# Record

Authorised form of name | Cayley; Arthur (1821 - 1895); mathematician |

Dates | 1821 - 1895 |

Nationality | British |

Place of birth | Richmond, Surrey, England |

Date of birth | 16 August 1821 |

Place of death | Cambridge |

Date of death | 26 January 1895 |

Occupation | Barrister |

Research field | Mathematics |

Astronomy | |

Activity | Education: MA Career: Fellow, Trinity College, Cambridge. |

Membership category | Fellow |

Date of election | 03/06/1852 |

Royal Society activity | Medals and prizes: Royal Medal 1859; Copley Medal 1882 |

Sources | Sources: Bulloch's Roll; DNB; DSB Obituaries: Proc Roy Soc 1895 vol 58 pp i-xliii, signed by A R F References: I M James, 'James Joseph Sylvester, FRS (1814-1897)' in NR 1997 vol 51 pp 247-261 Tony Crilly, 'The Young Arthur Cayley' in NR 1998 vol 52 pp 267-282, plate Alex D D Craik, 'James Ivory's last papers on the 'Figure of the Earth' (with biographical additions) in NR 2002 vol 56 pp 187-204 T Crilly, 'Arthur Cayley FRS and the four-colour map problem' in NR 2005 vol 59 pp 285-304 |

Virtual International Authority File | http://viaf.org/viaf/69046313 |

Royal Society code | NA6944 |

Archives associated with this Fellow

Reference number | Title | Date |

IM/000778 | Cayley, Arthur | nd |

EC/1852/03 | Cayley, Arthur: certificate of election to the Royal Society | |

MM/15/24 | Letter from J J Sylvester, Maddox Street, to Arthur Cayley | 1878 |

AP/40/8 | Unpublished paper, 'On certain formulae for differentation' by Arthur Cayley | 1857 |

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 |

IM/000780 | Cayley, Arthur | 2002 |

IM/000779 | Cayley, Arthur | 1995 |

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 |

AP/41/6 | Unpublished paper, 'On the theory of internal resistance and of internal friction in fluids: and on the theories of sound and of auscultation' by Robert Moon | 1858 |

AP/39/35 | Paper, 'On a class of dynamical problems' by Arthur Cayley | 16 May 1857 |

AP/40/20 | Unpublished paper, 'On the surface which is the envelope of planes through the points of an ellipsoid at right angles to the radius vectors from the centre' by Arthur Cayley | 1858 |

AP/58/10 | On Clairantian Functions and Equations | 1876 |

RR/3/49 | Referee's report by Bartholomew Price, on five unnamed papers by Arthur Cayley | 1857 |

RR/4/36 | Referee's report by William Spottiswoode, on two unnamed papers by Arthur Cayley | 27 May 1859 |

NLB/2/27 | Copy letter from Herbert Rix, to Professor Arthur Cayley, Fellow of the Royal Society | 10 December 1887 |

NLB/2/901 | Copy letter from Herbert Rix, to Professor Arthur Cayley, Fellow of the Royal Society | 12 December 1888 |

NLB/3/205 | Copy letter from Herbert Rix, to Professor Arthur Cayley, Fellow of the Royal Society | 10 April 1889 |

NLB/3/1043 | Copy letter from Herbert Rix, to Messrs Clay & Sons, Cambridge | 23 December 1889 |

NLB/10/728 | Copy letter from Theodore E James, to Messrs Harrison & Sons | 28 January 1895 |

NLB/10/738 | Copy letter from Herbert Rix, to Henry James Chaney, Board of Trade, Standard's Department | 29 January 1895 |

NLB/11/413 | Copy letter from an unknown correspondent, to the Cambridge Engraving Company, Cambridge | 24 June 1895 |

NLB/11/376 | Copy letter from Herbert Rix, to Professor Andrew Russell Forsyth, care of Andrew Russell, 14 Amberley Street, Liverpool | 18 June 1895 |

NLB/11/578 | Copy letter from Herbert Rix, to Messrs Harrison & Sons | 26 July 1895 |

RR/4/42 | Referee's report by James Joseph Sylvester, on a paper 'On Tschirnhausen’s transformation' by Arthur Cayley | 31 May 1862 |

RR/2/43 | Referee's report by William Thomson, Lord Kelvin, on a paper 'An introductory memoir upon quantics' by Arthur Cayley | 12 August 1854 |

RR/3/53 | Referee's report by Philip Kelland, on five unnamed papers by Arthur Cayley | 23 February 1857 |

RR/4/72 | Referee's report by Arthur Cayley, on a paper 'On the laws of operation, and the systematization of mathematics' by Alexander John Ellis | 1 June 1859 |

RR/3/62 | Referee's report by Batholomew Price, on a paper 'Sixth memoir on quantics' by Arthur Cayley | 22 December 1858 |

RR/3/82 | Referee's report by Arthur Cayley, on a paper 'On the theory of the gyroscope' by William Cook | 8 May 1857 |

RR/3/59 | Referee's report by Bartholomew Price, on two papers 'Fourth and fifth memoirs on quantics' by Arthur Cayley | 4 May 1858 |

RR/3/123 | Referee's report by Arthur Cayley, on a paper 'Elementary considerations on the subject of rotatory motion' by William Gravatt | 20 May 1856 |

