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§ 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.)

§ 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.

§ 121. Radiation by a moving electron.
§ 122. Transition probabilities.
§ 123. Compton scattering.
§ 124. Transverse self energy of a particle.

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’.)

Introduction.

§ 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.

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.

§ 28. Non-Coulombian energy.

§ 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’.)

§ 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”’.)

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

§ 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.

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.)

§ 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.

Abstract.

§ 1. Introduction.
§ 2. The theoretical formulae.
§ 3. Comparison of theory and observation.
§ 4. Values of the constants.
§ 5. The problem of consistency.
§ 6. The β-coefficients.
§ 7. The constant e/mec.
§ 8. The constant h/e.

(This manuscript, which is marked as having been received by the Physical Society on 8 June, was evidently used as the copy for the text printed in the Society's Proceedings.)

Slater has marked this paper ‘CRTQT’ in red ink, but in his book it is referred to by the letter ‘D’ (see p. 9).

(The accompanying list of attendees (C2/1b) is subscribed ‘Lemaître [one of the attendees] 1924’, which may indicate the year in which the lectures were given.)

§ 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.

These papers are both in Eddington’s own hand.

In 1912 Eddington led an expedition from the Royal Observatory to Brazil to observe and photograph a total eclipse of the sun. These letters contain an account of the expedition. Eddington specifically asked his mother to preserve the letters because he was keeping no other record of events (see A2/5), and she seems to have been careful in carrying out his request, as the sequence is probably complete. The letters are numbered from 1 to 9 in a contemporary hand, and the ninth letter, finished when the writer was about three days’ sail from home, was almost certainly the last. These letters formed the basis of the account in Eddington’s Notebook (ff. 96–102), and they were consulted by Douglas, who quoted from A2/8 (pp. 18–19).

Eddington and his assistants C. R. Davidson and J. J. Atkinson left Southampton aboard the steamship Arlanza on 30 August and arrived at Rio de Janeiro on 16 September, where they were joined by T. N. Lee, an Englishman deputed by the Brazilian Government to assist them, and J. H. Worthington, an amateur astronomer. Six days later the party arrived at Passa Quatro, their chosen observation point—preferred to other possible sites at Cruxeiro, Christina, and Alfenas—and on 3 October they were joined by two volunteers, Leslie Andrews and O. Couto de Aguirre. A local man, Pierre Seux, also volunteered to help by counting seconds during totality. The eclipse took place on the 10th, but unfortunately observations of the phenomenon were prevented by rain and the expedition was largely unsuccessful. Eddington and his companions left Passa Quatro on 20 October and sailed for home on the Danube on the 23rd. The date of their arrival in England is not recorded, but towards the end of the voyage they were expecting to be at Southampton on 10 November. A report of the expedition, by Eddington and Davidson, was printed in MNRAS (lxxiii, 386–90) the following year. Notes also appeared in The Observatory, xxxv (1912), 328–30, 410, and xxxvi (1913), 62–5.

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.

§ 1∙1. The conditions of observability.
§ 1∙2. Measurables.
§ 1∙3. The fundamental tensor.
§ 1∙4. The comparison fluid.
§ 1∙5. Wave functions.
§ 1∙6. Density and mass.

(Earlier than B2/17. Contains two-number references.)