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University of Cambridge Institute of Astronomy.—Describes the contents of the second of two boxes of Eddington papers formerly in the possession of Noel B. Slater.

These manuscripts are all in Eddington’s own hand, with the exception of the ringed pencil number on the first page of each and the foliation (in red biro, except B2/20), which were added by Slater, the former in June 1945, the latter about the end of 1947. Other notes by Slater indicate that there is a sheet missing from B2/22 between ff. 4 and 5, and that B2/29 f. 14 is a modification of f. 4.

§ 2∙1. Particles with spin.
§ 2∙2. Relativity rotations.
§ 2∙3. Neutral space-time.
§ 2∙4. Strain vectors.
§ 2∙5[a]. Reality conditions.
§ 2∙5[b]. Flat space-time.
§ 2∙6. Determinants and eigenvalues.
§ 2∙7. Phase space.
§ 2∙8. Probability distribution of strain vectors.

(§§ 2∙1 and 2∙2 were renumbered from 1∙1 and 1∙2 and, as a result, §§ 2∙3, 2∙4, and 2∙5[a] were renumbered from 2∙2, 2∙3, and 2∙4 respectively; but the necessary alterations to the numbering were carried no further. The title of § 2∙8 was altered from ‘Probability distribution of phase space’.)

§ 96. The gauge transformation (molar application).
§ 97. Action invariants.
§ 98. The gauge transformation (microscopic application).
§ 99. Complementary electromagnetic fields.

§ 87. Angular momentum.
§ 88. The gradient operator.
§ 89. Wave equation of the hydrogen intracule.
§ 90. Solution of the wave equation.
§ 91. The Coulomb energy.
§ 92. Fixed-scale units.

§ 76[a]. Angular momentum.
§ 74[a]. Polar coordinates.
§ 74[b]. The differential wave equation.
§ 75. The symbolic frame in relative space.
§ 76[b]. Reality conditions in relative space.
§ 77[a]. Relation of quantal and scale-free physics.
§ 77[b]. Relation of quantal and scale-free physics.
§ 78. The metastable states of hydrogen.
§ 79. Particle and wave properties.
§ 80. The internal wave equation.

(§ 76[a] was renumbered from 73, but the equations were not renumbered accordingly.)

§ 77. The metastable states of hydrogen.
§ 78. Deuterium and neutron.
§ 79. Mass of the neutron.
§ 80. Atomic mass of deuterium.
§ 81. Simple and double intracules.
§ 82. Atomic mass of helium.
§ 83. The separation constant of isobaric doublets.
§ 84. Nuclear spin.
§ 85. Mass of the mesotron.

§ 64. The EF-frame.
§ 65. Chirality of a double frame.
§ 66. The interchange operator.
§ 67. Duals.
§ 68. The CD-frame.
§ 69. Double vectors.
§ 70. Double phase space.
§ 71. Uranoid and aether.
§ 72. The Riemann-Christoffel tensor.
§ 73. The tensor identities.
§ 74. The contracted Riemann-Christoffel tensor.
§ 75. Interstates.
§ 76. Antisymmetrical wave functions.

(The chapter number has been altered in pencil to ‘VIII’.)

§ 51. Idempotency.
§ 52. Standard form of idempotent vectors.
§ 53. Spectral sets.
§ 54. Table of symbolic coefficients.
§ 55. The wave identities.
§ 56. Matrix representation of E-numbers.
§ 57. Factorisation of E-numbers.
§ 58. Wave tensors.
§ 59. Phase space.
§ 60. Space tensors of the second rank.
§ 61. The quantum-classical analogy.
§ 62[a]. Space tensors of the second rank.
§ 62[b]. The symbolic frame in relative space.
§ 63. Reality conditions in relative space.

(Drafted Mar. 1943, revised Dec. 1943. The chapter number has been altered in pencil to ‘VII’.)

