| Reference number | Title | Date |
| EC/1925/11 | Proudman, Joseph: certificate of election to the Royal Society | |
| IM/003785 | Proudman, Joseph | nd |
| RR/23/75 | Referee's report by Hector Munro Macdonald, on a paper 'Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere' by Joseph Proudman, Arthur Thomas Doodson and G Kennedy | May 1916 |
| RR/26/118 | Referee's report by F P Pidduck, on a paper 'The principles of internal Ballistics' by Joseph Proudman | 21 June 1921 |
| RR/71/244 | Referee's report by Geoffrey Ingram Taylor, on a paper 'On the mixing of sea water by turbulence' by Joseph Proudman | 31 May 1948 |
| RR/37/16 | Referee's report by Joseph Proudman, on a paper 'Two-dimensional potential problems concerning a single closed boundary' by W G Bickley | February 1929 |
| RR/33/103 | Referee's report by Joseph Proudman, on a paper 'Fluid resistance to moving spheres' by R G Lunnon | November 1925 |
| RR/67/230 | Referee's report by Joseph Proudman, on a paper 'The pressure of water waves upon a fixed obstacle' by Thomas Henry Havelock | 18 April 1940 |
| RR/23/79 | Referee's report by Augustus Edward Hough Love, on a paper 'On the motion of solids in a liquid possessing vorticity' by Joseph Proudman | April 1916 |
| RR/35/42 | Referee's report by Joseph Proudman, on a paper 'A theory of internal ballistics based on a pressure-index law burning for propellants' by C A Clemmow | 16 January 1928 |
| RR/45/31 | Referee's report by Joseph Proudman, on a paper 'The diurnal tide in an ocean bounded by two meridians' by D C Colborne | nd [January 1931] |
| NLB/61/734 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Professor [Joseph] Proudman, FRS; the University of Liverpool | 20 October 1921 |
| RR/49/136 | Referee's report by Joseph Proudman, on a paper 'Ocean currents produced by evaporation and precipitation' by George Ridsdale Goldsbrough | [June 1933] |
| RR/53/107 | Referee's report by Joseph Proudman, on a paper 'The calculation of wave resistance' by Thomas Henry Havelock | [February 1934] |
| RR/72/40 | Referee's report by Harold Jeffreys, on a paper 'Observations on the turbulent fluctuations of a tidal current' by K F Bowden and Joseph Proudman | 1949 |
| RR/58/6 | Referee's report by Joseph Proudman, on a paper 'Wave resistance: the mutual action of two bodies' by Thomas Henry Havelock | May 1936 |
| RR/60/48 | Referee's report by George Clarke Simpson, on a paper 'On the temperature of the surface waters of the Irish sea' by Joseph Proudman, H Mabel Lewis and A Leslie Dennis | 4 December 1936 |
| RR/64/29 | Referee's report by Joseph Proudman, on a paper 'The seiches in a strait connecting two seas' by George Ridsdale Goldsbrough | [August 1937] |
| RR/70/19 | Letter from Joseph Proudman, on a paper 'The generation and propagation of ocean waves and swell. I. Wave periods and velocities' by N F Barber and F Ursell | 5 July 1947 |
| RR/68/200 | Referee's report by Joseph Proudman, on a paper 'Relaxation methods applied to engineering problems. VII. Problems relating to the percolation of fluids through porous materials' by F S Shaw and Richard Vynne Southwell | 23 January 1941 |
| RR/67/342 | Referee's report by Geoffrey Ingram Taylor, on a paper 'On the turbulence of a tidal current' by Joseph Proudman | 1940 |
| RR/71/22 | Referee's report by Joseph Proudman, on a paper 'The behaviour of waves on tidal streams' by N F Barber | 19 November 1948 |
| RR/67/358 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the author | 11 October 1945 |
| RR/67/361 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the author | 15 November 1945 |
| RR/67/343 | Letter from Joseph Proudman, on his paper 'On the salinity of the surface waters of the Irish Sea' to J D Griffith Davies, Assistant Secretary of the Royal Society | 1 November 1940 |
| RR/67/362 | Letter from Joseph Proudman, on his paper 'On the salinity of the surface waters of the Irish Sea' to J D Griffith Davies, Assistant Secretary of the Royal Society | 19 November 1945 |
| RR/67/352 | Letter from unknown communicator, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to Cambridge University Press | 24 December 1940 |
