| Reference number | Title | Date |
| MM/12/87 | Memorandum by JA Broun on the '4th and 5th heads of inquiry proposed by the Board of Trade' | c.1876 |
| MM/11/186 | Letter from G B Airy, Royal Observatory Greenwich, to J F W Herschel | 24 October 1849 |
| MM/11/184 | Letter from Edward Sabine, Woolwich, to J F W Herschel | 29 September 1846 |
| MM/11/185 | Letter from Humphrey Lloyd, Trinity College Dublin, to J F W Herschel | 20 October 1846 |
| MC/7 | Volume 7 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1864-1866 |
| MM/15/69 | Letter from J A Broun to George Gabriel Stokes | 4 June 1877 |
| MC/5 | Volume 5 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1851-1858 |
| M/140 | Royal Medal | 1878 |
| RR/4/26 | Referee's report by George Biddell Airy, on a paper 'On the bifalar magnetometer' by John Allan Broun | 25 April 1860 |
| RR/4/25 | Referee's report by Humphrey Lloyd, on a paper 'On the bifalar magnetometer' by John Allan Broun | 11 April 1860 |
| RR/4/24 | Referee's report by Edward Sabine, on a paper 'On the bifalar magnetometer' by John Allan Broun | 9 May 1860 |
| RR/7/487 | Referee's report by John Allan Broun, on a paper 'On the variations of the daily range of atmospheric temperature as recorded at the Kew Observatory' by Balfour Stewart | 1876 |
| RR/7/437 | Referee's report by Balfour Stewart, on a paper 'On the variations of the daily mean horizontal force of the earth's magnetism produced by the suns rotation and the moon's synodical and tropical revolutions' by John Allan Broun | 12 January 1876 |
| RR/7/438 | Referee's report by John Couch Adams, on a paper 'On the variations of the daily mean horizontal force of the earth's magnetism produced by the suns rotation and the moon's synodical and tropical revolutions' by John Allan Broun | 1876 |
| RR/7/486 | Letter from John Allan Broun, on a paper 'On the variations of the daily range of atmospheric temperature as recorded at the Kew Observatory' by Balfour Stewart | 30 August 1876 |
| RR/7/481 | Letter from John Allan Broun, on a paper 'A contribution to terrestrial magnetism; being the record of observations of the magnetic inclination, or dip, made during the voyage of H. M. S. ‘Iron Duke’ to China and Japan 1871-75' by Charles Frederick Alexander Shadwell | 31 August 1876 |
| RR/7/482 | Referee's report by John Allan Broun, on a paper 'A contribution to terrestrial magnetism; being the record of observations of the magnetic inclination, or dip, made during the voyage of H. M. S. ‘Iron Duke’ to China and Japan 1871-75' by Charles Frederick Alexander Shadwell | 1876 |
| EC/1853/03 | Broun, John Allan: certificate of election to the Royal Society | |
| NLB/4/389 | Copy letter from Michael Foster, to John Arthur Godley, Under Secretary of State for India, India Office, S.W. | 8 May 1890 |
| RR/8/63 | Referee's report by John Allan Broun, on a paper 'A contribution to terrestrial magnetism; being the record of observations of the magnetic inclination, or dip, made during the voyage of H. M. S. ‘Iron Duke’ to China and Japan, &c., 1871-75' by Charles Frederick Alexander Shadwell | 30 July 1877 |
| MC/5/118 | Letter from John Allan Broun, Trevandrum Observatory, Travancore, India, to the Secretary of the Royal Society | 17 September 1853 |
| MC/7/225 | Letter from John Wilson, Bombay, to Walter White, Assistant Secretary of the Royal Society | 6 June 1865 |