| Reference number | Title | Date |
| MM/15/24 | Letter from J J Sylvester, Maddox Street, to Arthur Cayley | 1878 |
| MM/15/25 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | nd |
| MM/15/22 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 24 February 1875 |
| MM/15/15 | Letter from J J Sylvester, Maddox Street, to Arthur Cayley | 29 January 1875 |
| MM/15/21 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 22 February 1875 |
| MM/15/13 | Letter from J J Sylvester to Arthur Cayley | 13 January 1875 |
| MM/15/20 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 20 February 1875 |
| MM/15/23 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 26 February 1875 |
| MM/15/18 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 4 February 1875 |
| MM/15/16 | Letter from J J Sylvester, Maddox Street, to Arthur Cayley | 1 February 1875 |
| MM/15/19 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 15 February 1875 |
| MM/15/14 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 26 January 1875 |
| MS/499 | Letters and papers of the Royal Society Sylvester Medal Fund | 1897-1901 |
| MS/426/300 | Copy letter from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to [James Joseph] Sylvester | 13 November 1847 |
| NLB/2/326 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 26 April 1888 |
| NLB/2/901 | Copy letter from Herbert Rix, to Professor Arthur Cayley, Fellow of the Royal Society | 12 December 1888 |
| NLB/4/177 | Copy letter from Herbert Rix, to Professor James Jones Sylvester, Fellow of the Royal Society | 5 March 1890 |
| NLB/3/10 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 13 February 1889 |
| NLB/3/64 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 1 March 1889 |
| NLB/4/1142 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 28 January 1891 |
| NLB/7/175 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 14 December 1892 |
| NLB/14/466 | Copy telegram from Robert William Frederick Harrison, to Professor Foster, [Fellow of the Royal Society] | [16 March 1897] |
| NLB/14/465 | Copy letter from Theodore E James, to Messrs Harrison & Sons | 16 March 1897 |
| NLB/13/812 | Copy letter from Robert William Frederick Harrison, to Major Percy Alexander MacMahon, Fellow of the Royal Society | 1 December 1896 |
| NLB/14/481 | Copy letter from Robert William Frederick Harrison, to J H Enthoven, 14 Connaught Place, W. | 17 March 1897 |
| NLB/14/461 | Copy letter from Robert William Frederick Harrison, to J H Enthoven | 16 March 1897 |
| NLB/14/479 | Copy letter from Arthur William Rucker, to Professor Alfred George Greenhill, [Fellow of the Royal Society] | 17 March 1897 |
| NLB/14/480 | Copy letter from Robert William Frederick Harrison, to Professor Michael Foster, [Fellow of the Royal Society] | 17 March 1897 |
| NLB/14/470 | Copy letter from Arthur William Rucker, to Lord Rayleigh [John William Strutt], [Fellow of the Royal Society] | 16 March 1897 |
| NLB/14/721 | Copy letter from Robert William Frederick Harrison, to Major Percy Alexander MacMahon, Fellow of the Royal Society | 3 May 1897 |
| NLB/16/22 | Copy letter from Robert William Frederick Harrison, to the Italian Ambassador | 13 January 1898 |
| NLB/15/688 | Copy letter from Robert William Frederick Harrison, to Major Percy Alexander MacMahon, Fellow of the Royal Society | 16 November 1897 |
| MC/4/187 | Letter from [James Joseph] Sylvester, 26 Lincoln Inn Fields, to Charles Richard Weld, [Assistant Secretary of the Royal Society] | 1 November 1847 |
| NLB/35/766 | Copy letter from Robert William Frederick Harrison, to Rabbi Henry Cohen, Congregation B'nai Israel, Galveston, Texas | 15 July 1907 |
| MC/26/14 | Letter from [Henry Frederick] Baker, 4 Kyneton Terrace, Northumberland, Norfolk, to Mr [Robert] Harrison, the [Royal Society] | 13 September 1911 |