RR/3/256 | Referee's report by Arthur Cayley, on a paper 'On the determination of unknown functions which are involved under definite integrals' by Joaquin Gomes da Souza | 9 July 1856 |

RR/3/216 | Referee's report by Arthur Cayley, on a paper 'On some remarkable relations which obtain among the roots of the four squares into which a number may be divided, as compared with the corresponding roots of certain other numbers' by Frederick Pollock | 15 June 1858 |

RR/3/164 | Referee's report by Arthur Cayley, on a paper 'On the representation of polyedra' by Thomas Penyngton Kirkman | 2 February 1856 |

RR/3/45 | Referee's report by James Booth, on an unnamed paper by Arthur Cayley | 23 October 1855 |

RR/4/120 | Referee's report by Arthur Cayley, on a paper 'On the problem of three bodies' by Charles James Hargreave | 7 March 1859 |

RR/7/211 | Referee's report by Arthur Cayley, on a paper 'On the contact of surfaces' by William Spottiswoode | 10 April 1872 |

RR/4/41 | Referee's report by William Spottiswoode, on a paper 'On Tschirnhausen’s transformation' by Arthur Cayley | 15 January 1862 |

RR/4/50 | Referee's report by William Spottiswoode, on a paper 'On a new auxiliary equation in the theory of equations of the fifth order' by Arthur Cayley | 4 May 1861 |

RR/7/17 | Referee's report by Bartholomew Price, on a paper 'A ninth memoir on quantics' by Arthur Cayley | 30 July 1870 |

RR/3/170 | Referee's report by Arthur Cayley, on a paper 'On the partitions of the R-pyramid, being the first class of R-gonous X-edra' by Thomas Penyngton Kirkman | 19 January 1858 |

RR/3/52 | Referee's report by James Booth, on a paper 'A memoir upon caustics' by Arthur Cayley | 10 February 1857 |

PT/49/3 | Paper, 'An introductory memoir upon quantics' by A [Arthur] Cayley | [1854] |

RR/7/16 | Referee's report by William Spottiswoode, on a paper 'A ninth memoir on quantics' by Arthur Cayley | 30 May 1870 |

RR/4/47 | Referee's report by Bartholomew Price, on a paper 'A seventh memoir on quantics' by Arthur Cayley | 1 May 1861 |

RR/5/192 | Referee's report by Arthur Cayley, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock | 2 November 1863 |

RR/4/91 | Referee's report by Arthur Cayley, on a paper 'On the construction of life-tables, illustrated by a new life-table of the healthy districts of England' by William Farr | 4 May 1859 |

RR/5/22 | Referee's report by Arthur Cayley, on a paper 'On the differential equations of dynamics. A sequel to a paper on simultaneous differential equations' by George Boole | 19 March 1863 |

PT/54/9 | Paper, 'On the representation of polyedra [polyhedra]' by Rev Tho [Thomas] P [Penyngton] Kirkman | [1855] |

RR/4/15 | Referee's report by Arthur Cayley, on a paper 'On simultaneous differential equations of the first order in which the number of the variables exceeds by more than one the number of the equations' by George Boole | 25 June 1862 |

RR/4/46 | Referee's report by William Spottiswoode, on a paper 'A seventh memoir on quantics' by Arthur Cayley | 4 May 1861 |

RR/3/63 | Referee's report by William Spottiswoode, on a paper 'Sixth memoir of quantics' by Arthur Cayley | 28 December 1858 |

RR/6/54 | Referee's report by Bartholomew Price, on a paper 'An eighth memoir on quantics' by Arthur Cayley | 21 February 1867 |

PT/65/7 | Paper, 'On Tschirnhausen's transformation' by A [Arthur] Cayley | [1861] |

RR/4/52 | Referee's report by Bartholomew Price, on a paper 'On the double tangents of a curve of the fourth order' by Arthur Cayley | 20 August 1861 |

RR/6/53 | Referee's report by Philip Kelland, on a paper 'A supplementary memoir on caustics' by Arthur Cayley | 29 December 1866 |

RR/6/52 | Referee's report by William Spottiswoode, on a paper 'Addition to the memoir on Tschirnhausen's transformation' by Arthur Cayley | 2 March 1866 |

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/3/56 | Referee's report by Philip Kelland, on an unnamed paper by Arthur Cayley and an unnamed paper by Reverend Robert Carmichael | 15 March 1858 |

RR/4/150 | Referee's report by Arthur Cayley, on a paper 'On the theory of the polyedra' by Thomas Penynton Kirkman | 1862 |

RR/4/16 | Referee's report by Arthur Cayley, on a paper 'On the theory of probabilities' by George Boole | 25 June 1862 |

RR/4/43 | Referee's report by William Spottiswoode, on a paper 'On the analytical theory of the conic' by Arthur Cayley | 8 June 1862 |

RR/4/51 | Referee's report by William Spottiswoode, on a paper 'On the double tangents of a curve of the fourth order' by Arthur Cayley | 3 August 1861 |

RR/4/189 | Referee's report by Arthur Cayley, on a paper 'The higher theory of elliptic integrals, treated from Jacobi's functions as its basis' by F W Newman | 4 May 1859 |

