James MacCullagh

James MacCullagh
James MacCullagh (1809–1847)
Born	1809 Landahaussy, Ireland
Died	24 October 1847
Nationality	Irish
Fields	Physics Mathematics
Known for	Theory of elasticity
Notable awards	Copley Medal (1842)

James MacCullagh (1809 – 24 October 1847) was an Irish mathematician.

MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10. He was a fellow of Trinity College Dublin and a contemporary there of William Rowan Hamilton. In 1835 he was appointed to the Chair of Mathematics at Trinity.

Although he worked mostly on optics, he is also remembered for his work on geometry; his most significant work in optics was published in the mid-to-late 1830s; his most significant work on geometry On surfaces of the second order was published in 1843. He was awarded the Cunningham Medal of the Royal Irish Academy in 1838.

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, entitled "An essay towards a dynamical theory of crystalline reflection and refraction" was presented to the Royal Irish Academy in December 1839. The paper begins by defining what was then a new concept, subsequently, by James Clerk Maxwell in 1870, called the curl of a vector field. MacCullagh first showed that the curl is a covariant vector in the sense that its components are transformed in the appropriate manner under coordinate rotation. Taking his cue from George Green, he set out to develop a potential function for a dynamical theory for the transmission of light. 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. It was accepted that his radical choice ruled out any hope for a mechanical model for the ethereal medium. Nevertheless, the field equations stemming from this purely gyrostatic medium were shown to be in accord with all known laws, including those of Snell and Augustin-Jean Fresnel.