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Flamsteed House, Greenwich - GA is taking a vacation in France: 'my nervous system seems I think more than usually shaken'. Regarding high academical instruction in mathematics: 'I have no doubt of the want of a Code. Yet it will not do to make this exclusive or suppressive of novelties - not because it would not be best if it could be maintained, but because it cannot be maintained for an unlimited time, and the more pestiferously it is kept up for a time, the more sudden and complete and anarchical will be its fall at some period... Therefore my general notion would be, to define subjects which ought to be kept, leaving a fair space for others which may be introduced as new tastes or the influence of individuals may prevail, and not to risk the chance of such a treatise as Babbage proposed "On the principles of d-ism, in opposition to the dot-age of the University"'. As to particular authors, GA recommends Newton, Lagrange and Monge, and reluctantly Laplace's Mechanique Celeste - though 'this is by no means so systematic a work as those above'. Regarding the works of [Leonhard] Euler GA is not very familiar: 'But to some of these which I did read, there is this objection, that Euler gives the whole course of his ideas, dilating upon his crude notions in a way which requires great labour for following him, and then quietly informing you that it is all useless and that he can give you something much better'. GA agrees with WW in emphasising 'the great standard works of all times rather than to the last steps made'.

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'.

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?'