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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.

§ 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.

§ 3∙1. The rigid-field convention.
§ 3∙2. Scale-free distributions.
§ 3∙3. Partition of the energy tensor.

§ 2∙1. The Bernoulli fluctuation.
§ 2∙2. The standard of length.
§ 2∙3. Non-uniform curvature of space.
§ 2∙4. The extraneous standard.
§ 2∙5. Pseudo-discrete wave functions.

(The title of § 2∙5 was altered from ‘Occupation factors’.)