He was educated at Eton, where he did not row, but played in the Eton cricket eleven in 1845.
He was Number. In 1850, he became a Fellow of Brasenose College, Oxford. In 1851 he rowed again for Brasenose in the Ladies" Challenge Plate, Stewards" Challenge Cup, and Visitors Challenge Cup. He went Head of the River at Oxford in 1852.
He had also become known as a fine skater and one of the best Alpine climbers of the day.
In 1853, Hornby went to Durham University as Principal of Bishop Cosin"s Hall until 1864 when he returned to Brasenose as classical lecturer. Students long after recalled with pleasure the animation of his Virgil lectures and his excellent way of teaching Latin prose.
He was also made Senior Proctor. In 1865 Hornby was the first to ascend the northwest ridge of the Silberhorn.
In 1867, he was appointed Second Master of Winchester College, which was seen as a stepping stone to the headmastership of Eton, which had become vacant.
He remained at Winchester little more than a year, and was then appointed Headmaster of Eton, in succession to Balston. His appointment was made possible by the conclusions of the Northcote Commission which had removed restrictions among educational endowments, among which was the tradition that the Eton headmaster should come from King"s College, Cambridge. With the restrictions gone, Hornby was the first to exercise the increased independent authority of the headmaster.
He "taught Eton the art of self-government" and his sixteen years" Headmastership was very successful.
As he had not been an Eton master, he had to overcome a certain amount of resentment by his good work, sympathetic temper and his pleasant manners. Guy Nickalls, at Eton in the early 1880s, recalled: "In spite of the swishings I got, I liked the headmaster, Hornby, the perfectly mannered and sonorously-voiced old English gentleman.
Handsome, alert, witty, a great athlete in his day, a good judge of wine, and the finest after-dinner speaker I ever listened to, with a charm of manner I have never forgotten." Hornby retired in 1884 to take the post of provost of Eton and was succeeded by another Etonian and Balliol oarsman, Edmond Warre. Hornby had also become a Doctor of Civil Law and a Queen's Chaplain.
As chairman of the Governing Body, he presided over the meetings at the time of Warre"s resignation, when Edward Lyttelton was elected Warre"s successor.
He remained provost until his death in 1909, to be succeeded again by Warre.