§ 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’.)
§ 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.
(See the general note on this file.)
(This is an early version of part of a report to the Royal Society by the Joint Permanent Eclipse Committee. The latest date mentioned in it is 14 July 1919, and the report was received by the Society on 30 October and read on 6 November.)
Transcript
1912 Sept 11
R.M.S.P. Arlanza {1}
My very dear Mother
We are getting near Pernambuco now. The time at sea has passed very rapidly and pleasantly and I shall be very sorry when the voyage is over. The slightly overcast skies which we had about Madeira have given place to continual bright sunshine, but there has been a strong refreshing breeze always. Most of the regular travellers on this route say they have never known it so fresh and cool all the way. The only time I find it really hot is when I come down from the deck at night to the cabin; then for an hour or so it seems very close and I usually read for an hour to get cool again before going to sleep. The dining saloon, decks, & smoking rooms are beautifully cool. Of course I am wearing the thinnest things possible.
We did not land at St Vincent but were surrounded by boats (as at Madeira)[.] These were all occupied by negroes; the little nigger boys were very amusing[;] I tried to photograph them. I saw a shark whilst we were at anchor. We see lots of flying fish, regular shoals of them, skimming from wave to wave. Most of them are very small[,] almost like butterflies. They look very pretty in the sunlight.
I have got to know some of the southern stars now but they are poor compared with the northern ones. The Southern Cross is not visible yet[;] it is the wrong time of the year for it. The Chief Officer took me up on to “Monkey Island” above the Bridge where one gets a good clear view of the sky.
One day is much like another and I hardly keep account of time. We have had Sports, Games, Fancy Dress ball, etc. I went in for several of the Competitions—including spar-boxing (with the pillow), life-belt race, Are you there?, deck quoits, threading the needle (with Lady Grant holding the needle), but did not have much success, except at chess. I got to the Final Round at Chess, and had to play quite a young opponent for the final. We drew one game and he won the replay. They had a specially good dinner to celebrate the 90th Anniversary of the Independence of Brazil, and some speeches (chiefly in Portuguese)[,] also a dance which did not interest me.
Of course I know a good many people by now. One man that we see a great deal of is Major Caroll (an Irishman)[;] he is a very nice fellow. The Captain comes down to dinner generally; although he is said to be the most popular man in the service I dont care much for him. He seems generally grumbly—a pig-headed old man I think; though I have no doubt as a Captain he is very good indeed. Lady Grant also is a tiresome old lady, with an enormous appetite. The Unwins are quite nice people.
We pass a great number of ships chiefly tramp steamers. The Avon passed us quite close a few days ago and I saw it. We had one little excitement yesterday as a tramp steamer required a Doctor (a man having got an iron splinter in his eye) so we stopped whilst he was brought on board and attended to.
We crossed the Equator about 3 o’clock yesterday afternoon but there were no traditional observances; everyone (at the time[)] was excited about a tug-of-war Married v Single. Atkinson pulled in it as well as Davidson & I. The “married” were ever so much heavier than we were, and pulled us over easily.
It is curious having no letters or English news of any sort. We have not even had the daily Marconigram since leaving Lisbon—have heard nothing whatever. I hope you are getting on well.
We expected to be in the Doldrums the last three days—a region of calm close air with rain—but instead of that we have had delightful fresh weather[;] it is most unusual just here.
With very dear love from
your affectionate son
Stanley
I hope Winnie is having a got {2} time at Lynton[.]
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Letter-head of the Royal Mail Steam Packet Company. Numbered ‘3’ at the head in pencil.
{1} ‘R.M.S.P.’ is printed.
{2} A slip for ‘good’.
