In total Ivory presented 15 papers to the Royal Society and received 3 medals.
His first paper was in 1809, and he gave 3 more before he was elected a member in 1815. His papers were generally regarded as elucidating and innovative although he is considered to have unfairly criticised Laplace over a portion of Mecanique Celeste. His papers continued reasonably regularly until his last in 1839, at the age of 74.
The medals Ivory received were the Copley, in 1814, for his contributions to the Philosophical Transactions, and two Royal Medals, in 1826 and 1839, for papers on astronomical refractions (nos. 6 and 14 in the list of his papers to the Royal Society). The latter paper was the Bakerian Lecture for 1838.
All these papers can be found in the Philosophical Transactions of the Royal Society of London.
- On the Attractions of Homogenous Ellipsoids. (Phil. Trans. 1809, p.345)
- On the Grounds of the Method which Laplace has given in the second chapter of the third book of his Mecanique Celeste for computing the Attractions of spheroids of every description. (ibid. 1812, p.1)
- On the Attractions of an extensive class of Spheroids. (ibid. 1812, p.46)
- A New Method of deducing a first Approximation to the Orbit of a Comet from three Geocentric Observations. (ibid. 1814, p.121) 5 On the Expansion in a series of the Attraction of a Spheroid. (ibid. 1822, p.99)
- On the Astronomical Refractions. (ibid. 1823, p.409)
- On the figure requisite to maintain the Equilibrium of a Homogenous Fluid Mass that revolves upon an axis.(ibid. 1824, p.85)
- On the Equilibrium of Fluids, and the Figure of a Homogenous Planet in Fluid State. ibid. 1831, p.109)
- On the Theory of the Elliptic Transcendents.(ibid. 1831, p.349)
- On the Theory of the Perturbations of the Planets.(ibid. 1832, p.195)
- On the Development of the Disturbing Function, upon which depend the inequalities of the Motions of the Planets, caused by their Mutual Attraction.(ibid. 1833, p.559)
- On the Equilibrium of a Mass of Homogenous Fluid at liberty.(ibid. 1834, p.491)
- Of such Ellipsoids consisting of homogenous matter as are capable of having the resultant of the attraction of the mass upon a particle in the surface, and a centrifugal force caused by revolving about one of the axes, made perpendicular to the surface.(ibid. 1838, p.57)
- On the Theory of Astronomical Refractions.(ibid. 1838, p.169)
- On the Condition of Equilibrium of an Incompressible Fluid, the particles of which are acted upon by Accelerating Forces.(ibid. 1839, p.243)