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Observatory - GA 'tried the rings on the diamond this morning, and they succeeded perfectly' [light polarised through a diamond].

Observatory - GA gives a description of his observations of light polarised through glass and a diamond: 'At the first angle of incidence where this takes place (viz. the polarising angle of the glass) the rings go out, evanesce, and disappear: and on increasing the angle they appear in as good proportions at the first instant when visible as when tolerably bright - the white center having the same proportion to the 1st ring did. Of this I am quite certain, having looked carefully. But at the second angle (viz. the polarising angle of the diamond), where the white-centered rings change into black-centered, there is no such thing; the rings do not vanish at all though they become faint; but the first black ring contracts, squeezes out the white center, and itself becomes the black center. This also I have examined carefully. The same thing takes place when, at an angle between the polarizing angles, the tourmaline or prism is turned round'. Amongst other things this proves that the 'diamond does not polarise perfectly at any angle'. Vibrations in the plane of incidence change from + to - on passing through the angle where the polarisation is nearest to perfection. This is 'not by becoming =0 (as certainly they do in glass & all things that polarise perfectly) but by an alteration of the plane.'

Observatory - Gives a note on perturbations intended for John W. Lubbock: 'If perturbations are applied to x y & z, there is no practicability of dividing the time of an apposition into different parts, as the calculation does not give the means of correcting the elements for the beginning of each part. Consequently the series used must be such as will apply from the beginning of an apposition to the end. It seems to me very probable that 5th or higher powers may be wanted'.

Observatory - GA gives his views regarding Barlow's [correction] of ship-magnetism: 'The importance of its error (other changes not considered) increases as the directive force of terrestrial magnetism on the horizontal needle decreases, that is as the dip increases. Under this circumstance, the absolute error is small, because the section perpendicular to the dip is nearly the same in all portions of the ship. So that the error is small in the circumstance in which its relative effect is great. On this account it is doubtless a good thing when most wanted' GA gives his breakdown of the 'facts' concerning the theory of humming tops.

Royal Observatory Greenwich - Answers WW's queries: when Newton's 'analysis is carried to perfection (i.e. so as to shew Fraunhoffer's lines), it has certainly developed original properties of light... Their existence in the diffraction spectrum tends most strikingly to confirm this. - You may also say that persons who have tried the experiments with great care do not believe in [David] Brewster's changes of colour. - The changes of colour are certainly the only source of his objections'. The French have always associated Thomas Young with the discovery of the undulating theory of light.

Royal Observatory Greenwich - The clock for the Northumberland telescope is nearly finished. Could WW get [James] Challis to send to [William] Simms or GA 'the breadth of the hole that is left by the side of the south pier of the polar axis for the clock weights to drop into; as that will determine the construction of our weights'. Could WW ask the President of the Council of the Cambridge Philosophical Society, whether they would present to the library of the Royal Observatory a copy of the Transactions of the Society. This will help bind the links between the Observatory and Cambridge.

Royal Observatory Greenwich - In response to Colonel Everest's pamphlet, GA wrote to the East India Company to inquire into the nature of Major Jervis's appointment. They wrote back stating that it was for the entire management of the India Survey: 'There is a charming appointment for you! Given a furious fellow like Everest on one side, and a not-over-wise one like Jervis on the other, I do not think that a better appointment could have been devised for the purpose of setting them together by the ears and dragging some innocent persons into the quarrel'.

Royal Observatory Greenwich - Could WW send GA 'a parcel of the mild Trinity ale - for which my "government" have a great esteem'. When GA was last in Cambridge Deighton [book publisher] told him that nearly all of GA's tracts were gone and wished to know what he intended to do: 'Can you help me with your council? I have hardly time to give such attention to the thing as would be necessary to keep it to level...also it is very likely that somebody else would do it better'.

Flamsteed House, Greenwich - Thanks WW for the ale [see GA to WW, 10 October 1839]: 'we shall consume it I believe before time has done it justice'. GA has not seen WW's lecture to the Philosophical Society on tides: 'I should much like to see it; and shall be glad if you can send it to me. I have not duly consulted Herschel, but I remember his general notions about forced oscillations and so far in application to tides they must agree with mine. By the bye, my correlative terms are forced tide wave and free tide wave. In the simplest cases which can be conceived, the two are mixed together so as to produce phenomena that, viewed as observations from which empirical laws are to be deduced must appear inextricably confused. In one case only, namely when a limited space is very small, the tide becomes a simple tilt, like that of water in a basin. This cannot be the case in a sea so large and (comparatively) shallow as the Pacific, but upon one supposition one of the waves there may predominate, and there may be phenomena something like Fitzroy's. But I should like to see what you have said'.

Flamsteed House, Greenwich - Could WW send him a tracing of the Kamschatham waves? - preferably the whole course of the water in rising and falling.