RR/4/37 | Referee's report by William Spottiswoode, on a paper 'On the equation of differences for an equation of any order, and in particular for the equations of the orders two, three, four, and five' by Arthur Cayley | 25 May 1860 |

RR/4/253 | Referee's report by Arthur Cayley, on a paper 'On the contact of curves' by William Spottiswoode | 17 February 1862 |

RR/3/60 | Referee's report by Archibald Smith, on a paper 'On the envelope of planes through the points of an ellipsoid at right angles to the radius vectors from the centre' by Arthur Cayley | 5 May 1858 |

RR/4/246 | Referee's report by Arthur Cayley, on a paper 'On an extended form of the index symbol in the calculus of operations' by William Spottiswoode | 23 February 1860 |

RR/4/44 | Referee's report by Bartholomew Price, on a paper 'On the analytical theory of the conic' by Arthur Cayley | 14 June 1862 |

RR/4/251 | Referee's report by Arthur Cayley, on a paper 'On internal and external division in the calculus of symbols' by William Spottiswoode | 3 April 1862 |

RR/5/38 | Referee's report by William Spottiswoode, on a paper 'On certain developable surfaces' by Arthur Cayley | 14 January 1863 |

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/6/66 | 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/5/39 | Letter from Arthur Cayley, to George Gabriel Stokes, regarding a paper 'On certain developable surfaces' by Arthur Cayley | 30 January 1863 |

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/5/252 | Referee's report by Arthur Cayley, on a paper 'On the equations of rotation of a solid body about a fixed point' by William Spottiswoode | 28 July 1863 |

RR/3/50 | Referee's report by Bartholomew Price, on a paper 'A memoir on curves of the third order' by Arthur Cayley | 26 January 1857 |

RR/5/196 | Referee's report by Arthur Cayley, on a paper 'On the mysteries of numbers alluded to by Fermat' by Jonathan Frederick Pollock | 19 January 1865 |

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/3/48 | Referee's report by Phillip Kelland, on an unnamed paper by Arthur Cayley | 1856 |

PT/70/13 | Paper, 'A second memoir on skew surfaces otherwise scrolls' by A [Arthur] Cayley | [1864] |

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/7/222 | Referee's report by Arthur Cayley, on a paper 'Researches in the dynamics of a rigid body by the aid of the theory of screws' by Robert Stawell Ball | 30 September 1873 |

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 |

RR/6/60 | Referee's report by Bartholomew Price, on a paper 'Addition to memoir on the resultant of a system of two equations' by Arthur Cayley | 24 December 1867 |

RR/6/56 | Referee's report by William Spottiswoode, on a paper 'An eighth memoir on quantics' by Arthur Cayley | 25 February 1867 |

RR/6/237 | Referee's report by Arthur Cayley, on a paper 'Fundamental views regarding mechanics' by Julius Plücker | 16 June 1866 |

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/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/6/57 | Referee's report by James Joseph Sylvester, on a paper 'On the curves which satisfy given conditions' by Arthur Cayley | 2 July 1867 |

RR/6/55 | Referee's report by James Joseph Sylvester, on a paper 'A supplementary memoir on caustics' by Arthur Cayley | 21 February 1867 |

RR/6/51 | 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/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/6/50 | Referee's report by William Spottiswoode, on a paper 'A supplementary memoir on the theory of matrices' by Arthur Cayley | 4 February 1866 |

RR/6/61 | Referee's report by Philip Kelland, on a paper 'Addition to memoir on the resultant of a system of two equations' by Arthur Cayley | 31 December 1867 |

RR/6/67 | Referee's report by George Salmon, on two papers 'A memoir on the theory of reciprocal surfaces' and 'A memoir on cubic surfaces' by Arthur Cayley | 9 February 1869 |

RR/6/187 | Referee's report by Arthur Cayley, on a paper 'On the integrability of certain partial differential equations proposed by Mr. Airy' by R Moon | 25 July 1867 |

RR/9/138 | Referee's report by Arthur Cayley, on a paper 'On Abel’s Theorem and Abelian functions' by Andrew Russell Forsyth | 20 February 1883 |

RR/3/47 | Referee's report by William Spottiswoode, on a paper 'Third memoir upon caustics' by Arthur Cayley | 24 April 1856 |

RR/7/84 | Referee's report by Thomas Archer Hirst, on a paper 'On the problem of the in-and-circumscribed triangle' by Arthur Cayley | 22 February 1871 |

RR/10/291 | Referee's report by Arthur Cayley, on a paper 'On certain geometrical theorems' by William Henry Leighton Russell | 29 July 1889 |

RR/6/185 | Referee's report by Arthur Cayley, on a paper 'On Poisson’s solution of the accurate equations applicable to the transmission of sound through a cylindrical tube; and on the general solution of partial differential equations' by R Moon | 7 February 1867 |

RR/7/15 | Referee's report by Thomas Archer Hirst, on a paper 'A memoir on abstract geometry' by Arthur Cayley | 14 February 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/7/291 | 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/7/74 | Referee's report by Arthur Cayley, on a paper 'On Jacobi's theorem respecting the relative equilibrium of a revolving ellipsoid of fluid, and on ivory's discussion of the theorem' by Isaac Todhunter | 19 February 1870 |

