Apart from a printed copy of his LL.D. thesis on the idea of atonement amongst the ancient Hebrews, and a copy of examination questions in mathematics set by him, Duff's papers are almost entirely concerned with his application for the Bradford position in 1877. These comprise letters of recommendation from J. W. Dawson, Alexander Johnson (Vice-Dean of the Faculty of Arts), and two professors at Andover Theological Seminary, as well as copies of a letter from A.M. Fairbairn of Aberdeen, encouraging Duff to apply for the post. There is also a copy of Duff's letter to the secretary of the Congregational College in which he declines an offer of teaching work.