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ff. 1–9:
§ 1. Introduction.
§ 2. The theoretical formulae.
§ 3. Comparison of theory and observation.
§ 4. Alternative experimental methods.
§ 5. Values of the constants.

f. 10:
§ 5. The problem of consistency [beginning].

f. 11:
[§ 6. The β-coefficients [conclusion].]

ff. 12–21:
[§ 2. The theoretical formulae [conclusion].]
§ 3. Comparison of theory and observation
§ 4. Values of the constants.
§ 5. The problem of consistency.
§ 6. The β-coefficients.
§ 7. The spectroscopic e/mec.

ff. 22–5:
§ 6. The β-coefficients.
§ 7. The constant e/mec [beginning].

(This item comprises various superseded parts of B3/19. The sheets have been numbered in the order in which they were found, but it is possible that some jumbling has taken place. At least six different states of this paper may be distinguished, as follows:
(i) B3/18, ff. 1–9.
(ii) B3/19, ff. 1–6; B3/18, ff. 12–21
(iii) B3/19, ff. 1–12; B3/18, f. 10.
(iv) B3/19, ff. 1–15; B3/18, ff. 22–25;
(v) B3/19, ff. 1–16; B3/18, f. 11; B3/19, ff. 18–?.
(vi) B3/19, ff. 1–17, 17a, 18–23.)

(A typed copy of B3/14, with alterations which appear in the printed version B5/1.)

§ 28. Non-Coulombian energy.

Introduction.

Introduction.

Part I: The Uncertainty of the Reference Frame.
§ 1. The uncertainty of the origin.
§ 2. The Bernoulli fluctuation.
§ 3. The standard of length.
§ 4. Range of nuclear forces and the recession of the nebulae.
§ 5. Uranoids.
§ 6. The extraneous standard and scale-free physics.
§ 7. Stabilised characteristics.
§ 8. Pseudo-discrete states.

Part II: Multiplicity Factors.
§ 9. The rigid field treatment.
§ 10. Rigid fields in scale-free physics.
§ 11. Standard carriers.
§ 12. Mass-ratio of the proton and electron.
§ 13. The inversion of quantum energy.
§ 14. Rigid coordinates.
§ 15. Mutual and self energy.

Part III: Electrical Theory.
§ 16. Interchange of comparison particles.
§ 17. Electric energy.
§ 18. The β-factors.
§ 19. The fine structure constant.
§ 20. Comparison with observation.

Part IV: Gravitation, Exclusion and Interchange.
§ 21. Physical and geometrical momenta.
§ 22. The creation of proper mass.
§ 23. Determination of m0 and m.
§ 24. The constant of gravitation.
§ 25. Exclusion.
§ 26. The negative energy levels
§ 27. Interchange of external particles.
§ 28. Non-Coulombian energy.

(For the date, see Slater, p. 12. The titles of §§ 11 and 22 were altered respectively from ‘Initial and transition energy’ and ‘The origin of proper mass’.)

§ 1. Relation between quantum theory and relativity theory.
§ 2. The standard of length.
§ 3. The two ways of representing energy.
§ 4. Representation of energy by curvature.
§ 5. Representation of energy by waves.
§ 6. Wave analysis of the uranoid.
§ 7. The specified particles.
§ 8. Determination of m/m0.
§ 9. Degeneracy pressure.
§ 10. The cosmical constants.
§ 11. The relation E/V=3P.
§ 12. The time-periodicity of wave functions.
§ 13. Nuclear physics.

(This appears to be the English original of a paper given by Eddington at Warsaw in 1938 and printed as ‘Applications cosmologiques de la théorie des quanta’ in Les nouvelles théories de la physique (Institut International de Coopération Intellectuelle, Paris, 1939).)

(Contains a reference to the printed version of ‘The Theoretical Values of the Physical Constants’, published in Nov. 1942. Cf. B3/19).

(Refers to a letter by Dirac published in Nature on 20 Feb.)

§ 73. Fermi-Dirac particles.
§ 74. Multiple occupation symbols.
§ 75. Wave functions.
§ 76. The wave representation of phase.
§ 77. The cosmical number.
§ 78. Epistemological foundations.
§ 79. The primitive measurement.

These papers are all manuscripts in Eddington’s hand, with the exception of B3/17, which is typed, and B3/12, which is a carbon copy of a typescript.

§ 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.)

§ 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.

§ 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’.)

§ 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’.)

§ 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’.)

§ 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.

§ 3∙1. Idempotent vectors.
§ 3∙2. Spectral sets of particles.
§ 3∙3. The linear wave equation.
§ 3∙4. Matrix representation of E-numbers.
§ 3∙5. Wave vectors and tensors.
§ 3∙6[a]. Space tensors and strain tensors of the second rank.
§ 3∙7[a]. Angular momentum.
§ 3∙8. The differential wave equation.
§ 3∙6[b]. The differential wave equation.
§ 3∙7[b]. Angular momentum.

§ 11. The Bernoulli fluctuation.
§ 12. The standard of length.
§ 13. Non-uniform curvature of space.
§ 14. The extraneous standard.
§ 15. Scale-free physics.
§ 16. Pseudo-discrete wave functions.
§ 17. Stabilised characteristics.
§ 18. Stabilisation of tensors.

§ 1. The conditions of observability.
§ 2. The Gaussian distribution.
§ 3. Relative distribution functions.
§ 4. Relative wave functions.
§ 5. The weight function.
§ 6. Uranoids.
§ 7. Spherical space.
§ 8. The zero-temperature uranoid.
§ 9. Primitive observables.
§ 10[a]. V3 and V4 particles [incomplete].
§ 10[b]. V3 and V4 particles.

§ 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’.)

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

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.

§ 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.)

§ 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.

§ 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.

§ 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.)

§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.

[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.

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.