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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.

Orleans - GA has not heard from John Herschel and is not sure whether he has reached Paris yet - perhaps he is with Arago? Could WW send the GA's papers to his forthcoming address in Paris [see GA to WW, 10 August 1826]. [Henry] Kater was perfectly satisfied with the correction of Lambton's error: 'moreover I discussed with him most vehemently the question of disappearance and reappearances versus disappearances only and persuaded him at least to confess that the disappearances only would not give a right result except all circumstances such as the rate of the pendulum on the clock, the arcs of the two pendulums, and the magnitudes of the discs, were the same. He hoped that in giving an account to the Royal Society we should not spare Parkinson'. GA outlines the part of the account he is to contribute. He is 'thinking of means to make chronometers transportable in a kibble & various other things, and will bring you a complete plan for conducting the operations. Of course I shall not do anything till I have seen you'.

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].

Royal Observatory Greenwich - WW is in Augustus De Morgan's 'collection of Authorities for the History of Science...in one of the early pages'. GA has had a large amount of observations made around Ireland (twenty-eight stations): 'Of course the reduction in the way in which I wish to reduce them will be a formidable work'. GA gives Cubitt's rule for blowing down chalk [see GA to WW, 24 February 1843]. WW is not attaching the names of 'Clairaut, D. Besneulli, &c...to the proper part of the subject. The equilibrium-theory as a statical theory of quiescent fluid, is very good (the proof of elliptic form &c being excellent, though the mere combination of effects of two bodies and the laws of the compound result are very simple). And I do not call the theory contemptible in itself, but as applied to the tides'. Abstractly the equilibrium theory is very good while Laplaces's is only admissable. As applied the equilibrium theory is absurd and Laplace's theory is very imperfect.: 'As to your opinion that Laplace's theory is not in the right direction because it does not at once give limits in longitude, I think that you have not sufficiently considered the order in which all results founded on differential equations proceed'. 'As to the combination of equilibrium theory with that of waves, I repudiate it absolutely... The failure of Laplace's on wave theory is merely one of mathematics and will, I hope, be conquered in time'.

Keswick - If WW is in Cambridge could he correct the proofs to his paper on Trigonometry for the Encyclopaedia Metropolitana: 'I have just got a letter from [Edward] Smedley who is in an awful fright about it...If you take this upon you, would it be worth the trouble to say so to Smedley? he would then send proofs directly'.

Royal Observatory Greenwich - Christie has sent him Belcher's observations at Tahiti: 'The solar tide there from whatever cause, is almost exactly equal to the lunar tide (April & May 1840), & that at quadratures the tide disappears'. GA gives his opinion of WW's distinction between an unlimited canal and a re-entering canal: 'In the formation of the differential equations there is no difference whatever (the laws of fluids, as regards transmission of pressure and the effect of pressure and external force on motion, applying in both cases to every point of the fluid: and this being all that the differential equations express). In the solution of the differential equations there is no difference except this - that, in the nature of the thing, it is impossible to permit solutions in the reentering canal which are not periodical in the completion of the circuit of the canal. There is however usually no temptation to introduce such, because the expression for the forces (on which the distinctive function in the solution must depend) are necessarily periodic in the completion of the circuit'. GA outlines some of the complications involved with the distinctive function (and arbitrary function) and the type of canal.

Royal Observatory Greenwich - GA wants WW to delete the last paragraph of his last letter concerning tides [see GA to WW, 6 March 1843]: 'I find on consideration that in the case when the main wave is a forced wave (as in a tidal wave in a canal round the earth) the partial differential equation, upon making the second substitution, will not have that peculiar form which introduces the factor x'.

Royal Observatory Greenwich - GA invites WW to dine at 'our visitation Dinner on Saturday June 3 at the Crown & Sceptre'. He also sends copies of papers on the London, Southampton and Norwich tides: 'The great difference in the general phenomena of the Southampton and Norwich tides, and the small difference in the mathematical formulae which represent them, appear to me very remarkable. I cannot at present explain them'. He has not received all his Irish tide observations: 'Till I have received all, I cannot set the reductions regularly a-going, because for certain matters all are to be combined. But I can see, in the tables already drawn out, some curious things'.

Royal Observatory Greenwich - If WW is in London can he come and dine 'at our visitation dinner on Saturday next'.

Oxford - Struve [Friedrich G. W. von Struve] and GA intend to come to Cambridge on Sunday - 'I believe Otto Struve will also accompany us'.

Royal Observatory Greenwich - GA just missed WW at York. He has since been with Richarda to Kingstown in Dublin on the first stage of the chronometric project to Valentia: 'The chronometers had already been in oscillation some time, Sheepshanks [Richard Sheepshanks] doing the Astronomical part at Kingstown. For the transmission of the chronometers, I had had to establish a wonderful system of boxes screwed upon railway carriages and in steamboat cabins, all which boxes could be opened by the same keys; and agents were appointed to transfer the chronometers at the proper places'. GA has marked out all that he intends doing with regard to the Irish tides - 'I have analysed every one of my 1300 tides' and he gives an overview of some of the more 'curious' conclusions he has drawn.

Royal Observatory Greenwich - GA has persuaded Lamont of Munich [Johann von Lamont] - an astronomer and magnetician - to stay a few days more and come with him to Cambridge: 'I have known Lamont some years, and have a high opinion of his acuteness and originality and singular good sense'.

Royal Observatory Greenwich - GA sends WW 'all that I can discover of my Camera Obscura'.

Royal Observatory Greenwich - GA acknowledges a letter WW recently sent concerning the Smith's Prize paper: 'As regards the paper and your comments on it, first I was glad to find that you think lightly of [William?] Hopkins's attempt to force in mathematics where [they?] have no business. In my opinion, Hopkins has done more to injure the credit of mathematics than any person that I know. This is the fault of the geologists (who would praise without attempting to understand), and I think, primarily the fault of Sedgwick.. In the next place , I was glad to see a question concerning the mathematical theory of waves. This is a subject which ought, I think, to be in some way brought into the curriculum of the university'. Although he has not yet settled the longitude of Valentia [see GA to WW, 2 Nov. 1844], 'I expect it will turn out an excellent work of its kind. We are much more puzzled in making the geodetic computations to compare with it (in large triangles upon a spheroid of assumed dimensions) than in the astronomical and chronometrical part: but after repeated trials I think we have managed to compute round the three sides of a triangle nearly or more than 100 miles each and to return within two or three feet to our starting point. This was to be the criterion of our method'. GA's paper on Irish tides is being printed. Similarly the printing of the Reduction of the Greenwich Planetary Observations 1750 to 1830 is finished. The reduction of the Greenwich Lunar Observations (1750 to 1830) is in the main finished: 'I am preparing to correct the elements of the Tables: and this I think upon the whole one of the greatest works that has ever been done in Astronomy'.