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Papers of Sir Arthur Eddington
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Chapter X: The Wave Equation

§ 105. Field momentum.
§ 106. The gradient operator.
§ 107. Isostatic compensation.
§ 108. Wave equation of the hydrogen intracule.
§ 109. Solution of the wave equation.
§ 110. The interchange momentum.
§ 111. The two-frame transformation.
§ 112. Electromagnetic potentials.

Chapter XI: The Molar Electromagnetic Field

§ 113. Gauge transformations (molar theory).
§ 114. Action invariants.
§ 115. Gauge transformations (microscopic theory).
§ 116. Indices of wave tensors.
§ 117. Magnetic moments.
§ 118. Magnetic moment of the hydrogen atom.
§ 119. Magnetic moment of the neutron.

(There is no § 120.)

Summary of Chapters XII (second part), XIII, and XIV, with an editorial note

Chapter XII [continued].
§ 125. Symbolic occupation.
§ 126. Einstein-Bose particles.
§ 127. Photons.
§ 128. Life-time of the mesotron.

Chapter XIII: Epistemological Theory.
[§§ 129–136.] As in Proceedings of the Cambridge Philosophical Society, vol. xl (1944), p. 37, expanded.

Chapter XIV. Summary.
§ 137. The principles of fundamental theory.

Chapter VIII: Double Frames

§ 79. The EF-frame.
§ 80. Chirality of a double frame.
§ 81. The interchange operator.
§ 82. Duals.
§ 83. The CD-frame.
§ 84. Double-wave vectors.
§ 85. The 136-dimensional phase space.
§ 86. Uranoid and aether.
§ 87. The Riemann-Christoffel tensor.
§ 88. The de Sitter universe.
§ 89. The tensor identities.
§ 90. The contracted Riemann-Christoffel tensor.
§ 91. States and interstates.
§ 92. The recalcitrant terms.

Chapter IX: Simple Applications

§ 93. The metastable states of hydrogen.
§ 94. Neutrium and deuterium.
§ 95. Mass of the neutron.
§ 96. Double intracules.
§ 97. Comparison with field theory.
§ 98. Mass of the deuterium atom.
§ 99. Mass of the helium atom.
§ 100. The separation constant of isobaric doublets.
§ 101. Isotopic spin.
§ 102. Radii of nuclei.
§ 103. The nuclear planoid.
§ 104. Mass of the mesotron.

Chapter VII: Wave Vectors

§ 66. Idempotency.
§ 67. Standard form of idempotent vectors.
§ 68. Spectral sets.
§ 69. Catalogue of symbolic coefficients.
§ 70. The wave identities.
§ 71. Matrix representation of E-numbers.
§ 72. Factorisation of E-numbers.
§ 73. Wave tensors of the second rank.
§ 74. Wave tensors of the fourth rank.
§ 75. Phase space.
§ 76. Relative space.
§ 77. Vectors in micro space.
§ 78. The quantum-classical analogy.

Chapter IV: Gravitation and Exclusion

§ 34. Unsteady states.
§ 35. Under-observation.
§ 36. Structural and predictive theory.
§ 37. Physical and geometrical distribution functions.
§ 38. The weight function.
§ 39. The genesis of proper mass.
§ 40. Absolute determination of m0.
§ 41. Exclusion.
§ 42. The negative energy levels.
§ 43. Determination of m0 by exclusion theory.
§ 44. Super-dense matter.
§ 45. The degeneracy pressure.

Chapter V: The Planoid

§ 46. Uranoid and planoid.
§ 47. Interchange of extracules.
§ 48. The special planoid.
§ 49. The energy of two protons.
§ 50. Non-Coulombian energy.
§ 51. The constant of gravitation.
§ 52. Molar and nuclear constants.

Chapter VI: The Complete Momentum Vector

§ 53. The symbolic frame.
§ 54. Miscellaneous properties of E-symbols.
§ 55. Equivalence and chirality.
§ 56. Rotations.
§ 57. Five-dimensional theory.
§ 58. Ineffective relativity transformations.
§ 59. Strain vectors.
§ 60. Real and imaginary E-symbols.
§ 61. Reality conditions.
§ 62. Distinction between space and time.
§ 63. Neutral space-time.
§ 64. Congruent spaces.
§ 65. Determinants and eigenvalues.

