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."

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 ease and rapidity: and having written them he very rarely had occasion to re-write them, though he often added insertions and interlineations, even in the most important official letters. Without this it would have been impossible for him to have turned out the enormous quantity of correspondence that he did. He never dictated letters, and only availed himself of clerical assistance in matters of the most ordinary routine. In his excursions, as in his work, he was always energetic, and could not endure inaction. Whatever there was of interest in the places that he visited he examined thoroughly and without delay, and then passed on. And he thus accomplished a great deal in a short vacation. His letters written to his wife, while he was on his excursions, are very numerous and characteristic, and afford ample proofs of his incessant energy and activity both of body and mind. They are not brilliantly written, for it was not in his nature to write for effect, and he would never give himself the trouble to study the composition of his letters, but they are straight-forward, clear, and concise, and he was never at a loss for suitable language to express his ideas. He had a wonderful capacity for enjoyment: the subjects that chiefly interested him were scenery, architecture, and antiquities, but everything novel or curious had an interest for him. He made several journeys to the Continent, but by far the greater number of his excursions were made in England and Scotland, and there were few parts of the country which he had not visited. He was very fond of the Lake District of Cumberland, and visited it very frequently, and each time that he went there the same set of views had an eternal freshness for him, and he wrote long descriptions of the scenery and effects with the same raptures as if he had seen it for the first time. Many of his letters were written from Playford, a village in a beautiful part of Suffolk, a few miles from Ipswich. Here he had a small property, and generally stayed there for a short time once or twice a year. He was extremely fond of this country, and was never tired of repeating his walks by the well-known lanes and footpaths. And, as in Cumberland, the Suffolk country had an eternal freshness and novelty for him. Wherever he went he was indefatigable in keeping up his acquaintance with his numerous friends and his letters abound in social reminiscences.

His memory was singularly retentive. It was much remarked at school in his early days, and in the course of his life he had stored up in his memory an incredible quantity of poetry, ballads, and miscellaneous facts and information of all sorts, which was all constantly ready and at his service. It is almost needless to add that his memory was equally accurate and extensive in matters connected with science or business.

His independence of character was no doubt due to and inseparable from his great powers. The value of his scientific work greatly depended upon his self-reliance and independence of thought. And in the heavy work of remodelling the Observatory it was a very valuable quality. This same self-reliance made him in his latter years apt to draw conclusions too confidently and hastily on subjects which he had taken up more as a pastime than as work. But whatever he touched he dealt with ably and in the most fearless truthseeking manner, and left original and vigorous opinions.

He had a remarkably well-balanced mind, and a simplicity of nature that appeared invulnerable. No amount of hero-worship seemed to have the least effect upon him. And from a very early time he was exposed to a great deal of it. His mind was incessantly engaged on investigations of Nature, and this seems to have been with him, as has been the case with others, a preserving influence. This simplicity of character he retained throughout his life. At the same time he was sensible and shrewd in his money matters and attentive to his personal interests. And his practical good sense in the general affairs of life, combined with his calm and steady consideration of points submitted to him, made his advice very valuable. This was especially recognized by his own and his wife's relations, who consulted him on many occasions and placed the fullest confidence in his absolute sense of justice as well as in his wise counsel. He was extremely liberal in proportion to his means, and gave away money to a large extent to all who had any claim upon him. But he was not in any sense reckless, and kept a most cautious eye on his expenses. He was not indifferent to the honours which he received in the scientific world, but he does not appear to have sought them in any way, and he certainly did not trouble himself about them.

His courtesy was unfailing: no amount of trouble could shake it. Whether it was the Secretary of the Admiralty, or a servant girl wanting her fortune told: whether a begging-letter for money, or miscellaneous invitations: all had their answer in the most clear and courteous language. But he would not grant personal interviews when he could avoid it: they took up too much of his time. His head was so clear that he never seemed to want for the clearest and most direct language in expressing his meaning, and his letters are models of terseness.

In all his views and opinions he was strongly liberal. At Cambridge at an early date he was one of the 83 members of the Senate who supported the application to permit the granting of medical degrees without requiring an expression of assent to the religious doctrines of the Church of England. And in 1868 he declined to sign a petition against the abolition of religious declarations required of persons admitted to Fellowships or proceeding to the degree of M.A. And he was opposed to every kind of narrowness and exclusiveness. When he was appointed to the post of Astronomer Royal, he stipulated that he should not be asked to vote in any political election. But all his views were in the