| Reference number | Title | Date |
| EC/1861/14 | Smith, Henry John Stephen: certificate of election to the Royal Society | |
| S/0020 | Sculpture bust of Smith, Henry John Stephen | 1883 |
| RR/7/212 | Referee's report by Henry John Stephen Smith, on a paper 'On the contact of surfaces' by William Spottiswoode | 7 November 1872 |
| RR/5/43 | Referee's report by Henry John Stephen Smith, on a paper 'A second memoir on skew surfaces, otherwise scrolls' by Arthur Cayley | 12 September 1864 |
| RR/4/243 | Referee's report by William Spottiswoode, on a paper 'On systems of linear indeterminate equations and congruences' by Henry John Stephen Smith | 12 April 1861 |
| RR/5/40 | Referee's report by Henry John Stephen Smith, on a paper 'On skew surfaces, otherwise scrolls' by Arthur Cayley | 28 April 1863 |
| RR/5/224 | Referee's report by Henry John Stephen Smith, on a paper 'On the calculus of symbols.—Third memoir' by William Henry Leighton Russell | 14 October 1863 |
| RR/6/273 | Referee's report by Arthur Cayley, on a paper 'On the orders and genera of ternary quadratic forms' by Henry John Stephen Smith | 8 May 1867 |
| RR/6/66 | Referee's report by Henry John Stephen Smith, on a paper 'A third memoir on skew surfaces, otherwise scrolls' by Arthur Cayley | 17 August 1868 |
| RR/6/64 | Referee's report by Henry John Stephen Smith, on two papers 'A memoir on the theory of reciprocal surfaces' and 'A memoir on cubic surfaces' by Arthur Cayley | 5 May 1869 |
| RR/7/40 | Referee's report by Henry John Stephen Smith, on a paper 'On the mechanical performance of logical inference' by William Stanley Jevons | 28 July 1870 |
| RR/6/69 | Referee's report by Henry John Stephen Smith, 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 | 21 April 1868 |
| RR/7/14 | Referee's report by Henry John Stephen Smith, on a paper 'A memoir on abstract geometry' by Arthur Cayley | 25 January 1870 |
| RR/7/85 | Referee's report by Henry John Stephen Smith, on a paper 'On the problem of the in-and-circumscribed triangle' by Arthur Cayley | 23 May 1871 |
| RR/7/82 | Referee's report by Henry John Stephen Smith, on a paper 'On cyclides and sphero-quartics' by John Casey | 21 August 1871 |
| RR/7/291 | Referee's report by Henry John Stephen Smith, on a paper 'A memoir on the transformation of elliptic functions' by Arthur Cayley | 18 April 1874 |
| RR/9/29 | Referee's report by Henry John Stephen Smith, on a paper 'Memoir on the Theta-functions, particularly those of two variables' by Andrew Russell Forsyth | 5 June 1882 |
| RR/7/372 | Referee's report by Henry John Stephen Smith, on a paper 'On a class of identical relations in the theory of elliptic functions' by by James Whitbread Lee Glaisher | 11 May 1875 |
| RR/8/7 | Referee's report by Henry John Stephen Smith, on a paper 'On a new form of tangential equation' by John Casey | 18 April 1877 |
| RR/8/344 | Referee's report by Henry John Stephen Smith, on a paper 'On the forty-eight coordinates of a cubic curve in space' by William Spottiswoode | 23 March 1881 |
| RR/9/70 | Referee's report by Henry John Stephen Smith, on a paper 'On a class of invariants' by John Christian Malet | 5 June 1882 |
| RR/8/307 | Referee's report by Henry John Stephen Smith, on a paper 'On Riccati's equation and its transformations, and on some definite integrals which satisfy them' by James Whitbread Lee Glaisher | 14 September 1881 |
| RR/5/201 | Note by Henry John Stephen Smith, on a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | [1863] |
| RR/7/390 | Referee's report by Henry John Stephen Smith, on a paper 'On the theory of the solution of a system of simultaneous non-linear partial differential equations of the first order' by E J Nanson | 21 August 1875 |
| MS/427/110 | Copy letter from [Thomas Henry] Huxley, Secretary of the Royal Society; to the Secretary of the H. M. Treasury | 17 June 1881 |