Chapter I: The Uncertainty of the Reference Frame

§ 1. The uncertainty of the origin.
§ 2. The physical origin.
§ 3. The Bernoulli fluctuation.
§ 4. The standard of length.
§ 5. Range of nuclear forces and the recession of the galaxies.
§ 6. Spherical space.
§ 7. Uranoids.
§ 8. The extraneous standard.
§ 9. Scale-free physics.
§ 10. Pseudo-discrete states.
§ 11. Stabilisation.

Chapter II: Multiplicity Factors

§ 12. Complementary fields.
§ 13. The rigid-field convention.
§ 14. Separation of field and particle energy.
§ 15. Application of scale-free systems.
§ 16. The ‘top particle’.
§ 17. Standard carriers.
§ 18. Mass-ratio of the proton and electron.
§ 19. Rigid coordinates.
§ 20. The fine-structure constant.
§ 21. The inversion of energy.
§ 22. Mutual and self energy.
§ 23. Comparison particles.

Chapter III: Interchange

§ 24. The phase dimension.
§ 25. Interchange of suffixes.
§ 26. The two-particle transformation.
§ 27. Hydrocules.
§ 28. Separation of electrical energy.
§ 29. Current masses of the proton and electron.
§ 30. Molarly controlled charge.
§ 31. Secondary anchors.
§ 32. Calculated values of the microscopic constants.
§ 33. The Coulomb energy.

Draft of a testimonial by A. S. Eddington for W. M. Smart


Observatory, Cambridge
21 May 1936

Dr W. M. Smart’s application for the Chair of Regius Professor of Astronomy in the University of Glasgow has my warmest support. He is a man of established reputation in astronomical circles who would fill the office with distinction; and he has proved himself very successful as a lecturer and teacher. He would be much missed from this Observatory and from the University; but promotion to a professorial chair would be a fitting recognition of his work.

Dr Smart has been Chief Assistant in the Observatory and John Couch Adams Astronomer since 1921. There is only one other Assistant. The policy of the Observatory has been to avoid routine undertakings and to develop new methods. Two main lines of work have been developed during his tenure—an improved method of determining photographic proper motions of stars, and measurement of stellar magnitudes with a photo-electric cell. As regards the former it may, I think, be claimed that the Cambridge results set a new standard of accuracy for large series of proper motions. Photo-electric work is still confined to two or three observatories (Cambridge being the only British one). After a long struggle with pioneer difficulties the work is now proceeding with great success, and astonishing accuracy is obtained. A large share of the credit for these results is due to Dr Smart.

On the theoretical side his earlier work was in celestial mechanics. But in connection with the practical work above-mentioned his more recent interests have {1} been mainly in proper motions and other branches of stellar statistics, to which he is one of the most active contributors. He is a member of the Commission of the International Astronomical Union on Stellar Parallaxes and Proper Motions.

His teaching work covers elementary lectures on astronomy, advanced lectures on celestial mechanics and on stellar motions and a practical class at the observatory. Judging from the response of the students he is a stimulating lecturer. He normally supervises one or two research students.

An important part of his experience is his work as Secretary of the Royal Astronomical Society during the last five years. This brings him into touch with astronomers in all parts of the world, so that he is in full contact with all modern developments. It is perhaps not irrelevant to mention that he is Treasurer of the Royal Astronomical Society Dining Club—an office (of which the duties are by no means confined to the care of money) which is a tribute to his popularity with his colleagues.

To sum up:—He has shown himself able to make the most of the resources of a small observatory; he is well-known and esteemed internationally; he is successful with students; and is well used to administrative activity.


The various cancelled words and passages in this letter have not been recorded, except for the mistaken deletion noted below.

{1} Struck through by mistake.

‘The Cavendish Laboratory’

(This paper includes a description of Eddington’s visit to the Laboratory in Oct. 1934. W. E. Burcham described the circumstances of its composition as follows: ‘towards the end of 1934 Sir Arthur Eddington wrote a pamphlet describing the Cavendish and its achievements to form the basis of ‘an appeal to the friends of science and of Cambridge’. The pamphlet was published in Feb. 1935, and privately circulated to possible benefactors both within and outside Cambridge. See ‘The Cavendish High-voltage Laboratory 1935-39’, Notes and Records of the Royal Society of London, vol. liii, pp. 121-2. (The title appears under the heading ‘Miscellaneous’ in D2/3.))

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