§ 41. The symbolic frame.
§ 42. Miscellaneous properties of the E-symbols.
§ 43. Equivalence and chirality.
§ 44. Rotations.
§ 45. Effective and ineffective relativity transforma-tions.
§ 46. Real and imaginary symbols.
§ 47. Distinction between space and time.
§ 48. Neutral space-time.
§ 49. Strain vectors.
§ 50. Determinants and eigenvalues.

(Drafted Mar. 1943; revised Dec. 1943. The chapter number has been altered in pencil to ‘VI’.)

§ 31. Time.
§ 32. The weight function.
§ 33. The genesis of proper mass.
§ 34. Determination of m0.
§ 35. Exclusion.
§ 36. The negative energy levels.
§ 37. The planoid.
§ 38. Interchange of extracules.
§ 39. Non-Coulombian energy.
§ 40. Calculated values of the molar and nuclear constants.

§ 22. Mutual and self energy.
§ 23. Comparison particles.
§ 24. The phase coordinate.
§ 25. Interchange.
§ 26. Hydrocules.
§ 27. The β-factors.
§ 28. The observational system.
§ 29. Calculated values of the microscopic constants.
§ 30. The two-particle transformation.

(Drafted Dec. 1942; revised Aug. 1943.)

§ 12. Object-fields.
§ 13. The rigid field convention.
§ 14. Separation of particle and field energy.
§ 15. Application to scale-free systems.
§ 16. Standard carriers.
§ 17. Mass-ratio of the proton and electron.
§ 18. The fine-structure constant.
§ 19. Rigid coordinates.
§ 20. Unsteady states.
§ 21. The inversion of energy.

(Drafted Dec. 1942; revised Aug. 1943.)

§ 1. The uncertainty of the origin.
§ 2. The Gaussian distribution.
§ 3. The Bernoulli fluctuation.
§ 4. The standard of length.
§ 5. Range of nuclear forces and the recession of the galaxies.
§ 6. Non-uniform curvature.
§ 7. Uranoids.
§ 8. The extraneous standard.
§ 9. Scale-free physics.
§ 10. Pseudo-discrete distributions.
§ 11. Stabilisation.

(Drafted Dec. 1942; revised Aug. 1943.)

(i) Chapter IX: The Molar Electromagnetic Field.
Gauge transformations.

(ii) Chapter IX: The Molar Electromagnetic Field.
Affine field theory.

§ 61. The EF-frame.
§ 62. Chirality of the double frame.
§ 63. The interchange operator.
§ 64. Duals.
§ 65. The CD-frame.
§ 66. Double phase space.
§ 67. The uranoid and the aether.
§ 68. The tensor identities.
§ 69. The quantum-classical analogy.
§ 70. Recoil rotations.
§ 71. Transformation to a relative frame.

§ 1∙1. The conditions of observability.
§ 1∙2[a]. The Gaussian distribution.
§ 1∙3. Systems of description.
§ 1∙4. Relative distribution functions.
§ 1∙5. Application to wave functions.
§ 1∙6[a]. Uranoids.
§ 1∙7. Curvature of space.
§ 1∙8. Proper mass.
§ 1∙9[a]. Object-fields.
§ 1∙9[b]. Four-dimensional theory.
§ 1∙6[b]. Uranoids.
§ 1∙2[b]. The centroid as physical origin.

(The chapter title was altered from ‘The Uncertainty of the Reference Frame’. § 1∙9[b] is marked ‘rewrite under the heading “Stabilising relations”’.)

§ 73. Angular momentum.
§ 74[a]. The metastable states of hydrogen.
§ 75[a]. The symbolic frame in relative space.
§ 76. Reality conditions in relative space.
§ 75[b]. The symbolic frame in relative space.
§ 74[b]. The differential wave equation.

§ 5∙1. Electric charge.
§ 5∙2. The electrical stabilisation.
§ 5∙3. The time coordinate.
§ 5∙4. Quadratic and linear energy.
§ 5∙5. The Coulomb energy.
§ 5∙6. Pairing.
§ 5∙7[a]. [Untitled.]
§ 5∙7[b]. The electromagnetic potential.