| NLB/14/471 | Copy telegram from Robert William Frederick Harrison, to Professor Arthur William Rucker, [Fellow of the Royal Society] | [16 March 1897] |
| RR/7/72 | Referee's report by James Joseph Sylvester, on a paper 'On the contact of conics with surfaces' by William Spottiswoode | 28 May 1870 |
| RR/6/284 | Referee's report by Arthur Cayley, on a paper 'On the motion of a rigid body acted on by no external forces' by James Joseph Sylvester | 29 May 1866 |
| RR/6/57 | Referee's report by James Joseph Sylvester, on a paper 'On the curves which satisfy given conditions' by Arthur Cayley | 2 July 1867 |
| RR/5/42 | Referee's report by James Joseph Sylvester, on a paper 'A second memoir on skew surfaces, otherwise scrolls' by Arthur Cayley | 28 June 1864 |
| RR/6/55 | Referee's report by James Joseph Sylvester, on a paper 'A supplementary memoir on caustics' by Arthur Cayley | 21 February 1867 |
| RR/6/68 | Referee's report by James Joseph Sylvester, on a paper 'A third memoir on skew surfaces, otherwise scrolls' by Arthur Cayley | November 1868 |
| RR/6/58 | Referee's report by James Joseph Sylvester, on a paper 'Second memoir on the curves which satisfy given conditions; the principle of correspondence' by Arthur Cayley | 3 July 1867 |
| RR/5/41 | Referee's report by James Joseph Sylvester, on a paper 'On skew surfaces, otherwise scrolls' by Arthur Cayley | 11 June 1863 |
| RR/4/42 | Referee's report by James Joseph Sylvester, on a paper 'On Tschirnhausen’s transformation' by Arthur Cayley | 31 May 1862 |
| RR/10/88 | Referee's report by Arthur Cayley, on a paper 'On Hamilton's numbers' by James Joseph Sylvester and James Hammond | 20 June 1887 |
| RR/9/288 | Referee's report by James Joseph Sylvester, on a paper 'A memoir on the theory of mathematical form' by Alfred Bray Kempe | 17 November 1885 |
| RR/5/269 | Referee's report by Arthur Cayley, on a paper 'Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c' by James Joseph Sylvester | 2 October 1864 |
| RR/2/39 | Referee's report by James Joseph Sylvester, on a paper 'On the solution of linear differential equations' by B Bronwin | 8 July 1850 |
| RR/4/224 | Referee's report by James Joseph Sylvester, on a paper 'On the calculus of symbols - third memoir' by William Henry Leighton Russell | 2 July 1862 |
| RR/10/361 | Referee's report by James Joseph Sylvester, on a paper 'Memoir on symmetric functions of the roots of systems of equations' by Percy Alexander MacMahon | 4 March 1890 |
| MS/427/63 | Copy letter from Walter White, Assistant Secretary of the Royal Society, to the Hon. [Charles] W. Fremandle, Glasgow | 4 November 1880 |
| MS/426/372 | Note of a letter from [Charles Richard Weld, the Assistant Secretary of] the Royal Society; to Mr [James Joseph] Sylvester | 8 May 1849 |
| MS/426/227 | Copy letter from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to Lieut. Col. [James Joseph] Sylves [Sylvester] | 2 November 1846 |
| MS/426/688 | Copy letter from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to Prof [James Joseph] Sylvester | 12 March 1860 |
| EC/1839/24 | Sylvester, James Joseph: certificate of election to the Royal Society | |
| M/219 | Sylvester, James Joseph | |
| MM/15/17 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 3 February 1875 |
| NLB/2/419 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 13 June 1888 |
| NLB/3/544 | Copy letter from Herbert Rix, to Professor Edwin Ray Lankester, Fellow of the Royal Society, 42 Halfmoon Street | 8 July 1889 |
| NLB/10/149 | Copy letter from Herbert Rix, to Professor James Joseph Sylvester, Fellow of the Royal Society | 9 October 1894 |
| RR/6/283 | Referee's report by William Fishburn Donkin, on a paper 'On the motion of a rigid body acted on by no external forces' by James Joseph Sylvester | 22 June 1866 |
