| Reference number | Title | Date |
| RR/3/48 | Referee's report by Phillip Kelland, on an unnamed paper by Arthur Cayley | 1856 |
| MS/426/331 | Note of papers sent from [the Secretaries of] the Royal Society; to various Fellows | June 1848 |
| MS/426/369 | Note of papers sent from [the Secretaries of] the Royal Society; to various Fellows | 9 February 1849 |
| MS/426/469 | Note of letters from [the Secretaries of] the Royal Society; to various Fellows | 9 June 1852 |
| RR/4/122 | Referee's report by Philip Kelland, on a paper 'On the method of symmetric products, and on certain circular functions connected with that method' by Robert Harley | 23 March 1861 |
| 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 |
| 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/4/228 | Referee's report by Philip Kelland, on a paper 'On the calculus of symbols, with applications to the theory of differential equations' by William Henry Leighton Russell | 19 March 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/3/53 | Referee's report by Philip Kelland, on five unnamed papers by Arthur Cayley | 23 February 1857 |
| RR/3/54 | Referee's report by Philip Kelland, on a paper 'A memoir upon caustics' by Arthur Cayley | 23 July 1857 |
| RR/1/154 | Referee's report by Philip Kelland, on a paper 'On the total reflection from the surface of any crystal' by Michael Macann | 29 June 1848 |
| EC/1838/33 | Kelland, Philip: certificate of election to the Royal Society | 6 December 1838 |
| MS/426/543 | Note of letters from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to various Fellows | 15 May 1855 |
| 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/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 |
| HS/11/77 | Letter, from P[hilip] Kelland to Sir John Herschel, dated at Edinburgh | 18 March 1859 |
| MS/426/516 | Note of a letter from [the Secretaries of] the Royal Society; to various Fellows | 19 May 1854 |