We have reached Jeffery's university education without mentioning mathematics. That is because up to that time mathematics had not played a large role in his life. He took a degree in economics at Acadia University, but while studying for this degree he took two mathematics courses, one in calculus and one in analytic geometry. This may not seem like a particularly good foundation for research in mathematics, but Jeffery had come to love the subject so much that he went to Cornell University to undertake graduate studies. He continued his studies during a year at Harvard and then, in 1924, he was appointed Head of Mathematics at Acadia University. At this point Jeffery had not completed his doctorate so, in 1928, he returned to Cornell University to finish off his work. He obtained his doctorate in 1928 after submitting his dissertation The Uniform Approximation of a Sequence of Integrals and the Sequence of Functions Which Define a Definite Integral Containing a Parameter.
Before he submitted his thesis, Jeffery was publishing papers such as Definite integrals containing a parameter and The Continuity of a Function Defined by a Definite Integral, the latter being in the American Mathematical Monthly. He published a paper based on the results of his thesis in the Annals of Mathematics, then published further papers such as The uniform approximation of a summable function by step functions (1931), Non-absolutely convergent integrals with respect to functions of bounded variation (1932), Relative summability (1932), Sets of k-extent in n-dimensional space (1933), and Derived numbers with respect to functions of bounded variation (1934).
Jeffery remained at Acadia University until 1942, except for one year which he spent as acting as Head of Mathematics at the University of Saskatchewan in 1938. Then in 1942 he moved to Queen's University, Kingston, Ontario when offered the position of Head of Mathematics there replacing John Matheson. The attraction of the move from Acadia to Queen's was undoubtedly the greater research opportunities which he would have in his new position. The Mathematics Department at Queen's was fairly small with seven faculty members when Jeffery became Head. When he retired in 1960 it was a stronger Department with nine faculty members. He had also built up a strong graduate programme and brought undergraduate teaching to a high standard. Queen's University honoured Jeffery's outstanding contribution by naming a new building, built between 1967 and 1969 to house the Department of Mathematics and Statistics, as Jeffery Hall.
An important book which Jeffery published in 1951 was The Theory of Functions of a Real Variable. Haslam-Jones, in a review of the book, writes:-
The author states that his main purpose in this book is to present the contents of chapter VI (The inversion of derivatives) and of chapter VII (Derived numbers and derivatives). The former includes, in addition to standard theorems concerning absolutely continuous functions and the integrals of finite summable derivatives, an interesting discussion of the problem of determining a continuous function from its finite (but not summable) derivative by a denumerable infinity of operations: the chapter is a useful introduction to the Denjoy integral. In chapter VII properties of the non-differentiable functions of Weierstrass and of Besicovitch are established, followed by an exhaustive analysis of the distribution of the derivates and approximate derivates of an arbitrary function of one variable. ...Jeffery was elected a Fellow of the Royal Society of Canada in 1937 and latter served as its President. His presidential address to the Society was Trigonometric series which he gave in 1953 and three years later it was published as a 39 page book by the University of Toronto Press. One of his greatest achievements was to establish the Summer Research Institute of the Canadian Mathematical Society and he directed the Institute each summer from 1950 to 1965. During these years, from 1957 to 1961, he served as President of the Canadian Mathematical Society.
After retiring from Queen's University in 1960 at the age of 71, he returned to Arcadia University where he continued to teach until his 85th year.
As a lecturer his students described him as "slow and deliberate". He was also renowned as being absent minded but, as Robinson states in his obituary of Jeffery :-
Ralph Jeffery's easy-going manner and friendly approach to life made him loved by all who knew him.Jeffery received many honours for his outstanding work in encouraging mathematical research in Canada. He was awarded honorary degrees by Acadia University, Dalhousie University, St Mary's University, Memorial University, McMaster University, Windsor University and Queen's University. The Canadian Mathematical Society honoured him by setting up the Jeffery-Williams Prize to recognize mathematicians who have made outstanding contributions to mathematical research. The first award of the Prize was made in 1968.
In 1956 Nellie Jeffery died. In 1970, when he was 81 years old, Jeffery married Frances Lewis of Bedford. Robinson writes :-
Ralph's wife lives in Bedford, Nova Scotia. Her contributions to his life and accomplishments during the latter years was obvious to all.
Article by: J J O'Connor and E F Robertson