Transcript
Funchal
1919 March 27
My very dear Mother
We have been here nearly a fortnight, and though we are anxious to be getting on to Principe, it is very delightful being here and I am not at all tired of Madeira. We have had a variety of weather; but there is always a good deal of hot sunshine every day. At first we had three days of “leste”, a hot dry east wind coming from the Sahara; it blows in gusts—dead calm for a long time then quite suddenly a furious wind for about 10 minutes. It did a good deal of damage to the trees and to the tiles on the roof here. Afterwards we had brilliant weather all day, but not quite so hot. This last week we have had a good deal of rain—chiefly at night but some sharp showers in the day as well—with snow on the tops of the mountains. Now it is comparatively cold; but that is only relatively speaking; because I am still wearing my thinnest shirts & vests and can sit out of doors even at night.
I have been two good long walks on the mountains. The funicular railway is not running regularly but there are occasionally excursions. We went up one day starting at 12 o’clock and reached the top—Terreira de Lucta—(2800 feet) about one o’clock. Cottingham and I took some sandwiches, and walked on at first by road and then on the hillside, making for a special view-point in the centre of the island. He found it too hard work, so I left him for 1½ hours and finished the climb alone. The view-point, Ariero Observatory, is 4800 feet above sea-level, and is a balcony overlooking a magnificent gorge at least 2000 feet deep which winds down to the sea on the other side (north) of the island. After seeing this, I rejoined Cottingham and we walked back to Terreira de Lucta which we reached about 5 o’clock, and then came down into Funchal in a toboggan a run of about 4 miles.
The second expedition was to the Grand Curral a point further round to the west. Cottingham and I started at 9 o’clock, and we got back about 5∙30. The walk was nearly twenty miles; but the weather was cooler so it was easier. Most of the way was along paved roads often very steep. We got many fine views on the way; and in places the gorse was out, and looked very pretty. The Grand Curral (=great cattle-fold) is a small plain almost entirely surrounded by a ring of mountains—like the crater of a volcano. We looked down on it from a saddle 3300 feet above sea-level and more than 2000 feet above the Curral. On all other sides the mountains were much higher. It is extraordinary, how much of the land is cultivated, all the steep sides of the mountains are terraced into tiny fields up to a great altitude. There is an elaborate system of irrigation; the artificial water-courses (called “levadas”) tap all the rivers near their sources, taking away nearly all the water and leaving only stoney† beds.
The main place of resort in Funchal is the Casino. We often go there in the afternoon for tea. The tea (the beverage) is much better than at the hotel; it has been very scarce in Madeira. There is a roulette table which is well-patronised and it is interesting to watch the players.
The beach is very poor, very steep and stony; and is unattractive, because it is used as the general rubbish-heap. But it is interesting to sit on the pier especially when any of the large steamers are in. There has been no mail from England since I came; but we are expecting one today—the Chepstow Castle—. I did not know I should be here so long or I would have asked you to write here.
There are lots of bananas here and I usually get through about a dozen a day. There is not much other fruit. Prices are generally a bit lower than in England but there is not much difference. The meat here—mutton, veal, beef—is extraordinarily good the best I have ever tasted I think. We can get good cigarettes at 10 a penny; but I chiefly smoke a mixture of native tobacco at a penny an ounce with imported tobacco at a shilling an ounce—the native stuff is too dry to use by itself.
We made friends with a gentleman from the telegraph (cable) station, and he got us permission to see round it yesterday. It was very interesting. They have a lot of new improvements since I was at the station in Malta.
There was a British warship here one day, and they had a football match against the Cable station, which we went to see. The weather was more suitable for watching than for playing. They must have found it terribly hard.
We know a number of people in the hotel. Ritson a commercial traveller from Manchester, Ash a queer old gentleman, Mrs. Caswell a merry widow and her daughter, Mr and Mrs Thomas from Swansea and others. Most of them intend to go on to the Canaries next Sunday. The landlord & landlady Mr. & Mrs. Jones are extremely pleasant & good-natured people.
Three ships were torpedoed by submarine in Madeira harbour during the war, and one sees the masts of two of them sticking up out of the water. The town was also bombarded and there are a few traces visible.
I hope all is going well at Cambridge. I shall be glad to hear news of you when I reach Principe.
With very dear love from
your affectionate son
Stanley
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Numbered ‘3rd’ at the head. Four passages have been marked off and emended in pencil by a later hand.
