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Chapter IX: Wave Functions
EDDN/B/2/2 · Stuk · Apr. 1944
Part of Papers of Sir Arthur Eddington

§ 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.

EDDN/B/2/4 · Stuk · Feb. 1944
Part of Papers of Sir Arthur Eddington

§ 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.

Chapter VII: Double Frames
EDDN/B/2/5 · Stuk · Jan. 1944
Part of Papers of Sir Arthur Eddington

§ 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’.)

EDDN/B/2/9 · Stuk · Dec. 1942–Aug. 1943
Part of Papers of Sir Arthur Eddington

§ 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.)

EDDN/B/2/17 · Stuk · [before July 1942]
Part of Papers of Sir Arthur Eddington

§ 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”’.)

Chapter V: Electric Charge
EDDN/B/2/19 · Stuk · [before July 1942]
Part of Papers of Sir Arthur Eddington

§ 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.

[Chapter I]
EDDN/B/2/20 · Stuk · [early 1940s]
Part of Papers of Sir Arthur Eddington

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

EDDN/B/2/27 · Stuk · [before July 1942]
Part of Papers of Sir Arthur Eddington

§ 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.)

EDDN/B/2/34 · Stuk · [before July 1942]
Part of Papers of Sir Arthur Eddington

§ 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.

[Untitled]
EDDN/B/3/4 · Stuk · [before July 1942]
Part of Papers of Sir Arthur Eddington

§ 1. The conditions of observability.
§ 2. Correlation.
§ 3. The importance of systematic description.
§ 4. The uncertainty of the origin.
§ 5. Application to wave functions.
§ 6. Three-dimensional distributions.
§ 7. Extension to four dimensions.
§ 8. Curvature of space.
§ 9. Standard masses of the particles.

EDDN/B/4 · Bestanddeel · early 1940s-1982
Part of Papers of Sir Arthur Eddington

The note accompanying these papers (B4/8) begins as follows: ‘This card folder contains a small number of loose and partly unidentified sheets that were separated from the otherwise orderly arrangement of the Eddington papers that had been in the hands of Professor N. B. Slater.’ There follows a brief description of the three letters (B4/5–7) and the sheets in Eddington’s hand (B4/1–9). Eddington’s manuscripts have been listed as nine items. The first (B4/1) forms a sequence of four sheets numbered from 36 to 39, formerly stapled together, as Dewhirst’s note records. The first sheet was marked by Slater in red biro: ‘(Attached to MS §a).’, apparently referring to B3/1, which comprises thirty-five sheets, though the character represented by the section-mark is indistinct. The next three items also appear to form distinct sequences, possibly all from the same doc-ument: B4/2, comprising six sheets numbered from 3 to 8; B4/3, two sheets, of which the second, unnumbered, clearly follows the first, which is numbered 10; and B4/4, comprising two sheets numbered 12 and 13. The remaining five sheets have been listed singly (B4/5–9). The first two of these contain similar tables on the back. The folder, which was simply marked with a ringed ‘A’, has been discarded.

Chapter VII: Wave Vectors
EDDN/B/1/9 · Stuk · July 1944
Part of Papers of Sir Arthur Eddington

§ 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 X: The Wave Equation
EDDN/B/1/12 · Stuk · Sept. 1944
Part of Papers of Sir Arthur Eddington

§ 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.

EDDN/A/1/2 · Stuk · 2 July 1899
Part of Papers of Sir Arthur Eddington

Transcript

Dalton Hall, Victoria Park, Manchester

2. VII. ’99

Dear Mrs. Eddington,

You will be interested in hearing some details of Stanley’s Preliminary. They are astonishing enough.—I have heard them today from the Chairman of the Board of Studies. In

Mechanics. Full marks
Latin. Top of all
Eng History [ditto]
Mathematics [ditto] & 60 marks above everybody else

leaving Chemistry & Eng. Language as the only subjects in which any one excelled him.

This is a marvellous record; whether he ought to know it I leave to you.

The great thing now is not to overload him; and to keep up his exercise: but I see no danger of going wrong in either respect.

In Physics ii at Easter I find he got 99 per cent. in the College Examination, making 199 out of 200. He has half the prize in Latin, the Prize in Practical Physics as well as theoretical; and the 2nd place in Math iii. A.

He will now, I trust, go in for a good physical athletic holiday. With my hearty congratulations

I remain
Yours sincerely
J. W. Graham

EDDN/A/2 · Bestanddeel · 1912
Part of Papers of Sir Arthur Eddington

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.