Royal Greenwich Observatory - GA's paper 'On a New Construction of the Going Fusee, Adapted in the Clock-Work of the Northumberland Telescope' is ready, and he will be reading it on Monday evening at the Philosophical Society.

Royal Observatory Greenwich - Gives his comments regarding WW's paper on the history of optics and light in general [for his The Philosophy of the Inductive Sciences, Founded Upon their History?]: 'There is one fault in the general arrangement, which I do not see how to remove - namely, that the phenomena and explanations of fringes, gratings, &c, did precede in history and do precede in mental comprehension those relating to dipolarisation. But the things are very much interlaced all through'.

Royal Observatory Greenwich - Proposes to visit Cambridge on 10 November.

Royal Observatory Greenwich - GA has been reading WW's work on tides 'with great pleasure and profit'. He gives an outline of queries he finds between various collected observations - especially around the coast of Britain and parts of Europe - and theory.

Royal Observatory Greenwich - GA has looked at the account of [John Scott] Russell's Forth tides in the Athenaeum and 'think you will find that Russell's notion of the southern and northern waves exhibiting themselves separately is wholly untenable, both from theory, and from the consideration that they ought to shew themselves as well in the coast tides; but in fact if there are two they become one inseparable tide. The real explanation I have no doubt is in the theory of deep waves in shallow canals'. GA gives the formula and coefficient (for the rise of tide / depth of channel) showing the height of the water after running over a shallow bottom for a certain distance. GA has looked over WW's tide paper and has a problem with the figures and arrangement of the data given in the tables of Plymouth observations.

Royal Observatory Greenwich - Could WW send him 'bound or unbound' his copy of La Lande's 'Traite du Flux et Reflux de la Mes'.

Flamsteed House, Greenwich - Some time ago GA asked for WW's opinion about republishing his tracts [see GA to WW, 10 October 1839]. GA then wrote to Deighton [book publisher] - 'they say that the book sold very slowly and they do not like to publish again on their own risk; most certainly I shall not do on mine'. Has WW any suggestions on making it 'readable' or know of any young man who might take up the thing? - 'a treatise on Optics ought to exist in the world'. GA has not done much work on tides recently. The gale of wind of January 2 and the following morning 'produced a most marvellous effect on the succeeding tide in the Thames. He has received Bunt's [Thomas G. Bunt] Bristol observations taken from the self registering tide gages: 'It is a great pity that he does not go to low water; and also that there is not an infinity of tide gages and gages symmetrically distributed over the coasts and seas'. They should try and get the observations from Brest. Can WW get the readings from the wind mometers in Cambridge from January 1 to January 4. GA wants to find the course of the wind in connexion with the tide.

Flamsteed House, Greenwich - It was GA who brought the tide disturbance of January 3 to the attention of the Admiralty: 'The tide in the Thames was 6 feet lower than it ought to have been. I have received several of the Admiralty observations: the tide at Leith seems to have been scarcely affected' [see GA to WW, 21 January 1841]. GA gives a long descriptive and mathematical answer to WW's query regarding oblique arches.

Flamsteed House, Greenwich - GA returns 'Hewett's papers (letter, table, and picture) for which I am much obliged'.

Royal Observatory Greenwich - George Peacock has advised GA to apply to WW for names of weights and measures: 'I want a good name for 1/1000 part of an acre, or 1/100 of a square [chair?], or a square of 2 1/5 yards each side'.

Royal Observatory Greenwich - WW should translate Littrow's papers [Joseph J. Littrow] and send them to the secretary of the Astronomical Society: 'From the few words of account which you give, I doubt whether their value is great... It has probably this degree of novelty that it is not published; but it is such as any one would hit on in the time of need'. The remark about the ships compasses is curious and new to GA: 'I will ask Fisher (who I think knows more than almost any other person about compasses in ships) whether he has observed it. It is likely enough, theoretically, to be true'. The principal parts of Littrow's history may be put into the speech at the Royal Society.

Royal Observatory Greenwich - GA has put [Pierre-Simon] Laplace's theory of tides 'in a shape in which other people can read it, and a very beautiful theory it is. But as Laplace left it is so atrociously repulsive that I do not think that any person ever mastered it (for no body refers to it) and I imagine that no person living but myself has fairly attempted it. In this I think I have done good service to the literature of mathematics'. GA gives a solution to the age of the tide: 'The time of high water is accelerated, but more for the moon than for the sun. Consequently (referring to solar time) the moon's high tide on any day, happening earlier than corresponds to the moon's position, does happen at s solar time corresponding to the day when the moon's transit was earlier - that is to a preceding day; the solar tide corresponds equally (in solar time) to all days; and therefore their combination corresponds to an earlier day. Thus we have age of the tide'. Can WW give any accounts on the height of waves, experiments on waves generally and a notion of the changes which WW's 'researches will make in your old cotidal lines?'