| RR/67/363 | Memorandum from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman | 30 November 1945 |
| RR/69/94 | Memorandum from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On Dirac’s theory of quantum electrodynamics: the interaction of an electron and a radiation field' by C Jayaratnam Eliezer to Joseph Proudman | 3 July 1945 |
| RR/69/62 | Memorandum from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'Infinite irreducible representations of the Lorentz group' by Harish-Chandra to Joseph Proudman | 27 August 1946 |
| RR/72/73 | Referee's report by Joseph Proudman, on a paper 'The levels in the North Sea associated with the storm disturbance of 8 January 1949' by R H Corkan | 27 September 1949 |
| RR/70/18 | Referee's report by Joseph Proudman, on a paper 'The generation and propagation of ocean waves and swell. I. Wave periods and velocities' by N F Barber and F Ursell | 3 June 1947 |
| RR/72/132 | Referee's report by Joseph Proudman, on a paper 'The tides in oceans on a rotating globe. V' by George Ridsdale Goldsbrough | 1949 |
| RR/72/131 | Letter from Joseph Proudman, on a paper 'The tides in oceans on a rotating globe. V' by George Ridsdale Goldsbrough to D C Martin, Assisatn Secretary of the Royal Society | 30 June 1949 |
| RR/34/19 | Referee's report by Joseph Proudman, on a paper 'Generalised sturm-liouville expansions in series of pairs of related functions' by H Horrocks | [January 1927] |
| RR/31/39 | Referee's report by Sydney Chapman, on a paper 'The principal constituent of the tides of the North Sea' by Joseph Proudman and Arthur Thomas Doodson | [February 1924] |
| NLB/72/59 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Professor [Joseph] Proudman, FRS | 8 February 1929 |
| NLB/68/774 | Copy letter from William Bate Hardy, Secretary of the Royal Society; to Sir Gerald Lenox-Conyngham, FRS | 31 October 1925 |
| NLB/68/772 | Copy letter from William Bate Hardy, Secretary of the Royal Society; to Professor [Joseph] Proudman, FRS | 31 October 1925 |
| NLB/69/722 | Copy letter from Henry Hallett Dale, Secretary of the Royal Society; to Prof. Yamasaki, Imperial University, Tokyo | 13 September 1926 |
| NLB/69/712 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Prof. [Joseph] Proudman, FRS | 6 September 1926 |
| NLB/69/721 | Copy Letter from P. D. Rogers, Office Staff of the Royal Society; to Dr. [Henry Hallett] Dale, Secretary of the Royal Society | 9 September 1926 |
| NLB/72/54 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Professor [Joseph] Proudman, FRS | 6 February 1929 |
| NLB/66/35 | Copy letter from James Hopwood Jeans, Secretary of the Royal Society; to Prof. [Sydney] Chapman, FRS | 12 February 1924 |
| IM/005264 | Proudman, Joseph and Dodson, Arthur Thomas | 1995 |
| NLB/62/503 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Colonel [Henry George] Lyons, Chairman of the Gassiot Committee and FRS | 23 February 1922 |
| RR/67/350 | Letter from the Hydrographer to the Navy, the Admiralty, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the Secretary of the Royal Society | 14 December 1940 |
| RR/67/345 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to Gerald Ponsonby Lenox-Conyngham | 14 November 1940 |
| RR/67/355 | Letter from J N Carruthers, Hydrographic Department, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to J D Griffith Davies, Assistant Secretary of the Royal Society | 24 March 1941 |
| RR/67/359 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the author | 7 November 1945 |
| RR/67/347 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the author | 15 November 1940 |
| NLB/67/710 | Copy letter from unknown correspondent; to unknown correspondent | 19 February 1925 |
| AP/81/3/3 | Unpublished letter, regarding 'The measurement of tides by means of the Favé pressure gauge' from Joseph Proudman to the Assistant Secretary of the Royal Society | 12 December 1939 |
| RR/31/40 | Referee's report by Geoffrey Ingram Taylor, on a paper 'The principal constituent of the tides of the North Sea' by Joseph Proudman and Arthur Thomas Doodson | 28 January 1924 |
| RR/53/136 | Referee's report by Joseph Proudman, on a paper 'The figure of the earth from gravity observations and the precision obtainable' by James de Graaff-Hunter | [January 1935] |