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/7/71 | Referee's report by Arthur Cayley, on a paper 'On the contact of conics with surfaces' by William Spottiswoode | 20 April 1870 |

RR/7/403 | Referee's report by Arthur Cayley, on a paper 'On multiple contact of surfaces' by William Spottiswoode | 26 July 1875 |

RR/8/306 | Referee's report by Arthur Cayley, on a paper 'On Riccati's equation and its transformations, and on some definite integrals which satisfy them' by James Whitbread Lee Glaisher | 5 July 1881 |

RR/8/343 | Referee's report by Arthur Cayley, on a paper 'On the forty-eight coordinates of a cubic curve in space' by William Spottiswoode | 28 February 1881 |

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 |

RR/7/293 | Referee's report by Arthur Cayley, on a paper 'On Mr. Spottiswoode’s contact problems' by William Kingdon Clifford | 4 January 1874 |

RR/7/371 | Referee's report by Arthur Cayley, on a paper 'On a class of identical relations in the theory of elliptic functions' by by James Whitbread Lee Glaisher | 11 February 1875 |

RR/7/442 | Referee's report by William Kingdon Clifford, on a paper 'A memoir on prepotentials' by Arthur Cayley | 1876 |

RR/8/304 | Referee's report by Arthur Cayley, on a paper 'Formulae for sn 8u, cn 8u, dn 8u, in terms of sn u' by Ernest H Glaisher | 5 July 1881 |

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/9/287 | Referee's report by Arthur Cayley, on a paper 'A memoir on the theory of mathematical form' by Alfred Bray Kempe | 17 September 1885 |

RR/8/83 | Referee's report by Arthur Cayley, on a paper 'On the classification of Loci' by William Kingdon Clifford | 13 June 1878 |

RR/10/259 | Referee's report by Arthur Cayley, on a paper 'On the interchange of the variables in certain linear differential operators' by Edwin Bailey Elliott | 13 June 1889 |

RR/8/318 | Referee's report by Arthur Cayley, on a paper 'On toroidal functions' by William Mitchinson Hicks | 4 May 1881 |

RR/9/57 | Referee's report by Arthur Cayley, on a paper 'On a tangential property of regular hypoeycloids and epicycloids. (II.) On theorems relating to the regular polyhedra which are analogous to those of Dr. Matthew Stewart on the regular polygons' by Henry Martyn Jeffery | 13 November 1882 |

RR/8/281 | Letter from Arthur Cayley, to George Gabriel Stokes, regarding a paper 'On toroidal functions' by William Mitchinson Hicks, and two untraced papers by James Whitbread Lee Glaisher | 24 June 1881 |

RR/9/54 | Referee's report by Arthur Cayley, on a paper 'On a tangential property of regular hypoeycloids and epicycloids. (II.) On theorems relating to the regular polyhedra which are analogous to those of Dr. Matthew Stewart on the regular polygons' by Henry Martyn Jeffery | 12 July 1882 |

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/10/362 | Referee's report by Arthur Cayley, on a paper 'Memoir on symmetric functions of the roots of systems of equations' by Percy Alexander MacMahon | 12 March 1890 |

RR/9/342 | Referee's report by Arthur Cayley, on a paper 'On the discrimination of maxima and minima solutions in the calculus of variations' by E P Culverwell | 5 July 1886 |

RR/10/101 | Referee's report by Arthur Cayley, on a paper 'On the diameters of a plane cubic' by John James Walker | 1 August 1887 |

RR/10/163 | Letter from Arthur Cayley, to John William Strutt, 3rd Baron Rayleigh, regarding a paper 'A class of functional invariants' by Andrew Russell Forsyth | 7 June 1888 |

RR/10/156 | Referee's report by Arthur Cayley, on a paper 'Invariants, convariants, and quotient-derivatives associated with linear differential equations' by Andrew Russell Forsyth | 8 February 1888 |

RR/10/158 | Referee's report by Arthur Cayley, on a paper 'A class of functional invariants' by Andrew Russell Forsyth | 22 March 1888 |

RR/10/182 | Referee's report by Arthur Cayley, on a paper 'On the direct application of first principles in the theory of partial differential equations' by Joseph Larmor | 26 January 1888 |

RR/10/104 | Second referee's report by Arthur Cayley, on a paper 'On the diameters of a plane cubic' by John James Walker | 22 November 1887 |

RR/12/3 | Referee's report by Arthur Cayley, on a paper 'Memoir on the theory of the compositions of numbers' by Percy Alexander MacMahon | 21 December 1892 |

RR/12/194 | Referee's report by Arthur Cayley, on a paper 'A certain class of generating functions in the theory of numbers' by Percy Alexander MacMahon | 28 November 1893 |

RR/5/202 | Letter from Arthur Cayley, to George Gabriel Stokes, regarding a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 3 April [1863] |

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/2/228 | Referee's report by Arthur Cayley, on a paper 'Researches on the theory of invariants' by William Spottiswoode | 28 June 1855 |

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 |

RR/7/29 | Letter from Arthur Cayley, on a paper 'Tables of the numerical values of the sine-integral, cosine-integral, and exponential-integral' by James Whitbread Lee Glaisher to the Secretary of the Royal Society | 9 February 1870 |