| MS/427/259 | Copy letter from [William] Spottiswoode, President of the Royal Society; to the Secretary of the Treasury | 17 February 1883 |
| MS/427/266 | Copy letter from [Michael] Foster, Secretary of the Royal Society; to the Secretary of the Treasury | 15 March 1883 |
| RR/8/252 | Referee's report by Henry John Stephen Smith, on a paper 'Memoir on Abel's theorem' by R C Rowe, with an 'Addition to Mr Rowe's paper' by Arthur Cayley | 27 September 1880 |
| RR/5/188 | Referee's report by Henry John Stephen Smith, on a paper 'On a new geometry of space' by Julius Plücker | 28 March 1865 |
| RR/6/274 | Referee's report by Thomas Archer Hirst, on a paper 'On the orders and genera of ternary quadratic forms' by Henry John Stephen Smith | 14 March 1867 |
| RR/8/218 | Referee's report by Henry John Stephen Smith, on a paper 'A Memoir on the Single and Double Theta-Functions' by Arthur Cayley | 13 March 1880 |
| RR/5/226 | Referee's report by Henry John Stephen Smith, on a paper 'On the calculus of symbols.— Fifth memoir. With applications to linear partial differential equations, and the calculus of functions' by William Henry Leighton Russell | 22 June 1864 |
| RR/6/235 | Referee's report by Henry John Stephen Smith, on a paper 'On the mysteries of numbers alluded to by Fermat.—Second communication' by Sir Jonathan Frederick Pollock, 1st Baronet | 23 July 1868 |
| RR/8/82 | Referee's report by Henry John Stephen Smith, on a paper 'A tenth memoir on quantics' by Arthur Cayley | 7 September 1878 |
| RR/8/305 | Referee's report by Henry John Stephen Smith, on a paper 'Formulae for sn 8u, cn 8u, dn 8u, in terms of sn u' by Ernest H Glaisher | 14 September 1881 |
| PT/63/15 | Paper, 'On systems of linear indeterminate equations and congruences' by Henry J [John] Stephen Smith | December 1860 |
| RR/7/226 | Referee's report by Henry John Stephen Smith, on a paper 'On curvature and orthogonal surfaces' by Arthur Cayley | 17 May 1873 |
| RR/4/199 | Referee's report by Henry John Stephen Smith, on a paper 'On Fermat's theorem of the polygonal numbers' by Frederick Pollock | 31 August 1861 |
| RR/4/242 | Referee's report by Arthur Cayley, on a paper 'On systems of linear indeterminate equations and congruences' by Henry John Stephen Smith | 28 March 1861 |
| RR/5/237 | Referee's report by Henry John Stephen Smith, 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 | 18 February 1863 |
| RR/5/25 | Referee's report by Henry John Stephen Smith, on a paper 'On the differential equations which determine the form of the roots of algebraic equations' by George Boole | 12 September 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/6/63 | Referee's report by Henry John Stephen Smith, 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 | 27 April 1868 |
| RR/5/46 | Referee's report by Henry John Stephen Smith, on a paper 'On the sextactic points of a plane curve' by Arthur Cayley | 30 March 1865 |
| MC/7/98 | Letter from Henry J S [John Stephen] Smith, Savilian Professor of geometry, University of Oxford, Balliol College, Oxford, to General [Edward] Sabine, President of the Royal Society | 15 June 1864 |
| RR/6/59 | Referee's report by Henry John Stephen Smith, on two papers 'On the curves which satisfy given conditions' and 'Second memoir on the curves which satisfy given conditions; the principle of correspondence' by Arthur Cayley | 4 September 1867 |
| MC/7 | Volume 7 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1864-1866 |
| RR/5/190 | Referee's report by Henry John Stephen Smith, on a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 6 September 1862 |
| RR/5/199 | Second referee's report by Henry John Stephen Smith, on a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 31 May [1863] |
| RR/8/81 | Referee's report by Henry John Stephen Smith, on a paper 'Addition to memoir on the transformation of elliptic functions' by Arthur Cayley | 17 April 1878 |
