Mr Arthur, who was the son of a schoolmaster, was born in Fergushill, near Kilwinning, but at an early age moved to Glasgow, where he received his secondary education at Queen's Park Higher Grade School. He then proceeded to the University of Glasgow where he graduated M.A. with First Class Honours in Mathematics and Natural Philosophy in 1915. Thereafter, he went into active service with the Welsh Guards in the First World War and was decorated with the Military Cross. On returning home he joined the staff of Glasgow University and began a lifetime of loyal and devoted service to the University.
During his tenure of office, Mr Arthur lectured to most of the mathematical classes in the University and for many years had a special responsibility for the classes in Mathematics for Engineers. His lectures, which were in the highest tradition of University teaching, displayed a keen sharpness of mind, great clarity of thought and blackboard skill of an unusually high order. He undoubtedly made his mark on successive generations of students. Some of the fruits of his teaching are to be found in a treatise on trigonometry written in collaboration with the late Professor T M MacRobert and published in the late 1930s in four small volumes. Only the first and fourth relate to trigonometry in the ordinary sense of the term; the second and third discuss topics such as infinite series and products which pertain rather to a book on analysis. The fourth and smallest volume is on spherical trigonometry and would make profitable reading for any budding astronomer or geodesist. Mr Arthur was deeply interested in numerical mathematics and in statistics, his interest having been stimulated in the former by his elder colleague Dr John McWhan, who had been a disciple of Runge in Göttingen, and in the latter by Karl Pearson with whom he had worked for a short time. He served as Mitchell Lecturer in Statistics for seventeen years. Actuarial mathematics was another of his interests and he was an authority on the Federated Superannuation Scheme for Universities about which he was often consulted by colleagues in difficulty. After his retiral from the University he spent two and a half years teaching mathematics in Bethany College, West Virginia.
Displaying meticulous care and consummate skill in his own work, Mr Arthur demanded high standards from junior colleagues working under him and also from the young secretaries who began to make their appearance in University departments during his time. Although he treated them with benign firmness, he showed them understanding and consideration, and in return he was highly respected by them.
During the Second World War, Mr Arthur served as an Intelligence Officer on the staff of the District Commissioner for Civil Defence; the staff, which included a number of senior members of the University and persons prominent in the business and professional life of Glasgow, was vested with wide powers to deal with any emergency that might arise.
Mr Arthur was possessed of a Christian faith both simple and profound, and he was a prominent member of the Churches of Christ of whose annual conference he was president in 1958. Altogether, he was a man of fine qualities, and it is comforting to know that all of them, including his mental acumen, were sustained right to the end of his long life. He is survived by his wife and three sons one of whom, Peter, is a Senior Lecturer in Civil Engineering in Glasgow University.