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Could WW give 'an expressive name' to a proof which continually appears in a paper JWL is writing. He describes the operation and says that 'three-ing the series' came to mind, but he is not convinced such a phrase 'would be thought sufficiently elevated in style'.

JWL thanks WW for his philosophy ['The Philosophy of the Inductive Sciences, Founded upon their History', 2 vols., 1840] but prefers the History which is 'more to my taste' ['The History of the Inductive Sciences']. JWL is disappointed that WW attached so little importance to attempts to bring the moon, the planets and other satellites 'under one system because though I could not expect you to dive into the details of the calculations, namely it is an advance in the philosophy of any subject when divers phenomena before treated by separate and independent considerations are included in one course of symbolical reasoning'.

'It is as you say quite a scandal that no ascent has been made for scientific purposes since that of Gay Lussac. Though I hope when you see my paper on Refraction you will admit that this problem is nearly put at rest, for I make observations of steam, vapour of Alcohol and confirm my law of the connexion between pressure and temperature, which is quite different from what has been supposed'. JWL has had a long discussion with the aeronaut Mr Green: 'It would not do to set about the thing with less than £1,500 [to make a balloon to investigate the atmosphere?]. JWL is annoyed at John Herschel for leaving out all notice of his work on lunar theory in his address to the Astronomical Society.

29 Eaton Place - The Royal Society has determined that all the committee reports should be made general, and not specifically suited only to Captain Ross's [John Ross] voyage. Thus tides can now occupy a much larger place. Apart from the Physics committee, the others - Geology, Zoology and Botany - have set to work on preparing instructions for scientific travellers: 'so that they may in remote countries know how to add information when it is most wanted and Procure opinions of objects imperfectly known'. JWL believes he has discovered the true relation between elasticity and temperature in elastic fluids. Since this furnishes the condition of the atmosphere, he is testing it with light and hopes to produce a table of refractions.

14 Savile Row - BCB returns to WW a copy of John W. Lubbock's letter, but would like it back tomorrow so he can send it to the Astronomer Royal.

90 G.S. - Asks for his opinion on different modes of expression in treating the Differential Calculus. Amongst other examples, he points out 'we cannot talk of total partial diff: coeff: Would complete partial diff: coeff: do?' Thanks him for his book on comets, and notes that the tides are yet undone.

29 Eaton Place - Mr Hopkins' [William Hopkins] paper on cracks in the crust of the Earth's surface is a big disappointment: 'With respect to the hypothesis of a crust, in contact with an interior fluid it appears to me a state of things which could not subsist. Unless they be in contact and continue so, the fluid would exert no pressure against the crust. If they were once in contact the slightest irregularity in their expansibilities by heat would make this condition cease, and the higher tides, which would never amount to above a few feet, would never reach the crust'. JWL hopes WW will write something upon the tides as a whole.

29 Eaton Place - 'Mrs Ricardo (the widow of the celebrated political economist) has written to me to request me to write to you a line of nomination in favour of her grandson Mr William Austin who is gone up to your College. I know how much you must be troubled with similar requests but as Mrs Ricardo is a particular friend of Sir John and Lady Lubbock I hope you will excuse my writing to you on the subject'.

St Mildred's Court - JWL was going to send WW 'the Liverpool results of Parallax when I found that Mr Dessiou had already done so'. Dessiou also promises to send JWL the declination. They will at once be available to yourself, Poisson and others. The Dutch tides might be discussed if the BAAS would supply funds. JWL considers a year's observations ample for the sun's menstrual inequality. Can WW get the curves of the object glasses belonging to the large telescope at the observatory.

St Mildred's Court - Thanks WW for his letter and is 'glad to find that you agree with me thinking that Ptolemy describes an artificial globe, that is to say a representation of the sphere of the heavens and seen from the outside'. JWL claims that Dumfry's? paper was not published until well after his maps, but is extremely satisfied 'that it agreed to a minute in the determination of the establishment of that proof'.

RS sends WW two pieces of his work: 'The longitude of Brussels contains a better account of personal equation than I think you will find elsewhere'. He is disappointed with his article on the Transit: 'Still I believe it contains more on the subject of an elementary and practical nature than can be found elsewhere'. RS's 'old antagonist Sir James [James South] has issued a placard and an advertisement in the Times of Monday last, which I suppose he intends for a severe blow to the Astronomer Royal and to me'. RS believes this was induced by John W. Lubbock's 'folly in giving him a hearing by the Council of the Royal on the subject of their copies of their Transactions. This kind of notice, was pretty certain to revive his spirits and as no notice will be taken of his placard, I dare say he will feel encouraged to make another attack. It is hard that Lubbock's want of ordinary tact and sense should bring wrong on other people, for if in consequence of this, South should again assail the Society I feel certain that Sir John [John Herschel] will give small aid in quieting Sir James however easily he may be gulled by him'.

