| Reference number | Title | Date |
| EC/1841/03 | Melvill, Sir James Cosmo: certificate of election to the Royal Society | |
| MS/710/74 | Letter from James Cosmo Melvill, East India House, to Robert Were Fox | 2 November 1846 |
| AP/27/6/1 | Unpublished letter, 'An account of observations of the total eclipse of the Sun on the 21 December 1843' from J O E Ludlow to Steele | 10 January 1844 |
| MC/4/181 | Letter from James [Cosmo] Melvill, East India House, to the Marquis of Northampton, [President of the Royal Society] | 6 August 1847 |
| AP/27/6 | Unpublished paper, 'An account of observations of the total eclipse of the Sun on the 21 December 1843' by J O E Ludlow | 1844 |
| MS/426/375 | Copy letter from S H [Samuel Hunter] Christie, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 14 May 1849 |
| MC/4/235 | Letter from James [Cosmo] Melvill, East India House, to Dr [Peter Mark] Roget, [Secretary of the Royal Society] | 16 May 1848 |
| MS/426/454 | Copy letter from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 15 January 1852 |
| MS/426/664 | Copy letter from W [William] Sharpey, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 16 April 1859 |
| MC/5/159 | Letter from James C [Cosmo] Melvill, East India House, to Samuel H [Hunter] Christie, [Secretary of the Royal Society] | 30 March 1854 |
| MC/4/309 | Letter from James [Cosmo] Melvill, East India House, to Thomas Bell, [Secretary of the Royal Society] | 10 December 1849 |
| AP/27/6/3 | Unpublished letter, regarding 'An account of observations of the total eclipse of the Sun on the 21 December 1843' from James Cosmo Melvill to Peter Mark Roget | 19 July 1844 |
| MC/4/24 | Letter from James [Cosmo] Melvill, East India House, to the Marquis of Northampton, [President of the Royal Society] | 16 May 1844 |
| MC/3 | Volume 3 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1839-1843 |
| MC/3/230 | Letter from James [Cosmo] Melvill, East India House, to the Marquis of Northampton, President of the Royal Society | 25 June 1842 |
| MC/3/191 | Draft letter from the Royal Society to James Cosmo Melvill, Bombay Observatory | 15 October 1841 |
| MC/3/246 | Letter from James [Cosmo] Melvill, East India House, to Sir John William Lubbock, [Treasurer of the Royal Society] | 5 November 1842 |
| MC/4/291 | Letter from James [Cosmo] Melvill, East India House, to Samuel [Hunter] Christie, [Secretary of the Royal Society] | 27 June 1849 |
| MC/6/20 | Letter from J [James] Cosmo Melvill, India Office, to W [William] Sharpey, [Secretary of the Royal Society] | 5 April 1859 |
| MC/5/62 | Letter from James C [Cosmo] Melvill, East India House, to S H [Samuel Hunter] Christie, [Secretary of the Royal Society] | 19 November 1852 |
| MC/4/244 | Letter from James [Cosmo] Melvill, East India House, to the Marquis of Northampton, [President of the Royal Society] | 29 June 1848 |
| MS/426/380 | Copy letter from S H [Samuel Hunter] Christie, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 28 May 1849 |
| MS/426/392 | Copy letter from Thos [Thomas] Bell, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 23 October 1849 |
| MS/426/394 | Copy letter from Thos [Thomas] Bell, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 8 October 1849 |
| MS/426/439 | Copy letter from S H [Samuel Hunter] Christie, Secretary of the Royal Society; to J C [James Cosmo] Melvill | 30 November 1850 |
| MC/4/363 | Letter from James C [Cosmo] Melvill, East India House, to Samuel H [Hunter] Christie | 14 November 1850 |
| MS/426/452 | Copy letter from S H [Samuel Hunter] Christie, Secretary of the Royal Society; to J C [James Cosmo] Melvill Esq | 28 June 1851 |
| MC/5/25 | Letter from James [C] Melvill, East India House, to Samuel H [Hunter] Christie, [Secretary of the Royal Society] | 15 November 1851 |
| MC/4 | Volume 4 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1844-1850 |
| MS/426/485 | Copy letter from S H [Samuel Hunter] Christie, Secretary of the Royal Society; to J C [James Cosmo] Melvill, Esq | 29 April 1853 |
| MC/5/105 | Letter from James C [Cosmo] Melvill, East India House, to S [Samuel] Hunter Christie, [Secretary of the Royal Society] | 18 May 1853 |
| MC/5/130 | Letter from James C [Cosmo] Melvill, East India House, to S H [Samuel Hunter] Christie, [Secretary of the Royal Society] | 1 December 1853 |
| MS/426/515 | Copy letter from C R [Charles Richard] Weld, the Assistant Secretary of the Royal Society; to Sir J C [James Cosmo] Melvill | 5 May 1854 |
| MC/5 | Volume 5 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1851-1858 |
| MC/6/27 | Letter from J [James] Cosmo Melvill, India Office, to C R [Charles Richard] Weld, [Assistant Secretary of the Royal Society] | 8 June 1859 |
| MC/6 | Volume 6 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1859-1863 |