Orr is the eldest son of Fletcher Blakely Orr of Ballystockart, a unitarian farmer and millowner, and Elizabeth Orr, daughter of David Lowry, farmer, of Ballymacashin, County Down. He attends a local national school, spends two years at an intermediate school in Newtownards, and then attends Methodist College Belfast (MCB). He wins a Royal University of Ireland (RIU) scholarship in mathematics in 1883 and graduates in 1885 from Queen’s College Belfast, a constituent college of the RUI. He then matriculates at St. John’s College, Cambridge, where he is Senior Wrangler in 1888 and comes in first in part two of the Mathematical Tripos in 1889. Two years later he is elected into a fellowship at St. John’s, and the same year is appointed professor of applied mathematics at the Royal College of Science for Ireland in Dublin. When the Royal College is merged with University College Dublin (UCD) in October 1926, he becomes professor of pure and applied mathematics, a position he holds until his retirement in 1933.
Orr’s 1909 publication Notes on Thermodynamics for Students is seen as epitomising his style of teaching, with its emphasis on logical rigour and clear statement of underlying assumptions. Known for his generosity to staff and students who encounter difficulties, he is nonetheless a strict disciplinarian who abhors idleness and valued stoicism. He is elected Fellow of the Royal Society (FRS) in 1909 and is awarded an honorary degree of D.Sc. from Queen’s University Belfast (QUB) in 1919.
In 1892, Orr marries Elizabeth Campbell of Melbourne, Australia, whose father, Samuel Campbell, is from County Down. They live at 19 Pembroke Road, Dublin, and have three daughters. He dies at Douglas, Isle of Man on August 14, 1934, and is interred in Mount Jerome Cemetery, Dublin. He is survived by his two daughters.
(From: “Orr, William McFadden” contributed by Paul Rouse, Dictionary of Irish Biography, http://www.dib.ie)