Arthur had been a champion rower and boxer when a student at Cambridge University before the Great War. He was also a keen climber and in the Lake District in 1905 set a record of 59 miles (95km) of mountain summits and a total vertical ascent of 23,500 feet (7162m) in 22 hours. He later became President of the Fell & Rock Climbing Club.
His reputation and experience led to his appointment as medical officer to the 1922 Everest Expedition: he had been invited to the 1921 expedition but had been unable to leave his surgery. Although older than the other members and traumatised by his war experiences, his expertise proved essential to one of the first sustained high altitude climbing expeditions.
In 1924 he and the other 12 European expedition members received the Olympic medal in alpinism at the Summer Olympic Games.