| M/142 | Sylvester Medal of the Royal Society | 1901 |
| NLB/10/702 | Copy letter from Herbert Rix, to Professor Michael Foster | 22 January 1895 |
| RR/10/89 | Referee's report by Andrew Russell Forsyth, on a paper 'On Hamilton's numbers' by James Joseph Sylvester and James Hammond | 16 July 1887 |
| RR/10/161 | Second letter from James Joseph Sylvester, to John William Strutt, 3rd Baron Rayleigh, regarding a paper 'A class of functional invariants' by Andrew Russell Forsyth | 5 May 1888 |
| RR/10/160 | Letter from James Joseph Sylvester, to John William Strutt, 3rd Baron Rayleigh, regarding a paper 'A class of functional invariants' by Andrew Russell Forsyth | 29 April 1888 |
| RR/10/164 | Second letter from James Joseph Sylvester, to John William Strutt, 3rd Baron Rayleigh, regarding a paper 'A class of functional invariants' by Andrew Russell Forsyth | 12 June 1888 |
| RR/2/233 | Referee's report by William Spottiswoode, on a paper 'On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure' by James Joseph Sylvester | 5 August 1853 |
| PT/44/2/1 | Manuscript, 'Analytical researches connected with Steiner's extension of Malfatti's problem' by Arthur Cayley | April 1852 |
| PT/63/15 | Paper, 'On systems of linear indeterminate equations and congruences' by Henry J [John] Stephen Smith | December 1860 |
| RR/6/65 | Referee's report by James Joseph Sylvester, on a paper 'On the conditions for the existence of three equal roots, or of two pairs of equal roots, of a binary quartic or quintic' by Arthur Cayley | 23 June 1868 |
| PT/70/14/2 | Diagram, flow of two branches of curve by [James Joseph Sylvester] | [1864] |
| RR/5/267 | Referee's report by Arthur Cayley, on a paper 'Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c' by James Joseph Sylvester | 28 April 1864 |
| RR/5/268 | Referee's report by Henry John Stephen Smith, on a paper 'Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c' by James Joseph Sylvester | 25 May 1864 |
| RR/6/51 | Referee's report by James Joseph Sylvester, on a paper 'Addition to the memoir on Tschirnhausen's transformation' by Arthur Cayley | 17 February 1866 |
| RR/5/265 | Referee's report by James Joseph Sylvester, on a paper 'On the distribution of surfaces of the third order into species, reference to the absence or presence of singular points, and the reality of their lines' by Ludwig Schläfli | 15 March 1865 |
| PT/44/2/2 | Plate, unpublished diagram of surface of a plane by Arthur Cayley | April 1852 |
| MC/4 | Volume 4 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1844-1850 |
| MC/7/154 | Letter from J J [James Joseph] Sylvester, Woolwich Common, to Dr [William] Sharpey, [Secretary of the Royal Society] | 16 December 1864 |
| MC/7/184 | Letter from J J [James Joseph] Sylvester, Woolwich Common, to Dr [William] Sharpey, [Secretary of the Royal Society] | 22 February 1865 |
| MC/7 | Volume 7 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1864-1866 |
| RR/2/234 | Referee's report by William Spottiswoode, on a paper 'On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure [supplement]' by James Joseph Sylvester | 31 October 1853 |
| RR/4/225 | Referee's report by James Joseph Sylvester, on a paper 'On the calculus of functions' by William Henry Leighton Russell | 2 June 1862 |
| MC/10/235 | Letter from J J [James Joseph] Sylvester, Athenaeum Club, Pall Mall, to Walter White, Assistant Secretary of the Royal Society | 6 April 1875 |
| MC/10 | Volume 10 of miscellaneous correspondence regarding business matters, sent to the Royal Society | July 1873-1876 |
| PT/44/2 | Paper, 'Analytical researches connected with Steiner's extension of Malfatti's problem' by Arthur Cayley | April 1852 |
