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."

His energy and business capacity were remarkable. He was made for work
and could not long be happy without it. Whatever subject he was
engaged upon, he kept his object clearly in view, and made straight
for it, aiming far more at clearness and directness than at elegance
of periods or symmetry of arrangement. He wrote his letters with great