... was a missionary of rigid and exemplary character who felt it his duty to live continuously in, and for, India; and it fell to [the children's] mother, although of mixed Danish and Portuguese stock rooted in India, to take the children to Britain for their education. Family means were straitened and the divided home left a deep mark on [the children].

The life of a professor in a University College in those days was very different from that to which we are now accustomed. Endowed Chairs were the exception and stipends largely consisted of professors' shares of fees, so that there was a strong inducement to make one's teaching popular rather than profound, a temptation fortunately resisted in most cases, certainly in the case of Hill. Assistants were few, and often paid by the professor. When Hill first took up his duties, the department of Mathematics boasted only a single assistant. The bulk of the routine work of undergraduate teaching, such the correction of students' exercises, fell upon the professor, and this work Hill, trained as he had been in a hard school, performed with unflagging energy and zeal, and an unselfish devotion which won him the affection and admiration of generation after generation of students.

The rule for contracting the process of finding the Square Root. The rule (see Todhunter's 'Algebra') is this:-

When $n+1$ figures of a square root have been obtained by the ordinary method, n more may be obtained by division only, supposing $2n+1$ to be the whole number.

It will be shown in this paper that the rule cannot always be extended to cases in which the 2n+1 figures are followed by other figures, as is usually assumed.

As a teacher he had, to an extraordinary degree, that infinite capacity for taking pains in which Carlyle saw the mark of genius; and he possessed that rare quality, which students so keenly appreciate, of never slurring over difficulties: time spent on making a demonstration perfect was always to him time well spent. And he showed great sympathy with the occasionally devious mental processes of beginners and would even, sometimes, adapt his demonstrations to them. The writer remembers, in his student days, sending up to him a solution which, alas! meandered through as many pages as it should have taken lines, arriving at the desired result by a singularly laborious and inelegant process. Hill read patiently and carefully every line, and in the end his only (and characteristic) comment was that it was a "very courageous " solution! Above all, he loved his students, a feeling which was universally and deeply reciprocated.

The objects of this paper are (I) To draw attention to the indirect character of the argument in the Fifth Book of Euclid's Elements. (II) To reconstruct the argument showing how the indirectness may be removed. (III) To develop the theory of ratio from the reconstructed argument.

The object of this work is to remove the chief difficulties felt by those who desire to understand the Sixth Book of Euclid. It contains nothing beyond the capacity of those who have mastered the first four Books, and has been prepared for their use. It is the result of an experience of teaching the subject extending over nearly twenty years. The arrangement here adopted has been used by the Author in teaching for the past three years and has been more readily understood than the methods in ordinary use, which he had previously employed.

I desire in the first place to express my thanks to the members of the London Branch of the Mathematical Association for the honour they have done me in electing me to the office of president. I esteem it a privilege to take part in the efforts the Association is making to bring about improvements in the methods of teaching Mathematics.

In what position does the work of the Association now stand? Is it in fact in the position described by Sir J J Thomson in his address to the Association of Public School Science Masters? He is reported to have said that he had come to the conclusion that if you have intelligent masters and small classes it does not matter much what theory of education you adopt and if you have not these, well, it does not much matter either.

That seems to me to be a counsel of despair. I prefer to take my stand by the side of Professor Hobson, who said two notable things in his recent address on "The Democratisation of Mathematical Education."

The first was that the business of this Association was "the progressive adaptation of methods and matter of teaching to meet the needs of those who lacked any exceptional capacity."

The second was that "Education in Mathematics must be pronounced a failure if it did not rise beyond the purely practical aspect to the domain of principle. The most important educational aspect of the subject was an instrument for training boys and girls to think accurately and independently."

I am sorry that the twenty years, which have passed since you were with me, prevent me from remembering anything about you but your name. As soon as I can get more time I will look into Mr Ramanujan's paper about the Bernoulli's Numbers, but I cannot do this during term time. One thing however is clear. Mr Ramanujan has fallen into the pitfalls of the very difficult subject of Divergent series.

When he retired in 1924 from the Chair of Mathematics, his friends asked him in what way he would wish them to commemorate his long connection with University College; and he then, remembering the financial struggle of his early years, expressed the desire that any subscriptions received should be devoted to establishing a Loan Fund by means of which the difficulties of students in straitened circumstances might be temporarily relieved, while their spirit of independence was to be preserved by an undertaking of eventual repayment, so soon as they felt able to do so. It was done according to his wishes, and, indeed, no more fitting memorial could have been found of a life spent in the unselfish service of studious youth. Hill was one of those who fought for the establishment in London of a real teaching University; and from the re-constitution of the University in 1900 until 1926, when ill-health compelled his retirement, he was a member of its Senate, in which his balanced judgment, ever-courteous modesty, and, above all, his transparent honesty of purpose and that moral atmosphere which radiated from him and impressed all, even the bitterest opponents of his policy, who came into contact with him, soon gained for him a position of ascendancy.

Almost to the day of his death he continued at work, contending with surprising success against well-nigh insuperable obstacles, and planning a book on the foundations of Geometry. The end came swiftly and comparatively painlessly on January 11th, 1929.

... it was said that by his death the college lost one of the most commanding personalities among its members. No one who sat with him on the many boards and committees concerned with university and college administration could forget the power of his influence, and yet, it was added, he never allowed the administrator or the teacher to eclipse the scholar.