RR/6/233 | Referee's report by Arthur Cayley, on a paper 'On the mysteries of numbers alluded to by Fermat' by Sir Jonathan Frederick Pollock, 1st Baronet | 2 April 1866 |

RR/10/166 | Second referee's report by Arthur Cayley, on a paper 'A class of functional invariants' by Andrew Russell Forsyth | 31 October 1888 |

RR/4/40 | Referee's report by William Spottiswoode, on a paper 'On the porism of the in-and-circumscribed polygon' by Arthur Cayley | 27 June 1861 |

RR/3/61 | Referee's report by James Booth, on a paper 'Supplementary researches on the partition of numbers' by Arthur Cayley | 5 February 1858 |

RR/3/54 | Referee's report by Philip Kelland, on a paper 'A memoir upon caustics' by Arthur Cayley | 23 July 1857 |

RR/3/51 | Referee's report by John Thomas Graves, on a paper 'A memoir on curves of the third order' by Arthur Cayley | 31 January 1957 |

PT/58/6 | Paper, 'A memoir on curves of the third order' by A [Arthur] Cayley | [1856] |

RR/3/167 | Referee's report by Arthur Cayley, on a paper 'On the K-partitions of the R-gon and R-ace' by Thomas Penyngton Kirkman | 5 January 1857 |

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/5/44 | Referee's report by Arthur Cayley, on an unknown paper by an unknown author | nd |

RR/4/69 | Referee's report by Arthur Cayley, on a paper 'On the analytical theory of the attraction of solids bounded by surfaces of a hypothetical class including the ellipsoid' by William Fishburn Donkin | 26 January 1860 |

RR/4/39 | Referee's report by Bartholomew Price, on a paper 'On the conic of five-pointic contact at any point of a plane curve' by Arthur Cayley | 19 May 1859 |

RR/4/129 | Referee's report by Arthur Cayley, on a paper 'On the formulae investigated by Dr. Brinkley for the general term in the development of Lagrange’s expression for the summation of series and for successive integrations' by John Frederick William Herschel | 27 July 1860 |

RR/4/230 | Referee's report by Arthur Cayley, on a paper 'On quaternary cubics' by George Salmon | 27 July 1860 |

RR/10/45 | Referee's report by Arthur Cayley, on an untraced paper 'A geometrical interpretation of the first two periods of chemical elements' by Samuel Haughton | 11 June 1887 |

RR/8/253 | Referee's report by James Whitbread Lee Glaisher, on a paper 'Memoir on Abel's theorem' by R C Rowe, with an 'Addition to Mr Rowe's paper' by Arthur Cayley | 15 December 1880 |

MS/427/229 | Copy letter from Walter White, Assistant Secretary of the Royal Society; to R. B. Bell | 10 November 1882 |

PT/57/5/10 | Plate, figure 9 showing curve of caustic with two infinite branches by Arthur Cayley | [1856] |

IM/Maull/000777 | Cayley, Arthur | nd |

MM/15/17 | Letter from J J Sylvester, Athenaeum, to Arthur Cayley | 3 February 1875 |

NLB/10/881 | Copy letter from Dr Michael Foster, the President of the Royal Academy of Science, Turin | 25 February 1895 |

RR/3/233 | Referee's report by Arthur Cayley, on a paper 'On the stability of loose earth' by William John Macquorn Rankine | 7 November 1856 |

PT/59/3 | Paper, 'On the symmetric functions of the roots of certain systems of two equations' by A [Arthur] Cayley | [1856] |

RR/5/189 | Referee's report by Arthur Cayley, on a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 22 October 1862 |

RR/6/62 | Committee report, 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 | nd [1867] |

RR/5/200 | Second referee's report by Arthur Cayley, on a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 11 April [1863] |

RR/6/49 | Referee's report by Bartholomew Price, on a paper 'A supplementary memoir on the theory of matrices' by Arthur Cayley | 29 January 1866 |

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/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/6/123 | Referee's report by Arthur Cayley, on a paper 'Note on Professor Sylvester’s representation of the motion of a free rigid body by that of a material ellipsoid whose centre is fixed, and which rolls on a rough plane' by Norman Macleod Ferrers | 14 July 1869 |

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/10/102 | Detailed referee's report by Arthur Cayley, on a paper 'On the diameters of a plane cubic' by John James Walker | nd [1887] |

RR/10/168 | Second letter from Arthur Cayley, to John William Strutt, 3rd Baron Rayleigh, regarding a paper 'A class of functional invariants' by Andrew Russell Forsyth | 29 November 1888 |

RR/10/183 | Second referee's report by Arthur Cayley, on a paper 'On the direct application of first principles in the theory of partial differential equations' by Joseph Larmor | 1 March 1888 |

RR/3/46 | Referee's report by Philip Kelland, on a paper 'Second and third memoir on quantics' by Arthur Cayley | 2 November 1855 |

RR/9/346 | Letter from Arthur Cayley, on a paper 'On the discrimination of maxima and minima solutions in the calculus of variations' by E P Culverwell to John William Strutt, Lord Rayleigh | 28 December 1886 |

PT/44/2 | Paper, 'Analytical researches connected with Steiner's extension of Malfatti's problem' by Arthur Cayley | April 1852 |

