... under the martial regime of Chesney, who was at that time President, Greenhill's independent spirit was ill at ease.

Greenhill applied this theory to give an account of the steadiness of flight conferred upon an elongated projectile by rifling. He determined the least angular velocity about its axis for which steady motion of a solid of revolution can be stable. ... This practical application of what was regarded as a recondite mathematical theory earned for him much renown at Woolwich.

The chief characteristics of Greenhill's work were a desire for concrete realisation of abstract theories and the direction of investigation to the solution of definite problems. Hence he valued applications of analysis above the analysis itself, and was led to work out minutely the details of multitudes of special cases. He was above all things a problem solver, but, to interest him, a problem had to be a real problem about material things and the ways in which they behave.

There, with his books around him, his tables covered in neat disorder with innumerable scraps of material and apparatus to be used as dynamical models, his walls festooned with every variety of pendulum, simple or compound, contrived from articles purchased below a prescribed limit of cost at the local stores, upon his floor the treasured roll of Turkish carpet from his room of long ago at St John's, and above the mantelpiece the portrait of his beloved teacher, Clerk Maxwell, smiling approval - with all these and the precious memories they recalled, the scholar was content.

... he was keenly interested in antiquities, and had a profound knowledge of the antiquities of London. ... he had a considerable knowledge of music, and was a quite respectable performer on the organ and other instruments. He spoke French rather well, and read German easily. ... he was a sociable recluse, delighting especially in the conversation of people with tastes similar to his own.

There was in his character a sense of humour, kindliness, and light-heartedness, but it was too often rendered bewildering by his eccentricity. It is related that as far back as the seventies he astonished his two professional companions in a walking tour of Surrey by setting out in silk hat and frock coat, his night attire being carried in a cardboard box. His friends knew that in general conversation it was best to avoid asking him a direct question. Inquiries about his health were responded to either by silence or by an expression of annoyance, real or feigned ... To the question of whether he would take tea or coffee his reply was a simple affirmative ...