MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10.
[4] He was an inspiring teacher and taught notable scholars, including Samuel Haughton, Andrew Searle Hart, John Kells Ingram and George Salmon.
[2] In Passages from the Life of a Philosopher, Charles Babbage wrote that MacCullagh was "an excellent friend of mine" and discussed the benefits and drawbacks of the analytical engine with him.
MacCullagh's most important paper on optics, An essay towards a dynamical theory of crystalline reflection and refraction, was presented to the Royal Irish Academy in December 1839.
MacCullagh found that a conventional potential function proportional to the squared norm of the displacement field was incompatible with known properties of light waves.
In order to support only transverse waves, he found that the potential function must be proportional to the squared norm of the curl of the displacement field.
Not surprisingly, he argues against a mechanical interpretation of the luminiferous aether because he readily admits that no known physical medium could have such a potential function resisting only the rotation of its elements.
Despite the success of the theory, physicists and mathematicians were not receptive to the idea of reducing physics to a set of abstract field equations divorced from a mechanical model.
MacCullagh's ideas were largely abandoned and forgotten until 1880, when George Francis FitzGerald re-discovered and re-interpreted his findings in the light of Maxwell's work.