Greenwich - RA and George Airy were sorry they missed WW and EA in Spain [to witness the total eclipse]: 'I never before saw a country so uncivilized and so deficient'.
Devonshire Rd, Portland Place - Babbage received WW's thirty guineas and has paid 31 for his fees at the Royal Society. Three members of the Astronomical Society have donated 100 guineas toward the Cambridge Observatory (50 came from William Pearson). 'Sir J. B [Joseph Banks] is about to resign and has recommended Davies Gilbert. But all sorts of plans speculations and schemes are afloat, and all sorts of people proper and improper are penetrated with the desire of wielding the sceptre of science. Whether this elective throne shall be filled by a philosopher or peer a priest or prince is a problem pendent on the fortuitous course of events. The Society is in a position of unstable equilibrium or rather it is like a comet which has not made up its mind whether it shall soberly circulate round the light of truth or traverse boundless space through endless time frying and damning the predestined infidels of other systems until some starry giant shall fascinate to its destruction this erring ball which has "run a muck" through creation'.
Philadelphia - ADB is happy to contribute as best he can to the materials WW seeks for his book. He has made copies of the tracts on tides which accompanied WW's note, and intends to distribute copies 'to those who may aid by furnishing observations upon the plan which has been sketched'. ADB may be able to get the various tide observations 'kept irregularly and at different times, at places on the Atlantic coast of the United States'. Some of the gentlemen of the military service as well as men of science 'may be willing to observe systematically'.
Foreign Office - JB has enclosed a letter [no longer attached] from a 'Mr. Morin who is described to me as being engaged in making astronomical experiments, in Paris; from whence it has been sent to me together with many others of the like import for the "Directeurs des Observatories" at Gibraltar the Cape of Good Hope & Port Jackson'. JB does not know who the astronomer is that the letter is addressed to - does JL?
Islington, London - Sends WW a specimen of his proposed new translation - 'Martial Fragment of Tyrtaeus' [enclosed] - 'to be published as soon as a sufficient number of subscribers to the little work shall have been obtained'. Can he add WW's name? JWB announces the declining health of his father.
37 Tavistock Place - Would WW restate the formula he suggested 'for determining the specific gravity (reduced to a vacuum) of hollow bodies, not hermetically sealed'. FB has received a letter from Frederick Bessel in response to FB's 'remarks on his experiments with hollow cylinders (not hermetically sealed) which has rather staggered me; & makes me fear that I may myself be in error'. Although FB's 'case is not exactly the case in point: but is, in fact, one still more erroneous: - at least in my opinion'. Could WW give his opinion [an extract of FB's letter to MB is enclosed].
90 Eaton Square - WW's parcel for Mr Everett [Edward Everett] should be with him by the 18th. GB gives a brief description of his continental trip.
Edinburgh - Sends WW a copy of his dissertation in which he has attempted to apply the argument advocated in the Bridgewater Treatises to the subject of disease [A Dissertation on the Causes and Effects of Disease, Considered in Reference to the Moral Constitution of Man, 1837, not present].
Royal Institution - Thanks WW on behalf of the Royal Institution 'for your discourse on the idea of Polarity'.
PB returns WW's work On the Theory of the Moon and on the Perturbations of the Planets. PB is presently engaged on the production of 'a new magnetic chart founded on the most recent observations and as far as possible corrected for the local attraction of vessels and I would be much obliged to you if [you] could give me two copies of your chart of the tides for drawing in my first lines'.
Swansea - GA will be 'extremely glad' to have Neale as a pupil. However, further to his correspondence with Myers, he does not know whether Mr Hare had or had not already engaged a tutor for Neale. Could WW answer some questions further to the fellowship examination - 'In the first place must I sit at all? In the next place supposing that I sit, by what time must I be at Cambridge?'"