† Sic.
§ 1. The uncertainty of the origin.
§ 2. The physical origin.
§ 3. The Bernoulli fluctuation.
§ 4. The standard of length.
§ 5. Range of nuclear forces and the recession of the galaxies.
§ 6. Spherical space.
§ 7. Uranoids.
§ 8. The extraneous standard.
§ 9. Scale-free physics.
§ 10. Pseudo-discrete states.
§ 11. Stabilisation.
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.
§ 1. The conditions of observability.
§ 2. Correlation.
§ 3. The uncertainty of the origin.
(Earlier than B2/17. Contains a reference to an article by H. C. Corben in the Proceedings of the Cambridge Philosophical Society, xxxv (1939), 203.)
(Pasted inside the back cover is a statement of Eddington’s account with the Clarendon Press in respect of sales of Stars and Atoms during the year ending 31 Mar. 1944.)
Transcript
Meadow Brow, Grasmere.
VIII. ’02
Dear Mrs. Eddington,
My last duty is now one of simple good wishes.
The men up for Physics Hons. were a set much better than in any previous year. Any of the first three would have been top in any other year; & Stanley was well ahead of the others, & obtained over 80 per cent on the whole examination.
He will find a larger sphere and more competition at Cambridge; and I trust we shall hear he is bearing himself well under it.
With best wishes
I remain
Your friend sincerely
John W Graham
§ 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.)
Transcript
Observatory, Cambridge
21 May 1936
Dr W. M. Smart’s application for the Chair of Regius Professor of Astronomy in the University of Glasgow has my warmest support. He is a man of established reputation in astronomical circles who would fill the office with distinction; and he has proved himself very successful as a lecturer and teacher. He would be much missed from this Observatory and from the University; but promotion to a professorial chair would be a fitting recognition of his work.
Dr Smart has been Chief Assistant in the Observatory and John Couch Adams Astronomer since 1921. There is only one other Assistant. The policy of the Observatory has been to avoid routine undertakings and to develop new methods. Two main lines of work have been developed during his tenure—an improved method of determining photographic proper motions of stars, and measurement of stellar magnitudes with a photo-electric cell. As regards the former it may, I think, be claimed that the Cambridge results set a new standard of accuracy for large series of proper motions. Photo-electric work is still confined to two or three observatories (Cambridge being the only British one). After a long struggle with pioneer difficulties the work is now proceeding with great success, and astonishing accuracy is obtained. A large share of the credit for these results is due to Dr Smart.
On the theoretical side his earlier work was in celestial mechanics. But in connection with the practical work above-mentioned his more recent interests have {1} been mainly in proper motions and other branches of stellar statistics, to which he is one of the most active contributors. He is a member of the Commission of the International Astronomical Union on Stellar Parallaxes and Proper Motions.
His teaching work covers elementary lectures on astronomy, advanced lectures on celestial mechanics and on stellar motions and a practical class at the observatory. Judging from the response of the students he is a stimulating lecturer. He normally supervises one or two research students.
An important part of his experience is his work as Secretary of the Royal Astronomical Society during the last five years. This brings him into touch with astronomers in all parts of the world, so that he is in full contact with all modern developments. It is perhaps not irrelevant to mention that he is Treasurer of the Royal Astronomical Society Dining Club—an office (of which the duties are by no means confined to the care of money) which is a tribute to his popularity with his colleagues.
To sum up:—He has shown himself able to make the most of the resources of a small observatory; he is well-known and esteemed internationally; he is successful with students; and is well used to administrative activity.
—————
The various cancelled words and passages in this letter have not been recorded, except for the mistaken deletion noted below.
{1} Struck through by mistake.
§ 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.
§ 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.
(Marked by Slater: ‘Lectures as delivered orally.’ The date assigned to this document is the date the lectures were given.)
§§ 1–2. [Unfinished.]
§ 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.]
§ 1∙9 [continued].
Part of an unidentified chapter.
§ 1∙9. Individual and statistical particles.
§ 1∙8. Electric charge.
Rough calculations.