His nature was eminently practical, and any subject which had a distinctly practical object, and could be advanced by mathematical investigation, possessed interest for him. And his dislike of mere theoretical problems and investigations was proportionately great. He was continually at war with some of the resident Cambridge mathematicians on this subject. Year after year he criticised the Senate House Papers and the Smith's Prize Papers question by question very severely: and conducted an interesting and acrimonious private correspondence with Professor Cayley on the same subject. His great mathematical powers and his command of mathematics are sufficiently evidenced by the numerous mathematical treatises of the highest order which he published, a list of which is appended to this biography. But a very important feature of his investigations was the thoroughness of them. He was never satisfied with leaving a result as a barren mathematical expression. He would reduce it, if possible, to a practical and numerical form, at any cost of labour: and would use any approximations which would conduce to this result, rather than leave the result in an unfruitful condition. He never shirked arithmetical work: the longest and most laborious reductions had no terrors for him, and he was remarkably skilful with the various mathematical expedients for shortening and facilitating arithmetical work of a complex character. This power of handling arithmetic was of great value to him in the Observatory reductions and in the Observatory work generally. He regarded it as a duty to finish off his work, whatever it was, and the writer well remembers his comment on the mathematics of one of his old friends, to the effect that "he was too fond of leaving a result in the form of three complex equations with three unknown quantities." To one who had known, in some degree, of the enormous quantity of arithmetical work which he had turned out, and the unsparing manner in which he had devoted himself to it, there was something very pathetic in his discovery, towards the close of his long life, "that the figures would not add up."