JWL is grateful to WW for his 'hints': 'with respect to the first not having the paper before me I do not recollect sufficient to give an answer, I should have liked to know whether the argument is conclusive to you'. The Council have appointed a committee to consider the printing of some observations the Admiralty have sent. JWL has 'requested Capt. Beaufort [Francis Beaufort] to get from some of the places a specification of the manner in which the time was obtained and of the zero point from which the heights are reckoned'. Could WW tell Mr Lodge that the Library committee will meet on August the 2nd.

St James's Place - William Stratford agrees with JWL in thinking it desirable to print the comparison of the London and [Rothine or St. Catherine] docks. JWL would like WW to view the tidal gage and clock at these docks. If the Royal Society decide to print his paper on the development of R, JWL would like to make some additions to enable him to take in the terms dependent on the inclination and also to extend his table to include terms not wanted in the lunar theory: 'This method of developing R is a very great and undisputed improvement in my Lunar Theory on account of the great facility with which in this the coefficients of r dR/dr are obtained from those of the coefficients of R...the new method diminishes the labour prodigiously and I could now do by its means in one day what took me weeks to get through. Besides the operations are so simple that the probability of error is almost annihilated' ['On the Theory of the Moon, and on the Perturbations of the Planets', 1833].

St James's Place - JWL has tried to make some alterations (to meet the ideas of the Syndicate) to his work on comets but has found it got worse ['On the Determination of the Distance of a Comet from the Earth, and the Elements of its Orbit', 1832]: 'I am so much taken up in the city and in one way or another that I am only able to attend to these things when I can snatch half an hour or so'. JWL is disappointed with the attitude of the University Syndicate.

St James's Place - JWL has heard from Mrs Somerville [Mary Somerville] that 'you have been at work about the tides and I want much to see what you have done'. Did the Syndicate of the University Press agree to print his treatise? - if not he would like it back ['On the Determination of the Distance of a Comet from the Earth, and the Elements of its Orbit', 1832]. JWL hopes WW will be at the next Council: 'there was an unpleasant altercation between Mr Children and Mr Hudson at the last Council meeting' of the Royal Society which is likely to come before the council. WW will shortly receive a portion of the catalogue.

St James's Place - JWL omitted to answer one point in WW's letter about planetary perturbations, and describes why he thought the comparative advantages of both methods were superfluous.

St James's Place - LWL would not object at all if WW took up the cotidal lines and wrote a paper on the subject ['Essay Towards a first Approximation to a Map of Cotidal Lines', Phil. Trans., 1833]. JWL will send him the relevant references and authorities to the Athenaeum Club. He has been afraid to draw many inferences from his data on tides until 'they received either confirmation or correction and the chief utility which occurred to me in presenting that kind of information about the tides in a condensed form was to draw the attention of navigators to the subject, and so in the end get facts which can be depended upon'. He is glad that WW likes his little treatise on comets, and will look again at the method of Gauss [Karl F. Gauss].

St James's Place - Thanks WW for his letter 'which is a complete answer to my question'. JWL shows how he obtains a quadratic for the distance of the comet from the earth, and through which 'the necessity is entirely done away with of having recourse to repeated trials'. JWL likes WW's proposed plan in his Dynamics ['An Introduction to Dynamics Containing the Laws of Motion and the First Three Sections of the Principia', 1832] 'but think that it would be very desirable to refer to Clairant and D'Almebert the original authors and discoverers as I believe of by far the greatest part of the Mec. Celeste. Laplace as it seems to me did little more than employ their methods taking in terms which they omitted'.

St. James's Place - JWL forwarded WW's 'excellent report' to Capt. Smyth [William H. Smyth]. Could WW find out whether the Syndics of the university press would publish a short work on the determination of the orbit of a comet ['On the Determination of the Distance of a Comet from the Earth, and the Elements of its Orbit', 1832]. WW has no doubt seen 'a little mistake in the expression for the time in the parabola in your dynamics' ['An Introduction to Dynamics Containing the Laws of Motion and the First Three Sections of the Principia', 1832].