RR/3/44 | Referee's report by Joseph Dalton Hooker, on an unnamed paper by Arthur Cayley | 12 May 1855 |

NLB/8/715 | Copy letter from Herbert Rix, to Professor Arthur Cayley, Fellow of the Royal Society | 13 December 1893 |

RR/5/82 | Letter from Arthur Cayley, to George Gabriel Stokes, regarding a paper 'Second part of the supplement to the two papers on mortality published in the Philosophical Transactions in 1820 and 1825' by Benjamin Gompertz | 8 December 1864 |

RR/5/203 | Second letter from Arthur Cayley, to George Gabriel Stokes, regarding a paper 'On Fermat's theorem of the polygonal numbers. —Second communication' by Jonathan Frederick Pollock | 4 May [1863] |

RR/7/402 | Referee's report by Arthur Cayley, on a paper 'On the integration of algebraical functions, with illustrations in mechanics' by William Henry Leighton Russell | 21 April 1875 |

PT/57/5/18 | Plate, figure 17 showing curve of caustic with double point by Arthur Cayley | [1856] |

PT/63/2 | Paper, 'On an extension of Arbogast's method of derivations' by A [Arthur] Cayley | 25 September 1860 |

RR/4/79 | Referee's report by Arthur Cayley, on a paper 'On scalar and clinant algebraical coordinate geometry, introducing a new and more general theory of analytical geometry, including the received as a particular case, and explaining ‘imaginary points,’ ‘intersections,’ and ‘lines.’' by Alexander John Ellis | 25 April 1860 |

PT/52/5 | Paper, 'Second memoir upon quantics' by A [Arthur] Cayley | 11 April 1855 |

PT/44/2/2 | Plate, unpublished diagram of surface of a plane by Arthur Cayley | April 1852 |

PT/44/2/1 | Manuscript, 'Analytical researches connected with Steiner's extension of Malfatti's problem' by Arthur Cayley | April 1852 |

PT/59/5 | Paper, 'Tables of the Sturmian functions for equations of the second third fourth and fifth degrees' by A [Arthur] Cayley | [1856] |

PT/69/6 | Paper, 'On skew surfaces, otherwise scroles [scrolls]' by A [Arthur] Cayley | [1863] |

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 |

RR/2/59 | Referee's report by Arthur Cayley, on a paper 'On a class of differential equations, including those which occur in dynamical problems.- Part I' by William Fishburn Donkin | 29 March 1854 |

RR/2/42 | Referee's report by John Thomas Graves, on a paper 'An introductory memoir upon quantics' by Arthur Cayley | 13 May 1854 |

PT/57/5/19 | Plate, figure 18 showing curve of caustic broken into interior and exterior circle by Arthur Cayley | [1856] |

PT/52/6 | Paper, 'Further researches on the partition of numbers' by A [Arthur] Cayley | 11 April 1855 |

PT/57/5/3 | Plate, figure 2 showing tangential equation of caustic by Arthur Cayley | [1856] |

PT/53/12 | Paper, 'A third memoir upon quantics' by A [Arthur] Cayley | [1856] |

PT/59/2 | Paper, 'A memoir on the resultant of a system of two equations' by A [Arthur] Cayley | [1856] |

RR/3/162 | Referee's report by Arthur Cayley, on a paper 'On the enumeration of x-edra having triedral summits, and an (x—1)-gonal base' by Thomas Penyngton Kirkman | 13 July 1855 |

PT/59/4 | Paper, 'A memoir on the conditions for the existence of given systems of equalities among the roots of an equation' by A [Arthur] Cayley | [1856] |

PT/54/8 | Paper, 'On the enumeration of x-edra having triedral summits, and an (x-1)-gonal base' by Rev Tho [Thomas] P [Penyngton] Kirkman | May 1855 |

RR/3/95 | Referee's report by Arthur Cayley, on a paper 'On the equation of Laplace's functions' by William Fishburn Donkin | 5 January 1857 |

PT/57/3 | Paper, 'On autopolar polyedra' by Rev Thos P [Thomas Penyngton] Kirkman | [1856] |

RR/3/166 | Referee's report by Arthur Cayley, on a paper 'On autopolar polyedra' by Thomas Penyngton Kirkman | 30 October 1856 |

PT/57/3/1 | Manuscript, 'On autopolar polyedra' by Rev Thos P [Thomas Penyngton] Kirkman | [1856] |

PT/57/3/2 | Plate, hexahedron systems by Thomas Penyngton Kirkman | [1856] |

PT/57/3/3 | Plate, polyhedra relating to articles VI-XVII by Thomas Penyngton Kirkman | [1856] |

PT/57/3/5 | Plate, polyhedra relating to articles XXXII-XXXVI by Thomas Penyngton Kirkman | [1856] |

PT/57/3/4 | Plate, polyhedra relating to articles XIX-XXI by Thomas Penyngton Kirkman | [1856] |

PT/57/4 | Paper, 'On the K-partition of the R-gon and R-ace' by Rev Tho P [Thomas Penyngton] Kirkman | [1856] |

PT/57/5/2 | Plate, figure 1 showing tangential equation of caustic by Arthur Cayley | [1856] |