EDDN/A/2/2 · Stuk · 6 Sept. 1912
Part of Papers of Sir Arthur Eddington

Transcript

1912 Sept 6
R.M.S.P. Arlanza {1}

My very dear Mother

There is an unexpected opportunity of sending a letter today, as we are calling at St Vincent to obtain a supply of fresh water; we could not get it at Madeira. After that it is no good writing until we reach Rio.

Last time I wrote was just after leaving Lisbon, since then we have had very pleasant weather, little wind, calm sea, sky rather overcast but with sunshine filtering through, and not unpleasantly warm, although we entered the tropics last night. We had a day at sea on Tuesday and reached Madeira about 11 the next morning. As we approached we passed a great many islands. Madeira is rather mountainous but a layer of clouds about some 3000 feet above the sea just cut their tops off, and remained all day. We were soon surrounded by lots of small boats selling basket chairs & embroidery—the two main products of Madeira—; also small boys wanting to dive for sixpences, some of them climbed to our highest decks and dived from there.

We had about 4 hours at Madeira and most of us did the regular excursion. Atkinson & Davidson did not come; but I went with the Unwins and Lady Grant. First we rode in chariots (there is no other word for them) drawn by a pair of bullocks[.] The streets are all cobbles and the vehicles are on wooden runners like sleighs; the bullocks gallop along finely. Then we went up the mountain Terreira da Lucca in a funicular railway, not quite to the top but 3300 feet up. The town (Funchal) is built in terraces on a steep slope. The abundance of vines laden with grapes was very remarkable, they grow on low pergolas. There were sugar canes[,] bamboos, palms, and beautiful blue hydrangias growing luxuriantly. Towards the top it was all pine forest. Just below the terminus we ran into cloud so lost the view; but as we had a fine view of the bay nearly all the way up, it did not so much matter. We had lunch at the top, and then came the exciting part—we tobogganed down the whole 3300 feet. There is a steep zigzag cobbled path down from the summit passing through the town; we go in a sort of basket toboggan holding 3 passengers, with with† two men running on each side with ropes to guide the toboggan and hold it back where necessary. They go at a great pace, {2} sometimes getting on and riding behind. It was much more exciting and alarming than I expected. We took about half-an-hour to get down. The sharp corners are particular[ly] exciting at first, because they always get up as much speed as possible to go round them (I suppose because swinging round checks the toboggan). After that came another bullock drive through the town to the launch, and so back to the steamer.

Now we have got to the main part of the journey, and shall be a week or more without any chance of landing. They are arranging some sports and I have entered for some of them. Atkinson is in for the tug of war and should be a tower of strength (and weight) for the “married” v “single”.

Captain Pope has been down to dinner twice, and is very pleasant and chatty. We are generally in the dining room half an hour longer than any-one else.

Tomorrow there is to be a celebration of the Anniversary of the Independence of Brazil. A Brazilian committee are arranging it.

I have not got much work done yet.

With very dear love,
ever your affectionate son
Stanley

—————

Letter-head of the Royal Mail Steam Packet Company. Numbered ‘2’ at the head in pencil.

{1} ‘R.M.S.P.’ is printed.

{2} Comma added in pencil.

† Sic.

EDDN/A/2/5 · Stuk · 11 Sept. 1912
Part of Papers of Sir Arthur Eddington

Transcript

Hotel dos Estrangeiros, Rio de Janeiro
Thursday | 1912 Sept 19

My very dear Mother

We are still here at Rio de Janeiro; it is a most beautiful place, the weather is fine and pleasant, but progress is very unsatisfactory. The great characteristic of Brazil is “amanhã” (“tomorrow”) and the delays and muddles of the people who are supposed to be helping us are most vexatious.

The Arlanza arrived in Rio soon after dusk on Sunday. In some ways it was a pity to miss the sail up Rio harbour in daylight but the lights were very beautiful. It is a wonderful harbour winding about, with numbers of islands and mountains everywhere. The Sugar-loaf (about 1200 ft) is an extraordinary steep cone. It has far surpassed my expectations.