| MC/11/184 | Letter from Henry J S [John Stephen] Smith, Meteorological Office, 116 Victoria Street, London, to Sir Joseph [Dalton] Hooker, President of the Royal Society | 15 March 1878 |
| MC/11/185 | Letter from Henry J S [John Stephen] Smith, Meteorological Office, 116 Victoria Street, London, to [Sir Joseph Dalton Hooker], President of the Royal Society | 15 March 1878 |
| MC/11/229 | Letter from Henry J S [John Stephen] Smith, Chairman of the Meteorological Council, Meteorological Office, 116 Victoria Street, London, to the Secretary of the Royal Society | 27 June 1878 |
| MC/11/321 | Letter from Henry J S [John Stephen] Smith, Meteorological Office, 116 Victoria Street, London, to W [William] Spottiswoode, President of the Royal Society | 24 March 1879 |
| MC/11/388 | Letter from Henry J S [John Stephen] Smith, Chairman of the Meteorological Council, Meteorological Office, 116 Victoria Street, London, to the Secretary of the Royal Society | 19 June 1879 |
| MC/11 | Volume 11 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1877-1879 |
| MS/427/263 | Copy letter from [Michael] Foster, Secretary of the Royal Society; to [Robert Henry] Scott | 17 February 1883 |
| RR/6/114 | Referee's report by Henry John Stephen Smith, on a paper 'Second memoir on plane stigmatics' by Alexander John Ellis | 8 September 1866 |
| RR/6/234 | Referee's report by Henry John Stephen Smith, on a paper 'On the mysteries of numbers alluded to by Fermat' by Sir Jonathan Frederick Pollock, 1st Baronet | 8 September 1866 |
| RR/7/73 | Referee's report by Henry John Stephen Smith, on a paper 'On the values of the Integral 1 0 Qn Qn' dµ, Qn, Qn' being Laplace's coefficients of the orders n, n', with an application to the theory of radiation' by John William Strutt | 13 August 1870 |
| RR/6/236 | Referee's report by Henry John Stephen Smith and Bartholomew Price, on a paper 'On the mysteries of numbers alluded to by Fermat.—Second communication' by Sir Jonathan Frederick Pollock, 1st Baronet | nd [1868] |
| RR/8/66 | Referee's report by Henry John Stephen Smith, on a paper 'On hyperjacobian surfaces and curves' by William Spottiswoode | 14 June 1877 |
| AP/62/2 | Unpublished paper, 'On a uniform rotation machine and on the theory of electromagnetic tuning forks' by R H M [Robert Holford Macdowall] Bosanquet | 1882 |
| RR/5/194 | Memorandum by Henry John Stephen Smith, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock | 12 November 1863 |
| RR/5/225 | Referee's report by Henry John Stephen Smith, on a paper 'On the calculus of symbols.— Fourth memoir. With applications to the theory of non-linear differential equations' by William Henry Leighton Russell | 10 April 1864 |
| MC/14/16 | Letter from Professor [Thomas] Fowler, Oxford, to [Michael] Foster, [Secretary of the Royal Society] | 4 February 1885 |
| RR/5/23 | Referee's report by Henry John Stephen Smith, on a paper 'On the differential equations of dynamics. A sequel to a paper on simultaneous differential equations' by George Boole | 20 May 1863 |
| RR/5/67 | Referee's report by Henry John Stephen Smith, on a paper 'Introductory memoir on plane stigmatics' by Alexander John Ellis | 14 September 1865 |
| RR/5/68 | Letter by Henry John Stephen Smith, to George Gabriel Stokes, regarding a paper 'Introductory memoir on plane stigmatics' by Alexander John Ellis | 15 September 1865 |
| RR/5/191 | Referee's report by Henry John Stephen Smith, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock | 14 October 1863 |
| RR/5/193 | Second referee's report by Henry John Stephen Smith, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock | 10 November 1863 |
| MS/427/412 | Copy letter from [Michael] Foster, Secretary of the Royal Society; to Prof. Fowler, Corpus Christie College, Oxford | 19 February 1885 |
| MC/14 | Volume 14 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1885-1888 |