PT/57/5/4 | Plate, ray reflected at a circle by Arthur Cayley | [1856] |

PT/57/5/11 | Plate, figure 10 showing curve of caustic with two infinite branches and cusp on y-axis by Arthur Cayley | [1856] |

PT/57/5/5 | Plate, figures 3-4 showing caustics and refracting circles by Arthur Cayley | [1856] |

PT/57/5/6 | Plate, figure 5 showing caustic and refracting circle by Arthur Cayley | [1856] |

PT/57/5/1 | Manuscript, 'A memoir upon caustics' by A [Arthur] Cayley | [1856] |

PT/57/5/8 | Plate, figure 7 showing curve of caustic divided into unequal portions by reflecting circle by Arthur Cayley | [1856] |

PT/57/5/7 | Plate, figure 6 showing curve of caustic completely within reflecting circle by Arthur Cayley | [1856] |

PT/57/5/9 | Plate, figure 8 showing curve of caustic with single cusp on x-axis by Arthur Cayley | [1856] |

PT/57/5/14 | Plate, figure 13 showing curve of caustic with cusp on reflecting circle by Arthur Cayley | [1856] |

PT/57/5/13 | Plate, figure 12 showing curve of caustic with cusp at infinity on x-axis by Arthur Cayley | [1856] |

PT/57/5/17 | Plate, figure 16 showing curve of caustic with large outer circle by Arthur Cayley | [1856] |

PT/57/5/12 | Plate, figure 11 showing curve of caustic with two infinite branches and cusp on y-axis by Arthur Cayley | [1856] |

PT/57/5/15 | Plate, figure 14 showing curve of caustic made of two circles by Arthur Cayley | [1856] |

PT/57/5/16 | Plate, figure 15 showing curve of caustic with interior circle diminished to conjugate point by Arthur Cayley | [1856] |

PT/57/5 | Paper, 'A memoir upon caustics' by A [Arthur] Cayley | [1856] |

PT/58/6/2 | Plate, diagram showing theorems on conjugate poles of a cubic by Arthur Cayley | [1856] |

PT/58/9 | Paper, 'A memoir on the symmetric functions of the roots of an equation' by A [Arthur] Cayley | [1856] |

PT/58/6/1 | Manuscript, 'A memoir on curves of the third order' by A [Arthur] Cayley | [1856] |

RR/3/21 | Referee's report by Arthur Cayley, on a paper 'On the comparison of transcendents with certain applications to the theory of definite integrals' by George Boole | 2 June 1857 |

PT/63/11 | Paper, 'On the porism of the in-and-circumscribed polygon' by A [Arthur] Cayley | [1861] |

RR/4/38 | Referee's report by William Fishburn Donkin on a paper 'On the equation of differences for an equation of any order, and in particular for the equations of the orders two, three, four, and five' by Arthur Cayley | 16 May 1860 |

PT/60/6 | Paper, 'On the equation of differences for an equation of any order and in particular for the equations of the orders two three four and five' by A [Arthur] Cayley | [1860] |

PT/63/16 | Paper, 'On the method of symmetric products and on certain circular functions connected with that method' by Rev Robert Harley | 1 September 1860 |

RR/4/185 | Referee's report by Arthur Cayley, on a paper 'On a new method of approximation applicable to elliptic and ultra-elliptic functions' by Charles Watkins Merrifield | 27 July 1860 |

PT/60/14 | Paper, 'On quaternary cubics' by Rev George Salmon | [1860] |

PT/61/3 | Note, from 'On the formulæ investigated by Dr Brinkley for the general term in the development of Lagrange's expression for the summation of series and for successive integrations' by A [Arthur] Cayley | [1860] |

RR/4/200 | Referee's report by Arthur Cayley, on a paper 'On Fermat's theorem of the polygonal numbers' by Frederick Pollock | 23 July 1861 |

RR/4/48 | Referee's report by George Boole, on two papers 'On an extension of Arbogast’s method of derivations' and 'On the equation for the product of the differences of all but one of the roots of a given equation' by Arthur Cayley | 25 March 1861 |

RR/4/49 | Referee's report by William Spottiswoode, on two papers 'On an extension of Arbogast’s method of derivations' and 'On the equation for the product of the differences of all but one of the roots of a given equation' by Arthur Cayley | 7 February 1861 |

PT/63/3 | Paper, 'On the equation for the product of the differences of all but one of the roots of a given equation' by A [Arthur] Cayley | [1860] |

PT/63/5 | Paper, 'On the calculus of symbols, with applications to the theory of differential equations' by W H L [William Henry Leighton] Russell | [1860] |

RR/4/45 | Referee's report by Philip Kelland, on a paper 'On the porism of the in-and-circumscribed polygon' by Arthur Cayley | 27 May 1861 |

PT/63/13 | Paper, 'On a new auxiliary equation in the theory of equations of the fifth order' by A [Arthur] Cayley | [1861] |

PT/63/14 | Paper, 'A seventh memoir on quantics' by A [Arthur] Cayley | [1861] |

PT/63/17 | Paper, 'On the double tangents of a curve of the fourth order' by A [Arthur] Cayley | [1861] |

RR/4/249 | Referee's report by Arthur Cayley, on a paper 'On the calculus of symbols' by William Spottiswoode | 17 February 1862 |