St James's Place - JWL has received a letter from Mr. Children [John G. Children?] desiring a report from the President 'upon some schemes by the well known Mr Herapath' [William Herapath?]: JWL thinks the report should be short and drawn up by WW and George Peacock. He thinks it 'would be desirable that Cavendish's experiment should be repeated, but we never could entrust such a thing to the person in question'. What seems to support the idea that gravity is not the same for all substances 'is that the inequalities of Saturn appear to require a mass of Jupiter different from that which is given by the inequalities of the little planets. There can I apprehend be no doubt that corpuscular is not a modification of the Newtonian attraction'.

St James's Place - Thanks WW for the Calendar 'which exactly suits the purpose'. Not much is going on in Paris in the way of science. JWL gives the references to Cauchy's [Augustin Louis Cauchy] investigations connected to the theory of light. JWL is anxious to know what WW thinks of them and of Poisson's [Simeon D. Poisson] work on Capillary Attraction. Poisson told JWL that he thought it desirable that the moon should be treated like the planets. He also promised to examine Laplace's theory of the tides when he got JWL's tables: 'He seemed not to have thought much on the subject'.

St James's Place - JWL wrote last week to request a copy of the library regulations at Cambridge. Mr W. Tooke [William Tooke?] has asked him 'to acquaint you that they are in want of a Professor of Mathematics at the London University, and to request you to recommend them any one you may know competent to fill that situation'. JWL is going to Paris next week.

St James's Place - JWL is sorry WW has not got the time to take up the subject of tides: 'you would do so much better than myself'. JWL has been preparing his paper for the press and at the Royal Society ['On the Tides in the Port of London', Phil. Trans. of the Royal Society, 1831]: 'I should like to attempt a Theory of the Moon'. Dessiou [Joseph Foss Dessiou] is producing tables showing the effect of the changes in the moon's declination and on the time and height of high water. Mr Pond [John Pond] has promised JWL funds from the Nautical Almanac to enable him to write a paper on this subject. He has resigned the Vice Presidency at the Royal Society.

WW is perhaps aware that Mr Stratford [William Stratford] has been campaigning to get appointed to the office of superintendent of the Nautical Almanac, and is supported by Capt. Beaufort [Francis Beaufort]. Beaufort did not think that JWL should even consider the job. In response JWL wrote to him to assure him that he did 'you could hardly suppose that I should have felt objection to become the successor of such men as Dr. Maskelyne Dr. Young and Mr Pond'. However he learnt last night that Stratford was appointed to the post: 'he has not the mathematical knowledge of a second year man at Cambridge'. Beaufort has given JWL access to all the Admiralty Charts.

JWL has received WW's letter plus Quetelet's [Lambert Adolphe Jacques Quetelet] papers. He is sorry that WW cannot attend the Committee and thinks his suggestions excellent - reports on papers and a yearly report. If we had an exact copy of the constitutions of all Foreign Societies, we could graft the best aspect of each onto ours. The Council of the Royal Society have given him permission to employ Mr Walker to draw a map of the world under his direction to chart the progress of the tide, unfortunately 'Capt. Beaufort [Francis Beaufort] will not allow him to consult the Charts at the admiralty for fear he shall trouble them', so he has had to use books of sailing directions. Regarding WW's problem in biometry, JWL does not think 'we possess sufficient information with respect to the ages at which marriages take place and the intervals which lapse after marriage before children are born to arrive at any satisfactory conclusion with respect to the influence a general retardation of marriages would have upon the increase of the population'. Mr Dessiou [Joseph Foss Dessiou] has nearly completed his work on the tides and JWL has seen some of his results. He has begun work on a Physical Astronomy paper.

JWL has Richard Jones's medical statistics. Should he send one of his papers on Annuities to Mr Romilly at Dulwich? He has been working hard on tides and has discussed over 9,000 observations made at the London Docks.

JWL will be happy to be of assistance to WW's friend Jones [Richard Jones] in making the calculations of which WW speaks: 'I wish very much to see tables such as that in your letter instead of those vague appearances which are given by writers on population. I have not been able to find any attempt to put into mathematical formulas the relations which exist between the elements of the population. I have endeavoured to explain some of them which depend more immediately upon the law of mortality as the proportion of the living at each age, the ratio of the deaths to the whole population etc'. JWL gives the calculation for the probability of a person living n years ['On the Calculation of Annuities, and on Some Questions in the Theory of Chances', Trans. of the Camb. Phil. Soc., 1830].

Royal Society - Would WW ask the fellows or others whether they would like to subscribe, and could he bring the list with him when he comes to town.

St. James's Place - JWL has pleasure accepting WW's invitation.