| RefNo | Title | Date |
| EL/P2/6 | Letter, from Monsieur [Jean Louis] Petit to John Machin | 19 April 1730 |
| L&P/1/161 | Letter, 'The processus ravianus' from Robert Nesbitt to John Machin | 17 February 1742 |
| EL/H3/135 | Letter, from Thomas Haselden to John Machin, dated at Wapping | 27 August 1728 |
| EL/H4/30 | Letter, from John Hadley to John Machin | 21 May 1736 |
| MM/4/61 | Letter from Stephen Hall, Clapton, to John Machin | 24 January 1729 |
| MM/20/11 | Letter from John Machin to Cromwell Mortimer, Secretary, Royal Society | 21 March 1742/3 |
| MM/20/12 | Letter from John Machin to Cromwell Mortimer, Secretary, Royal Society | 17 November 1743 |
| RBO/16/36 | 'An account of a new Instrument for finding the Latitude etc mechanically and by inspection only' by Andrew Reid in a letter to John Machin | 1731 |
| LBO/23/50 | Copy letter from Dr Bevis, London, to John Machin | 23 February 1736/1737 |
| EL/H3/97 | Letter, from Alex Harrison to the Secretary of the Royal Society, dated at North Petherton near Bridgewater in Somerset | 17 December 1720 |
| LBO/21/92 | Copy letter from Mr Kingsley, York, to John Machin | 20 March 1734/1735 |
| LBO/20/80 | Copy letter from Monsieur de l'Isle, St Petersburg, to John Machin | 17 February 1733 |
| LBO/24/11 | Copy letter from Albert de Korff, President of the Imperial Academy at Petersbourg to John Machin | 15 October 1736 |
| LBO/21/54 | Copy letter from Pietro Michelotti, Venice, to John Machin | 9 September 1733 |
| EL/K/23 | Letter, from John Keill to John Machin, dated at Oxford | 21 May 1720 |
| L&P/1/67 | Letter, 'Of the comet' from Robert Simson to John Machin | 1 March 1742 |
| L&P/1/292/1 | Letter, 'Of an omphalocele' from H M Taube to John Machin | 1744 |
| L&P/1/258 | Letter, 'An improvement in the operation of tapping' from Christopher Warwick to John Machin | 1743 |
| L&P/1/293 | Letter, 'Observations concerning the planet Mercury' from John Bevis to John Machin | 1744 |
| L&P/1/251 | Letter, 'As to the sham feathered egg shown on Thursday last' from Thomas Stack to John Machin | 16 January 1743 |
| L&P/1/122 | Letter, 'A note relating to vivaprous fish shewed by Mr Ames' from Peter Collinson to John Machin | 1742 |
| L&P/1/172 | Letter, 'On the sex of the same child' from James Parsons to John Machin | 27 February 1742 |
| CLP/4ii/22 | Paper, 'Aurora borealis observed at Broxmouth, the Duke of Roxburge's seat in Scotland' by Mr [John] Machin | 1734 |
| CLP/14ii/37/2 | Engraving, skin condition by John Machin | [1731] |
| CLP/8ii/57 | Letter, regarding a comet observed at Greenwich [London] from John Bevis to John Machin | 23 February 1737 |
| CLP/8ii/57/1 | Manuscript, regarding a comet observed at Greenwich [London] from John Bevis to John Machin | 23 February 1737 |
| CLP/8ii/33/1 | Manuscript, regarding an invention to find latitude mechanically from Andrew Reid to John Machin | 1731 |
| CLP/8ii/69 | Letter, regarding the 'obliquity of the ecliptick' from John Machin to unknown recipient | 1733 |
| MS/82 | Correspondence of Dr Brook Taylor, Secretary of the Royal Society | 1712-1717 |
| CLP/10iii/45 | Letter, regarding multiplying grain from J [John] Eames to [John] Machin | 4 March 1729 |
| EL/F2/14 | Letter, from Thomas Farrant to the Secretary, dated at Winchester | 1726 |
| EL/M3/52 | Letter, from Abraham de Moivre to John Machin | January 1736 |
| L&P/1/291 | Letter, 'Of the injection of medicated liquors into the abdomen' from Christopher Warrick to John Machin | 12 May 1774 |
| EL/I2/12 | Letter, from William Jones to John Machin | 1730 |
| EL/M3/51 | Letter, from Colin MacLaurin to John Machin | 15 November 1732 |
| EL/K/38 | Letter, from George Kingsley to John Machin, dated at York | 20 March 1735 |
| EL/M3/32 | Letter, from Pietro Michelotti to John Machin | 1733 |
| L&P/1/147 | Letter, 'Of a double pear of the Carnelian kind' from Samuel Gruwy to John Machin | 20 January 1742 |
| RBO/14/33 | 'A method for finding the Longitude in a Letter from Mr Thomas Haselden to Mr Machin' | 1728 |
| CLP/14ii/37 | Extract, 'Extract from the minutes of the Royal Society March 16 1731 containing an uncommon case of a distemper'd skin' by John Machin | [1731] |
| CLP/14ii/37/1 | Extract, 'Extract from the minutes of the Royal Society March 16 1731 containing an uncommon case of a distemper'd skin' by John Machin | [1731] |
| CLP/8ii/33 | Letter, regarding an invention to find latitude mechanically from Andrew Reid to John Machin | 1731 |
| EL/M3/51a | Letter, from Andrew Mitchell to John Machin, dated at London | 18 February 1737 |
| EL/M2/2 | Letter, from Ferdinand Marsigli to the Secretary of the Royal Society | 24 December 1725 |
| EL/M2/63 | Letter, from Pietro Michelotti to John Machin, dated at Venice | 5 September 1733 |
| CLP/16/45/2 | Figures, Roman torture methods by Joanne Ward | 1729 |
| CLP/16/45 | Paper, 'De equuleo' [on a Roman torture method involving a horse] by Joanne Ward | 1729 |
| CLP/16/45/1 | Manuscript, 'De equuleo' [on a Roman torture method involving a horse] by Joanne Ward | 1729 |
| EL/F2/11 | Letter, from Thomas Forster to John Machin, dated at London | 12 May 1722 |
| EL/W3/121 | Letter, from John Woolhouse to William Rutty, dated at Paris | 7 May 1729 |
| EL/W3/122 | Letter, from John Woolhouse to William Rutty | nd |
| EL/K/41 | Translation of a letter, from [Johann Albrecht von] de Korff to John Machin, dated at St Petersburg | 1736 |