PT/64/11 | Paper, 'On the calculus of symbols (second memoir)' by W H L [William Henry Leighton] Russell | [1862] |

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 |

PT/64/12 | Paper, 'On the calculus of functions' by W H L [William Henry Leighton] Russell | [1861] |

RR/4/186 | Referee's report by Arthur Cayley, on a paper 'On a new method of approximation applicable to elliptic and ultra-elliptic functions - Second memoir' by Charles Watkins Merrifield | 7 June 1862 |

RR/4/57 | Referee's report by Arthur Cayley, on a paper 'On the differential coefficients and determinants of lines, and their application to analytical mechanics' by A Cohen | 17 June 1862 |

PT/66/6 | Paper, 'On the analytical theory of the conic' by A [Arthur] Cayley | [1862] |

RR/4/183 | Referee's report by Arthur Cayley, on a paper 'On the comparison of hyperbolic arcs' by Charles Watkins Merrifield | 4 May 1859 |

RR/5/45 | Referee's report by Thomas Archer Hirst, on a paper 'On the sextactic points of a plane curve' by Arthur Cayley | 8 February 1865 |

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/5/46 | 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 |

PT/69/11 | Paper, 'On the calculus of symbols - third memoir' by W H L [William Henry Leighton] Russell | [1863] |

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/5/269 | 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/5/24 | Referee's report by Arthur Cayley, on a paper 'On the differential equations which determine the form of the roots of algebraic equations' by George Boole | 29 June 1864 |

RR/5/187 | Referee's report by Arthur Cayley, on a paper 'On a new geometry of space' by Julius Plücker | 9 March 1865 |

MC/6/201 | Letter from A [Arthur] Cayley, 2 Stone Buildings [Lincoln's Inn], to [George Gabriel] Stokes, [Secretary of the Royal Society] | 12 February 1862 |

MC/6/202 | Letter from A C [Arthur Cayley] to [George Gabriel] Stokes, [Secretary of the Royal Society] | 13 February 1862 |

MC/6 | Volume 6 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1859-1863 |

RR/2/49 | Referee's report by Arthur Cayley, on a paper 'On the attraction of ellipsoids considered geometrically' by Matthew Collins | 28 October 1854 |

MC/7 | Volume 7 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1864-1866 |

MC/7/333 | Letter from William Huggins, Upper Tulse Hill, to Dr [William] Sharpey, [Secretary of the Royal Society] | 24 May 1866 |

MC/8/320 | Letter from A [Arthur] Cayley, Cambridge, to [George Gabriel] Stokes, [Secretary of the Royal Society] | 17 February 1869 |

AP/45/2 | On Climant Geometry, as a means of expressing the general relations of points on a plane, realising imaginaries and extending the theories of anharmonnic ratios. | 1863 |

RR/2/41 | Referee's report by George Peacock, on a paper 'Analytical researches connected with Steiner’s extension of Malfatti’s problem' by Arthur Cayley | 21 June 1852 |

RR/3/55 | Referee's report by George Boole, on three papers 'A memoir on the theory of matrices'; 'A memoir on the automorphic linar transformation of a bipartite quadric function'; 'On certain formulae for differentiation' by Arthur Cayley | 29 March 1858 |

RR/3/57 | Referee's report by William Fishburn Donkin, on three papers 'A memoir on the theory of matrices'; 'A memoir on the automorphic linear transformation of a bipartite quadric function'; 'On certain forumlae for diferentiation' by Arthur Cayley | 12 April 1858 |

RR/3/58 | Referee's report by William Spottiswoode, on four papers 'Fourth and fifth memoirs on quantics'; 'On the tangential of a cubic'; 'On the surface which is the envelope of planes through the points of an ellipsoid at right angles to the radius vectors from the centre' by Arthur Cayley | 29 April 1858 |

MC/8/456 | Letter from A [Arthur] Cayley, Cambridge, to [George Gabriel] Stokes, [Secretary of the Royal Society] | 24 November 1869 |

MC/8 | Volume 8 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1867-1869 |

MC/11 | Volume 11 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1877-1879 |

MC/11/122 | Letter from John Casey, 2 Iona Terrace, South Circular Road, Dublin, to the Royal Society | 16 November 1877 |

MC/11/125 | Letter from John Casey, 2 Iona Terrace, South Circular Road, Dublin, to the Royal Society | 26 November 1877 |

AP/41/6/1 | Unpublished manuscript, 'On the theory of internal resistance and of internal friction in fluids: and on the theories of sound and of auscultation' by Robert Moon | 30 March 1858 |

AP/40/20/1 | Unpublished manuscript, 'On the surface which is the envelope of planes through the points of an ellipsoid at right angles to the radius vectors from the centre' by Arthur Cayley | 1858 |

AP/40/20/3 | Unpublished figure, 'Radius sectors' by Arthur Cayley | 22 February 1858 |

AP/40/20/2 | Unpublished figure, ellipsoid by Arthur Cayley | 1858 |

## Collection highlights

Browse the records of some of our collections, which cover all branches of science and date from the 12th century onwards. These include the published works of Fellows of the Royal Society, personal papers of eminent scientists, letters and manuscripts sent to the Society or presented at meetings, and administrative records documenting the Society's activities since our foundation in 1660.