It was at Cambridge that he first showed an interest in computation in general, and in Bessel and the allied functions in particular. From then until his death he developed methods of computing these functions, and in the Philosophical Magazine and in the British Association Mathematical Tables he tabulated Neumann functions, sines and cosines in radian measure (required for the rapid computation of transcendental functions), the Lommel-Weber function and the confluent hypergeometric functions. Astronomers in particular are indebted to him, for we have it on the authority of Dr Comrie that the British Association Tables of Emden's Functions were calculated by methods suggested by Airey. Indeed, from 1911 he was an active member of the British Association Mathematical Tables Committee, in addition to serving as an editor of the Philosophical Magazine.
It is difficult to realise that during this period of high scientific productivity and selfless advisory labour Airey was the first headmaster of Morley Grammar School (1906 to 1912), the Principal of the West Ham Technical College, and from 1919 until his retirement in 1933 Principal of the Leeds City Training College. In each of these places he left his mark, and in an Address presented to him on his retirement in 1933 we read:-
Not only by your own achievements, but in your own addresses to us, you have held up the torch of learning-learning which can only be won by persistent and earnest effort.
Serene in calm and storm, you have at all times steered a straight course, your actions characterized by sincerity of purpose and a love of what is right.
You will live in our memories as a Principal and a friend whose words were few, and whose happy and kindly disposition shone out so brightly that even your reproofs were tinged with humour. Not least we shall cherish your memory because you showed us a religion based on simple faith and a reverential search for truth.
Airey was a D.Sc. of London (1915), and an Sc.D. of Cambridge (1926). He was elected a Fellow of the Society on 1931 June 12, and was also a Fellow of the Physical Society and the Edinburgh Mathematical Society. He died on 1937 September 16, being survived by his wife and a daughter.