We remained on board till the next morning, as I had a Marconigram to say that we should be met the next day. At 8 o’clock Dr Moritze† (the director of Rio observatory {1} [)] and Lee (the Englishman deputed to help us) came on board; {2} after arranging about the instruments, they took us off in a government launch. We were photographed by the newspapers on landing, and then whisked off in a motor-car to this Hotel. It is the swagger hotel though not up to much according to English standards. The Government is entertaining us here—very happily for us—money here has roughly 1/5 the value it has in England. I had to pay 2/8d for a cake of soap. Washing a dress-shirt costs 2/9d, an ordinary shirt 1/–. Carriage of our trunks up to the hotel (for three of us) cost 16/–; the tram-fare for say 1½ miles is 5d; a small bottle of ginger beer is 2/–; apples about ¼ each. The only things admitted into Brazil free of duty are human beings and they have to pay a duty of 2£ to get out again.

The currency here seems very funny[.] I am carrying about in my pocket now over 800,000 reis so am nearly a millionaire. 1000 reis = 1/4½ but its purchasing power is about 3d according to our standards. I am told that the salary of an engine-driver on a railway is (in English money) £900 a year.

We called on Sir William Haggard the British Minister {3} on Monday morning and in the afternoon went with him to be presented to the Minister for Foreign Affairs {4}. Sir William is quite a pleasant man, and we are to go lunch with him today.

They are very eager to entertain us well; but have not taken the least trouble to help us with our baggage. Instead of bringing it off in a special lighter as they undertook to do, they let it get all mixed with the other baggage and go to the custom-house[.] I have spent hours hunting round after it, and Lee is no use or help at all. It was all unloaded yesterday and I watched the process; but they only sent with me a man, who could talk no French or English, so it was very difficult doing anything. Now they tell me a case is missing (though I am sure it was all there yesterday) and I have to go—again with a man who talks nothing but Portuguese—to hunt it up. This has meant another day’s delay. {5}

I have decided to go to Passo Quatro; it is quite a good place and not so far away as Christina or Alfenas. Moritze† is to be there too; he is very pleasant[,] talks English (the worst English I ever heard) and is really doing his best for us I think. The chief objection to Passo Quatro is that all the ministers, ambassadors, reporters and tag rag and bobtail will be going there; but I think we shall not really be disturbed by them. I should have gone to Alfenas, if I could have depended on Lee, but the difficulties are too great when one has no real assistance. {5}

We have been made honorary members of the Club Central here, which is very convenient, as we are a good way from the main city at this Hotel.

The trees and gardens about here are very interesting and the palm-tree avenues in particular are beautiful. I do not think there is any chance of our sailing from here until Oct. 23 and I am looking forward to having a week’s sightseeing and so on before leaving.

We have got English news now up to Sept. 2.

Please keep these letters as I have no other record of events.

With very dear love from
your affectionate son
Stanley

Later (evening)

I had just finished this when the Portuguese gentleman came to go with me to the Customs-house but I was very glad to see with him Perrine of the Argentine expedition, who landed yesterday, and whom I have met in England. He was a great help to us. We motored to the Customs-house and there I found my baggage was all there—nothing missing—so the lost case was a false alarm, and saw it loaded on trucks to be taken to the Station—so we are really getting on.

There was just time to get to Sir William Haggard’s in time for lunch. The other guests were the American Ambassador {6}, Birch the Secretary of the British Legation, Lee, Worthington and another man. These with Lady Haggard & her daughter and our three selves made eleven. It was a very pleasant party; the Haggards & the American Ambassador are very genial and nice. The inevitable newspaper photographer turned up and we had to submit.

After leaving them we went on to the Botanical Gardens, and spent an hour or two there; they are just lovely. Very few flowers, but the trees are wonderful—magnificent avenues of palms, and tropical bushes of all sorts. We shall certainly visit them again.

We may get away tomorrow evening; but I expect it is more likely to be Saturday. There is a break of guage† on the railway at Cruxeiro and the baggage has to be changed over on to another waggon there.

Your loving son
Stanley

—————

Numbered ‘5’ at the head in pencil.

{1} Henrique Morize was Director of the Brazilian National Observatory at Rio de Janeiro from 1908 to 1930.

{2} A vertical line has been drawn in pencil in the margin, probably to mark the phrase ‘and Lee … came on board’.

{3} Sir William Haggard, brother of the novelist Rider Haggard, was British Envoy Extraordinary and Minister Plenipotentiary to Brazil from 1906 to 1914.

{4} Lauro Müller, who was Brazilian Minister of Foreign Affairs from 1912 to 1917.

{5} A vertical line has been drawn in pencil in the margin by this paragraph.

{6} Edwin V. Morgan, US Ambassador Extraordinary and Plenipotentiary to Brazil from 1912 to 1933.

† Sic.