§ 1∙9 [continued].
Part of an unidentified chapter.
§ 1∙9. Individual and statistical particles.
§ 1∙8. Electric charge.
Rough calculations.

§ 4∙1. Double frames.
§ 4∙2. Interchange.
§ 4∙3. The dual frame.
§ 4∙4. Double phase space.
§ 4∙5[a]. The relation between mass and density.
§ 4∙6. [Untitled.]
§ 4∙5[b]. [Untitled.]

§ 61. The EF-frame.
§ 62. [Title missing.]
§ 63. The dual frame.
§ 64. Double phase space.
§ 65. The two strain tensors.
§ 66. The Riemann-Christoffel tensor.

Memoranda.

Chapter III: Multiplicity Factors.
§ 3∙1. The rigid-field convention.
§ 3∙2. Scale-free systems.
§ 3∙3. Partition of the energy tensor.
§ 3∙4. Rigid coordinates.
§ 3∙5. The fine-structure constant.
§ 3∙6. Vector particles.
§ 3∙7. Mass-ratio of the proton and electron.
§ 3∙8. Radiant energy.

[Summary of Chapter IV.]

Chapter IV: Exclusion and Interchange.
§29. The phase coordinate.
§30. Mutual and self energy.
§31. Elision of comparison particles.
§32. Exclusion.
§33. The negative energy levels.
§35. The factor 3/5.
§36[a]. Interaction of V10 particles.
§38. Interchange.
§37[a]. The Newtonian potential.
§37[b]. The Newtonian potential.
§36[b]. The Newtonian potential.

§3∙1. The rigid-field.
§3∙2. Scale-free systems.
§3∙3. Allocation of the energy tensor.
§3∙4. Rigid coordinates.
§3∙5. The inversion of mass.
§3∙6. Standard particles and vector particles.
§3∙7. Mass-ratio of the proton and electron.
§3∙8. The fine-structure constant.
§3∙9. Radiant energy.

§ 19. Object-fields.
§ 20. The rigid-field convention.
§ 21. The rigid field in scale-free physics.
§ 22. Partition of the energy tensor.
§ 23. The inversion of energy.
§ 24. Rigid coordinates.
§ 25. Standard particles and vector particles.
§ 26. Transition particles.
§ 27. Protons and electrons.
§ 28. The mass m0.

(Formerly two chapters. The title was altered from ‘Fields and Particles’; ‘Chapter IV. Multiplicity Factors.’ has been struck through before § 25.)

§ 41. The symbolic frame.
§ 42. Miscellaneous properties of the E-symbols.
§ 43. Equivalence and chirality.
§ 44. Rotations.
§ 45. Real frames.
§ 46. Distinction between space and time.
§ 47. Neutral space-time.
§ 48. Strain vectors.
§ 49. Determinants and eigenvalues.
§ 50. Idempotency.
§ 51. Standard form of idempotent vectors.
§ 52. Spectral sets of particles.
§ 53. Dictionary of symbolic coefficients.

§ 1. Physical quantities.
§ 2. The definition of length.
§ 3. Molar theory and microscopic theory.
§ 3. Remarks on the definition.
§ 4. Length in an electromagnetic field.

Chapter VI: Wave Vectors.
§ 54. The linear wave equations.
§ 55. Matrix representation of E-numbers.
§ 56. Factorisation of E-numbers.
§ 57. Wave vectors and tensors.
§ 58. Space tensors of the second rank.
§ 59. Angular momentum.
§ 60. Symbolic coefficients in ξ-space.
§ 61. The differential wave equation.
§ 62. The eigen-scale.
§ 63. Perturbation theory [title only].

Chapter VII: The Hydrogen Atom and the Neutron.
§ 63. Symmetric degeneracy.