Mr Lidstone's outstanding contributions to actuarial science were recognized by the Actuarial Society of America at its annual meeting in 1910 when he was unanimously elected a Fellow of the Society. On moving to Edinburgh he was elected a Fellow of the Faculty of Actuaries, which he served with great distinction in many capacities; he was its President from 1924 to 1926.
It is not possible in a short memoir to describe Mr Lidstone's work and achievements in any detail. Merely to compile a complete list of his writings would be a formidable task. They began when he was a student with a letter to the Journal of the Institute of Actuaries suggesting an improvement in the textbook solution of an actuarial problem. A paper which brought him fame was written at the early age of 27. At that time the growing volume of endowment insurance was becoming a serious embarrassment to life offices at their periodical valuations. Mr Lidstone suggested an ingenious approximate method whereby the work could be reduced to a mere fraction of that previously involved and, what is more, an approximation so close as to be almost exact. The method is still used by most British life offices.
Mr Lidstone's deep learning and wide knowledge were not confined to the actuarial field. He had a keen interest in law and his purely mathematical attainments were considerable. He had the distinction of having his name given to a series, now known in mathematical analysis as the Lidstone series, by which a function is expressed in terms of its values at two points and the corresponding derivatives of even order. The series is itself a particular case of very wide generalizations of the Everett interpolation formulae which he published in 1929. His eminence was recognized in 1925 when the University of Edinburgh conferred upon him the Honorary Degree of LL.D.
In 1929, on medical advice, he retired from the position of Manager and Actuary of the Scottish Widows' Fund and shortly afterwards was elected a Director. In the same year the Institute and Faculty jointly presented him with a gold medal in recognition of "his unique services to actuarial science" - a signal honor.
In his later years he became completely blind - a severe trial for one who had for so long followed every detail of new work in actuarial subjects - but he bore his affliction with great fortitude and in a remarkable way succeeded in keeping abreast of developments in the profession he had adorned.
It is perhaps appropriate to conclude by saying of Lidstone, as he said of another eminent actuary, Sir George Francis Hardy, who had been his tutor and with whom he had much in common: "He will always remain a brilliant example."