Referee's report by George Biddell Airy, on a paper 'On the exact form of waves near the surface of deep water' by William John Macquorn Rankine Recommended for publication in the 'Philosophical Transactions of the Royal Society'. Returns the manuscript to Walter White. The main investigation appears mathematically sound, 'a very pretty piece of geometry'. The second investigation is less satisfactory, but is glad to see such a difficult subject attempted. The investigation is more of a variation on established methods, rather than a new method which could be applied to practical problems. Subject: Mathematics, Physics and Chemistry [Published in the Philosophical Transactions of the Royal Society, 1863] 30 March 1863