| RefNo | Title | Date |
| EC/1896/04 | Downing, Arthur Matthew Weld: certificate of election to the Royal Society | |
| NLB/4/681 | Copy letter from Herbert Rix, to Arthur Matthew Weld Downing, Royal Observatory Greenwich | 22 September 1890 |
| NLB/6/172 | Copy letter from Herbert Rix, to Arthur Matthew Weld Downing | 16 March 1892 |
| NLB/6/254 | Copy letter from Herbert Rix, to Arthur Matthew Weld Downing, Nautical Almanac Office, 3 Verulam Buildings, Gray's Inn, W.C. | 31 March 1892 |
| NLB/5/645 | Copy letter from Michael Foster, to the Secretary, the Admiralty, S.W. | 31 July 1891 |
| NLB/34/103 | Copy letter from Theodore E James, to Dr [Arthur Matthew Weld] Downing, Fellow of the Royal Society, 3 Granville Park, Blackheath, S.E. | [November 1906] |
| NLB/20/535 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Welding Downing, Fellow of the Royal Society, Nautical Almanac Office, 3 Verulam Buildings, Gray's Inn, W.C. | 16 May 1900 |
| NLB/18/525 | Copy letter from Robert William Frederick Harrison, to Dr Downing, Fellow of the Royal Society | 27 March 1899 |
| NLB/22/441 | Copy letter from Robert William Frederick Harrison, to Dr [Arthur Matthew Weld] Downing, Fellow of the Royal Society | 15 May 1901 |
| NLB/20/699 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society, Nautical Almanac Office, 3 Verulam Buildings, Gray's Inn, W.C. | 19 June 1900 |
| NLB/22/31 | Copy letter from Robert William Frederick Harrison, to Dr [Arthur Matthew Weld] Downing, Fellow of the Royal Society | 15 February 1901 |
| NLB/29/400 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 6 October 1904 |
| NLB/21/566 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 10 December 1900 |
| NLB/21/455 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 20 November 1900 |
| NLB/22/648 | Copy letter from Robert William Frederick Harrison, to Dr [Arthur Matthew Weld] Downing, Fellow of the Royal Society, Nautical Almanac Office, 3 Verulam Buildings, Gray's Inn, W.C. | 20 June 1901 |
| NLB/26/810 | Copy letter from Robert William Frederick Harrison to, Dr Arthur Mathew Weld Downing, Fellow of the Royal Society, Nautical Almanac Office | 5 June 1903 |
| NLB/26/307 | Copy letter from Robert William Frederick Harrison to, Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 27 February 1903 |
| NLB/27/707 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 17 November 1903 |
| NLB/29/808 | Copy letter from Robert William Frederick Harrison, to Dr [Arthur Matthew Weld] Downing, Fellow of the Royal Society | 13 December 1904 |
| NLB/30/75 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 24 January 1905 |
| NLB/33/198 | Copy letter from Robert William Frederick Harrison, to Arthur Matthew Weld Downing, Fellow of the Royal Society | 13 July 1906 |
| NLB/33/136 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 3 July 1906 |
| NLB/33/154 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society, 3 Granville Park, S.E. | 5 July 1906 |
| NLB/34/278 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 20 December 1906 |
| NLB/34/292 | Copy letter from Robert William Frederick Harrison, to Dr Arthur Matthew Weld Downing, Fellow of the Royal Society | 21 December 1906 |
| MC/15/210 | Letter from Evan Macgregor, Admiralty, to the Secretary of the Royal Society, Burlington House | 13 October 1892 |
| MC/15/71 | Letter from [Arthur Matthew Weld] Downing, Royal Astronomical Society, Burlington House, London, to the Secretary of the Royal Society | 15 April 1890 |
| MC/15/72 | Application for a grant from [Arthur Matthew Weld] Downing, Royal Astronomical Society | 15 April 1890 |
| NLB/18/453 | Copy letter from Robert William Frederick Harrison, to Dr A M W Downing, Fellow of the Royal Society, Nautical Almanac Office, [3 Verulam Buildings, Gray's Inn, W.C.] | 13 March 1899 |
| NLB/18/501 | Copy letter from Robert William Frederick Harrison, to Dr A M W Downing, Fellow of the Royal Society, Nautical Almanac Office, 3 Verulum Buildings, Gray's Inn, W.C. | 22 March 1899 |
| MC/15 | Volume 15 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1889-1892 |
| MC/19/244 | Letter from [Arthur Matthew Weld] Downing, Nautical Almanac Office, 3 Verulam Buildings, grays Inn, to [Robert William Frederick] Harrison | 12 December 1904 |
| MC/17 | Volume 17 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1897-1899 |
| MC/19 | Volume 19 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1904 |