| RR/67/356 | Order form from Joseph Proudman, on his paper 'On the salinity of the surface waters of the Irish Sea' to J D Griffith Davies, Assistant Secretary of the Royal Society | March 1941 |
| RR/67/360 | Letter from Joseph Proudman, on his paper 'On the salinity of the surface waters of the Irish Sea' to J D Griffith Davies, Assistant Secretary of the Royal Society | 13 November 1945 |
| RR/67/354 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to J N Carruthers, Hydrographic Department | 20 March 1941 |
| AP/81/3/2 | Unpublished diagrams, experimental apparatus and results by J [Joseph] Proudman, A T [Arthur Thomas] Doodson and R H Corkan | 1939 |
| AP/81/3/1 | Unpublished manuscript, 'The measurement of tides by means of the Favé pressure gauge' by J [Joseph] Proudman, A T [Arthur Thomas] Doodson and R H Corkan | 1939 |
| AP/81/3 | Unpublished paper, 'The measurement of tides by means of the Favé pressure gauge' by J [Joseph] Proudman, A T [Arthur Thomas] Doodson and R H Corkan | 1939 |
| RR/68/119 | Referee's report by James Hopwood Jeans, on a paper 'On Laplace’s differential equations for the tides' by Joseph Proudman | [June 1941] |
| RR/23/76 | Referee's report by Joseph Larmor, on a paper 'Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere' by Joseph Proudman, Arthur Thomas Doodson and G Kennedy | 25 May 1916 |
| RR/23/77 | Referee's report by Horace Lamb, on a paper 'Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere' by Joseph Proudman, Arthur Thomas Doodson and G Kennedy | July 1916 |
| RR/49/135 | Referee's report by Joseph Proudman, on a paper 'The tides in oceans on a rotating globe.—Part IV' by George Ridsdale Goldsbrough | [February 1933] |
| RR/56/78 | Referee's report by James de Graaff-Hunter, on a paper 'Tides in oceans bounded by meridians' by Joseph Proudman and Arthur Thomas Doodson | 19 October 1935 |
| RR/56/79 | Referee's report by George Ridsdale Goldsbrough, on a paper 'Tides in oceans bounded by meridians' by Joseph Proudman and Arthur Thomas Doodson | [November 1935] |
| RR/60/47 | Referee's report by Sydney Chapman, on a paper 'On the temperature of the surface waters of the Irish sea' by Joseph Proudman, H Mabel Lewis and A Leslie Dennis | 16 December 1936 |
| RR/67/344 | Memorandum from J D Griffith Davies, Assistant Secretary of the Royal Society on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to William Lawrence Bragg | 6 November 1940 |
| RR/67/346 | Letter from Joseph Proudman, on his paper 'On the salinity of the surface waters of the Irish Sea' to J D Griffith Davies, Assistant Secretary of the Royal Society | 14 November 1940 |
| RR/67/348 | Referee's report by Gerald Ponsonby Lenox-Conyngham on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman | 27 November 1940 |
| RR/67/349 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the Hydrographer to the Navy, the Admiralty | 5 December 1940 |
| RR/67/351 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the Hydrographer to the Navy, the Admiralty | 18 December 1940 |
| RR/67/353 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to members of the Sectional Committee for Physics | 27 December 1940 |
| RR/67/357 | Letter from J D Griffith Davies, Assistant Secretary of the Royal Society, on a paper 'On the salinity of the surface waters of the Irish Sea' by Joseph Proudman to the author | 19 June 1941 |
| RR/67/422 | Letter and referee's report by Joseph Proudman on a paper 'The production of waves by the sudden release of a spherical distribution of compressed air in the atmosphere' by J J Unwin | 6 September 1940 |
| RR/79/172 | Referee's report by Joseph Proudman, on a paper 'The North Sea storm surge of 31 January and 1 February 1953' by J R Rossiter | 31 July 1953 |
| RR/73/252 | Referee's report by Joseph Proudman, on a paper 'A study of motions in a rotating liquid' by G W Morgan | 20 October 1950 |
| RR/77/51 | Referee's report by Joseph Proudman, on a paper 'Edge waves on a sloping beach' by F Ursell | 6 March 1952 |
| RR/77/165 | Referee's report by Joseph Proudman, on a paper 'Free tidal oscillations in a rotating square sea' by R H Corkan and Arthur Thomas Doodson | 28 August 1952 |