTION OF
MATTER 59 35-36 Equations for a continuous medium. 37 The energy
tensor T v, and the equations of hydrodynamics. 38. The Law of
Conservation 39. Reaction of the gravitational field on matter. 40.
Propagation of gravitation CHAPTER VII. THE PRINCIPLE OF LEAST
ACTION 71 41. Expression ot the law of gravitation in the torm ot
Lagranges Equations 42. Principle of Least Action. 43. Energy of
the gravitational field 44 Method of Hilbert and Lorentz. 45-46.
Electromagnetic equations. 47 The JEJther. 48. Summary of the last
two chapters CHAPTER VIII. THE CURVATURE OF SPACE AND TIME 82 49.
Absolute rotation and the limits ol generalised relativity. 50
Einsteins curved space 51. T e Sitters curved space-time. 52.
Boundary Conditions. 53. Conclusion PREFACE TO FIRST EDITION. THE
relativity theory of gravitation in its complete form was published
by Einstein in November 1915. Whether the theory ultimately proves
to be correct or not, it claims attention as one of the most
beautiful examples of the power of general mathematical reasoning.
The nearest parallel to it is found in the applications of the
second law of thermo-dynamics, in which remarkable conclusions are
deduced from a single principle without any inquiry into the
mechanism of the phenomena similarly, if the principle of
equivalence is accepted, it is possible to stride over the
difficulties due to ignorance of the nature of gravita tion and
arrive directly at physical results. Einsteins theory has been
successful in explaining the celebrated astronomical discordance of
the motion of the perihelion of Mercury, without introducing any
arbitrary constantthere is no trace of forced agreement about this
prediction. It further leads to interesting conclusions with regard
to the deflection of light by a gravitational field, and the
displacement of spectral lines on the sun, which may be tested by
experiment. The arrangement of this Report is guided by the object
of reaching the theory of these crucial phenomena as directly as
possible. To make the treatment rather more elementarv, use of the
principle of least action and Hamiltonian methods has been avoided
and the brief account of these m Chapter VII...
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