James MacCullagh was an Irish

Ireland

Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

.

Born in Landahaussy

Landahaussy

Landahaussy or Landahussy is a small village and townland near Plumbridge in County Tyrone, Northern Ireland. It is within the Strabane District Council area....

, near Plumbridge

Plumbridge

Plumbridge is a small village in County Tyrone, Northern Ireland. It is a crossroads village, standing on the banks of the Glenelly River. In the 2001 Census it had a population of 267 people. It lies within the Strabane District Council area....

, County Tyrone

County Tyrone

Historically Tyrone stretched as far north as Lough Foyle, and comprised part of modern day County Londonderry east of the River Foyle. The majority of County Londonderry was carved out of Tyrone between 1610-1620 when that land went to the Guilds of London to set up profit making schemes based on...

, Ireland

Ireland

Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...

, but the family moved to Curly Hill, Strabane

Strabane

Strabane , historically spelt Straban,is a town in west County Tyrone, Northern Ireland. It contains the headquarters of Strabane District Council....

 when James was about 10. He was a fellow of Trinity College Dublin and a contemporary there of William Rowan Hamilton

William Rowan Hamilton

Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...

. Although he worked mostly on optics, he is also remembered for his work on geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

; 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.

In Passages from the Life of a Philosopher, Charles Babbage

Charles Babbage

Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...

 wrote that MacCullagh was "an excellent friend of mine" and discussed the benefits and drawbacks of the analytical engine

Analytical engine

The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine, a design for a mechanical calculator...

 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 Maxwell

James Clerk Maxwell

James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

 in 1870, called the curl

Curl

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl is represented by a vector...

 of a vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

. 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

George Green

George Green was a British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism...

, 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 Fresnel.
At several points, MacCullagh addresses the physical nature of an ethereal medium having such properties. Not surprisingly, he argues against a mechanical interpretation of the ether because he readily admits that no known physical medium could have such a potential function resisting only rotation of its elements. "Concerning the peculiar constitution of the ether, we know nothing and shall suppose nothing, except what is involved in the foregoing assumptions [rectilinear vibrations in a medium of constant density]... Having arrived at the value of [the potential function], we may now take it for the starting point of our theory, and dismiss the assumptions by which we were conducted to it." 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. The notion of the ether as a compressible fluid or similar physical entity was too deeply ingrained in nineteenth century physical thinking, even for decades after the publication of Maxwell's electromagnetic theory in 1864. MacCullagh's ideas were largely abandoned and forgotten until, in 1880, FitzGerald

FitzGerald

The surname FitzGerald is a translation of the French-Norman fils de Gérald, or son of Gerald . Variant spellings include Fitz-Gerald and the modern Fitzgerald. The name can also be used as two separate words Fitz Gerald...

 re-discovered and re-interpreted his findings in the light of Maxwell's work.

MacCullagh died in Dublin at his own hand, perhaps depressed by what he saw as the decline of his mathematical powers.

In May 2009, an Ulster History Circle plaque was unveiled at his family tomb at St Patrick's Church in Upper badoney. The plaque was part of events organised by the Glenelly Historical Society to mark his life.

External links

• James MacCullagh's Collected works at the Internet Archive
  Internet Archive
  The Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...