Trin: Coll: - Gives his 'critical' comments of WW's treatise on dynamics. He considers WW's enunciation of the laws of motion 'very far preferable to any other that I have seen'. GA emphasises the importance of attaching the same meaning to the word: 'It matters not whether there is at all such a thing as velocity in the world, provided we mathematicians know what we mean by it, and always attach the same meaning to the word. This latter is essential to logical reasoning: and in a science which is not founded on hypothesis but on experiments it is of the greatest consequence that the same word shall signify the same thing in the reports of the experiments and in the mathematical properties founded on them'. Drawing upon Atwood's machine and the philosophy of Locke, GA gives his definition of velocity: 'It is measured by causing the weights (as far as is in our power) to combine during a unit of time in the same rate of motion or at the time for which we desire to find the velocity, and the space thus described is called the velocity. To me the limit of ds/dt is rather difficult to get, but I find no difficulty in conceiving a body to continue to move with the same degree of motion which it has at any time (This perhaps appears absurd - but Locke says that we can comprehend relations between two things without having a clear idea of either)'. GA gives various mathematical corrections to WW's work: 'when I see Mr Whewell led astray in the use of the differential calculus by obscure principles and a bad notation I cannot help wishing that better were substituted'.
Orleans - GA and his students are settled in Orleans and 'in as satisfactory a state of stable equilibrium as can be expected'. If his paper in the Philosophical Transactions has been published could WW send him 70 copies. Could WW tell [Henry] Kater 'that I have investigated a theory of the pendulum...as he suggested to me: and that the interval to reappearance does not follow so simple a law as he seemed to imagine?' And if he sees Young, that further to his letter addressed to GA in the Quarterly Journal, 'I get a different result? The result however consolidates his influence. The problem is, to find the form of a thin revolving fluid surrounding a nucleus'.
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'.
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'.
Keswick - GA has just received a letter from Thomas Atkinson of Ainstable 'with a certificate from Hudson, which I transmit to you as being (I believe) Hudson's successor' [concerning TA's entry into Trinity College?].
Trinity College Cambridge - GA agrees with WW that his article on eye pieces should be printed immediately. If WW can arrange this, could he pass on the address of the printers and engraver. He has received the latest number of the Philosophical Journal which contains two letters by James Ivory about GA: 'I wish the man would not torment me by writing letters to me; I am amused by his idea that I have fallen into error from deference to high authorities; I never expected this accusation'.
Observatory - GA returns a parcel of amethystine crystals of which, due to their rough surfaces, he has been able to make nothing. 'I have lately determined an odd thing in the way of polarization, viz that the light of ladies eyes is polarized - at least when viewed in particular directions. When deprived of this light, the eye has a most unnatural appearance'.
Observatory - GA gives WW references to French works on polarisation written between 1808 and 1824: 'Most of Biot's papers are tremendous to a person who is not very familiar with the subject, & perfectly easy to one who is familiar with it and has thought upon it well'.
Observatory - There is not a word about undulations in the papers by William Herschel on Newton's rings, in the Philosophical Transactions for 1807 and 1809 respectively: 'I have been observing the following curious phenomenon. If Newton's rings be produced by two glasses, however they be viewed the central spot is black. But if a glass be placed on metal, and viewed with polarised light (polarised to plane of reflection) then up to the polarising angle the central spot is black, and instantly beyond that it is white. This I anticipated from Fresnel's [experiments]: it is confirmatory of them, and defies emissions'.
GA does not think WW's letter to David Brewster 'at all savage': 'If I had any discussion with Brewster on these points I would certainly hit him about his bad information and his influence in acting on it. The revenues of professorships &c is one point already reproached - another is the character of the professors "Whewell, Airy & Hamilton" the only true experimenters - Does not [James?] Cumming do more than all? And did [Sir W. R. ?] Hamilton since he drew vital air ever make or meditate an experiment or trouble himself about other peoples?...I wish Babbage's non-lecturing could somehow be lugged into this controversy'.
Observatory - GA describes his observation of the projection of a star on the moon's disk: 'Now imagine that you see the moon's limb well, and that you see the star well, with all its rings... The moon approaches the star - goes right over it...the outermost ring of the star considerably within the moon's limb - till when it is satisfied with shewing itself in this ridiculous manner puff it goes out - like a candle...what is one to make of all this?'
Observatory - Could JWL forward a copy of the enclosed to Knowle [enclosure not present].
Observatory - Henderson [Thomas Henderson] is with GA: 'I intend to bring him to hall; pray dine there if you have nothing better to do'. GA gives the two things which need correcting in his Venus paper.
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.