Royal Observatory Greenwich - GA had intended to be in Suffolk on Tuesday but Humboldt and the King of Prussia are expected to arrive in the Thames today, and Humboldt will probably want to see the Royal Observatory - 'I should much like to shew it to him'.

Weymouth - Is in Weymouth on part of his journey of tide observation: 'I have found more than once that a great deal of good is done by going to see with one's own eyes things which other people's words have made mysterious... And it has answered well. The tides appear to be all shallow-water-tides'. Although GA's theory of tides is in an unfinished state - 'it is in a state which any body else can complete who will take the trouble'. GA went to observe the surf at the Chesil Bank at Weymouth: 'The surf is the most majestic thing that I have seen'.

Royal Observatory Greenwich - GA can supply WW with absolutely no information concerning the Oxford candidates, although he did briefly meet Walker when he came to view an Anemometer: 'I do not think that either of them is known out of Oxford'.

Royal Observatory Greenwich - GA now remembers that he has heard something of one of the Oxford candidates [see GA to WW, 27 March 1842]: on referring to a letter he finds 'that Donkin has written 4 articles' in Gregory's mathematical journal on the subject of analytical geometry, signed M.N.N (1839, vol. 1 and 1841, vol. II). He has also written a paper on Greek music in 'Taylor & Walton's Dictionary of Antiquities': 'The mathematical papers are doubtless within your reach & you can therefore judge'.

Hotel Feder, Turin - GA gives an outline of his movements around Europe followed by a description of an eclipse: 'Well - the sun arose badly and the sky was very cloudy, but we saw the beginning and progress of the eclipse clearly, and saw the totality well. But it is difficult to give an idea of it. The gloominess increased, the country seemed annihilated... The moon was seen like a black patch in the sky surrounded by a ring of light (very slightly red I think) whose breadth was about 1/8 of her own diameter... As touching the ring of light, about which so much has been said, I have no hesitation in believing it to depend neither on the sun's atmosphere nor on the moon', but simply to arise from our own atmosphere'.

Royal Observatory Greenwich - GA returns Emy's [A.R. Emy, Du Movement des Ondes et des Travaux Hydrauliques Maritimes, 1831] and Brémontier's treatises on waves and sea-works: 'I have not found much in them that suited my purpose, but they are curious as shewing the efforts which hard-headed men have made, without adequate mathematics, to understand a subject which (as I am more and more convinced by increased reading) cannot be touched at all without a beginning of good mathematics, although the advance which the best mathematics can make is small'. Could WW help GA with 'one of my carnal wants', and remind Mr Clayton of GA's request for a supply of strong and mild ale.

Royal Observatory Greenwich - GA sends WW the first copy of his Tides and Waves: 'I have hit your theory pretty hard, but not so hard I trust as to hurt you'.

Royal Observatory Greenwich - GA fully understands why WW should be so much attached to his own theory on tides. GA strongly disagrees with WW 'that a fluid always tends to the condition of equilibrium and that this can be made in any way the base of a theory of motion. You would by this treat the theory of common waves (for instance) as that of water having a horizontal surface, and thus annihilate the waves altogether. Indeed I am rather surprised at this doctrine in general. When you come to particular cases, the inconsistency is remarkable. Perhaps the most curious of all the results of Laplaces's theory (I mean of course with the unnatural assumption of uniform depth and no dry land) is that of the non-existence of diurnal tides; and this stands irreconcilable with your equilibrium deduction... The cases to which it will apply may be so exceedingly restricted as to be practically useless; (e.g. Laplace's uniform depth, or my canals); nevertheless the theory is so far right: the equilibrium theory could not be right under any restriction...When you say that Laplace's theory gives us no light which the equil. theory had not given before, it seems to me that there is a moral perversion; you think that success founded on false principles is at least as good as failure founded on true principles which are imperfect (in extent, not in truth). I must protest against such a judgement in toto'. GA boils down WW's promotion of the equilibrium theory to the adverse effects WW thinks Laplace's theory would have on Cambridge students: 'I am free to say that the tone of my writings has been given by my vexation at seeing that you in every mathematical case and Lubbock in every case refer solely to the equilibrium theory'. GA does not knock cotidal lines - 'they are the greatest advance yet made in systematically representing the observations of ocean tides, but I think them inapplicable in some cases: and especially when the well marked series of waves interfere'. GA 'should be glad to lead on some attention to the theory of canal-waves with the conditions applicable to real rivers. First, I do not think that cotidal lines or mean levels can be made accurate till this is done, secondly, theory and observation can be compared to a very great extent here'. They (GA and Richarda Airy) went to see a cliff blown down at Dover organised by the engineer, Cubitt. The Herschels also went [see The Illustrated London News, 4 February 1843].