| RefNo | Title | Date |
| MM/15/3 | Letter from Fearon Fallows, Cape Town, to Sir John Barrow | 10 January 1824 |
| EC/1820/06 | Fallows, Fearon: certificate of election to the Royal Society | |
| MC/4/297 | Letter from [George Biddell] Airy, Royal Observatory Greenwich, to Thomas Bell, Secretary of the Royal Society | 14 November 1849 |
| PT/17/15 | Paper, 'A catalogue of nearly all the principal fixed stars between the zenith of Cape Town, Cape of Good Hope and the South Pole reduced to the first of January 1824' by Fearon Fallows | [1824] |
| PT/19/1 | Paper, 'Observations made with the invariable pendulum No 4 (Jones), at the Royal Observatory Cape of Good Hope for the purpose of determining the compression of the earth' by Fearon Fallows | [1830] |
| PT/19/2 | Paper, 'Note by Captain Sabine' by Edward Sabine | [1830] |
| MC/1/352 | Letter from Thomas Henderson, 1 Old Palace Yard, Westminster, [Dr. Peter Mark Roget and John George Children,] Secretaries of the Royal Society | 13 December 1831 |
| MC/1 | Volume 1 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1800-1831 |
| MC/4 | Volume 4 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1844-1850 |
| AP/14/17/2 | Unpublished copy letter, regarding notice of a meteor from Fearon Fallows to the Secretary of the Admiralty [John Wilson Croker] | 9 November 1829 |
| AP/14/17/1 | Unpublished copy letter, regarding notice of a meteor from W [William] Ronald to Fearon Fallows | 20 October 1829 |
| AP/14/17 | Unpublished copy letters, regarding notice of a meteor from W [William] Ronald and Fearon Fallows | October-November 1829 |
| AP/11/8 | Unpublished paper, on differences of longitude by Fearon Fallows | 6 June 1824 |
| MA/2/1 | Tidal tables kept at St. James's Bay, St. Helena, by Fearon Fallows | 1 October 1826-28 February 1827 |
| HS/7/159 | Letter, from Fearon Fallows to Sir John Herschel, dated at Cape Town | 26 June 1822 |
| HS/7/158 | Letter, from Fearon Fallows to Sir John Herschel | 6 June 1822 |
| HS/7/157 | Letter, from Fearon Fallows to Sir John Herschel, dated at Cape Town | 30 May 1822 |
| HS/25/1/17 | Copy letter, from Sir John Herschel to Fearon Fallows, dated at Slough | 9 January 1831 |
| HS/7/156 | Letter, from Fearon Fallows to Sir John Herschel, dated at St. John's College, Cambridge | 19 February 1820 |
| HS/7/161 | Letter, from Fearon Fallows to Sir John Herschel, dated at Cape Town | 16 March 1823 |
| HS/7/160 | Draft letter, from Sir John Herschel to Fearon Fallows, dated at Downing St. | 10 November 1822 |