| PT/70/14/1 | Manuscript, ['Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c'] by [James Joseph] Sylvester | [1864] |
| AP/48/6 | Unpublished appendix, 'Note to paper "On Poisson's solution of the accurate equations relating to the transmissions of sound through a cylindrical tube: and the general solution of partial differential equations"' by Robert Moon | 14 November 1866 |
| RR/2/226 | Referee's report by James Joseph Sylvester, on a paper 'Researches on the theory of invariants' by William Spottiswoode | 26 April 1855 |
| RR/2/232 | Referee's report by Arthur Cayley, on a paper 'On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure' by James Joseph Sylvester | 16 July 1853 |
| MC/12/323 | Letter from A [Alexander] Agassiz, Foreign Secretary of the National Academy of Sciences, Museum of Comparative Zoology, Cambridge, Massachusetts, to Professor J J [James Joseph] Sylvester, Baltimore | 23 April 1883 |
| AP/44/8 | Unpublished paper, 'On the true theory of pressure as applied to elastic fluids' by Robert Moon | 20 June 1862 |
| MC/12 | Volume 12 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1880-1883 |
| AP/48/5 | Unpublished paper, 'On Poisson's solution of the accurate equations relating to the transmission of sound through a cylindrical tube: and the general solution of partial differential equations' by Robert Moon | 1866 |
| AP/49/6 | Unpublished paper, 'On the integrability of certain partial differential equations proposed by Mr [George Biddell] Airy' by Robert Moon | 15 April 1867 |
| AP/50/11 | Unpublished paper, 'On the impact of compressible bodies, continued with reference to the theory of pressure' by R [Robert] Moon | 23 March 1868 |
| PT/47/7 | Paper, 'On a theory of the conjugate relations of two rational integral functions comprising an application to the theory of Sturm's functions and that of the greatest algebraical common measure' by J J [James Joseph] Sylvester | [1853] |
| PT/47/8 | Paper, ['General and concluding statement'] by James Joseph Sylvester | [1853] |
| PT/70/14 | Paper, ['Algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots, and an allied rule applicable to a particular class of equations, together with a complete invariantive determination of the character of the roots of the general equation of the fifth degree, &c'] by [James Joseph] Sylvester | [1864] |
| RR/2/61 | Referee's report by James Joseph Sylvester, on a paper 'Sur la théorie de I'orientation du plan oscillatoire du pendule simple, et son application à la recherche de I'aplatissement du sphéroide terrestre' by M Oliveira [Baptiste d'Oliveira on index card] | 19 March 1854 |
| RR/10/159 | Referee's report by James Joseph Sylvester, on a paper 'A class of functional invariants' by Andrew Russell Forsyth | 28 April 1888 |
| NLB/16/724 | Copy letter from Arthur William Rucker, to Professor [Karl] Pearson, Fellow of the Royal Society | 26 May 1898 |
| MC/17 | Volume 17 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1897-1899 |
| MC/26/13 | Letter from [Henry Frederick] Baker, A New Court, St John's College, Cambridge, to Mr [Robert] Harrison, the [Royal Society] | 13 July 1911 |
| MC/27/14 | Letter from [Henry Frederick] Baker, St John's College, Cambridge, to the [Royal Society] | 3 May 1912 |
| HS/17/164 | Letter, from James Joseph Sylvester to Sir John Herschel, dated at Woolwich Common | 5 March 1867 |
| HS/17/161 | Letter, from James Joseph Sylvester to Sir John Herschel, dated at Woolwich Common | 13 May 1861 |
| HS/17/162 | Letter, from James Joseph Sylvester to Sir John Herschel, dated at Woolwich Common | 25 March 1865 |
| HS/17/160 | Letter, from James Joseph Sylvester to Sir John Herschel, dated at 22 Doughty St. | 27 May 1841 |
| HS/17/163 | Letter, from James Joseph Sylvester to Sir John Herschel, dated at Woolwich Common | 2 October 1866 |