| RefNo | Title | Date |
| EC/1943/17 | Synge, John Lighton: certificate of election to the Royal Society | |
| IM/GA/WS/3592 | Synge, John Lighton | nd |
| RR/34/116 | Referee's report by Alfred Arthur Robb, on a paper 'On the geometry of dynamics' by John Lighton Synge | [March 1926] |
| RR/44/90 | Referee's report by Patrick Playfair Laidlaw, on a paper 'The tightness of the teeth, considered as a problem concerning the equilibrium of a thin incompressible elastic membrane' by John Lighton Synge | June 1932 |
| RR/51/94 | Referee's report by Richard Vynne Southwell, on a paper 'The stability of quadratic velocity-distributions for an inviscid liquid flowing between parallel planes' by John Lighton Synge | [November 1933] |
| RR/51/95 | Referee's report by Leonard Bairstow, on a paper 'The stability of quadratic velocity-distributions for an inviscid liquid flowing between parallel planes' by John Lighton Synge | 18 November 1933 |
| RR/65/256 | Referee's report by Geoffrey Ingram Taylor, on a paper 'On the stability of a viscous liquid between rotating coaxial cylinders' by John Lighton Synge | 13 May 1938 |
| RR/70/233 | Referee's report by Edmund Taylor Whittaker, on a paper 'The method of the hypercircle in function-space for boundary-value problems' by John Lighton Synge | 1947 |
| RR/67/416 | Referee's report by Charles Galton Darwin, on a paper 'On the electromagnetic two-body problem' by John Lighton Synge | July 1940 |
| RR/62/41 | Referee's report by Arthur Stanley Eddington, on a paper 'A criticism of the method of expansion in powers of the gravitational constant in general relativity' by John Lighton Synge | [January 1937] |
| RR/62/40 | Referee's report by Arthur Stanley Eddington, on a paper 'Integral electromagnetic theorems in general relativity' by John Lighton Synge | [June 1936] |
| RR/51/97 | Referee's report by Leonard Bairstow, on a paper 'On the disturbance of the steady flow of an inviscid liquid between parallel planes' by John Lighton Synge | [January 1934] |
| RR/44/88 | Referee's report by Louis Napoleon George Filon, on a paper 'The tightness of the teeth, considered as a problem concerning the equilibrium of a thin incompressible elastic membrane' by John Lighton Synge | February 1932 |
| RR/34/117 | Referee's report by Arthur Stanley Eddington, on a paper 'On the geometry of dynamics' by John Lighton Synge | [February 1926] |
| RR/44/89 | Second referee's report by Louis Napoleon George Filon, on a paper 'The tightness of the teeth, considered as a problem concerning the equilibrium of a thin incompressible elastic membrane' by John Lighton Synge | 25 May 1932 |
| RR/51/96 | Referee's report by Richard Vynne Southwell, on a paper 'On the disturbance of the steady flow of an inviscid liquid between parallel planes' by John Lighton Synge | [March 1934] |
| RR/67/415 | Referee's report by Arthur Stanley Eddington, on a paper 'On the electromagnetic two-body problem' by John Lighton Synge | 1940 |
| RR/73/39 | Letter from Harold Jeffreys, on a paper 'Finite strains in an anisotropic elastic continuum' by James Gardner Oldroyd to D C Martin, Assistant Secretary of the Royal Society | 24 February 1950 |