a distinguished mathematician, and author of several works on finance and political economy, was born at Edinburgh on the 11th of June 1743. Dr Hamilton's family was a branch of that of Preston, the eldest cadet of the ducal house of Hamilton. His grandfather was Dr William Hamilton, professor of divinity, and principal of the University of Edinburgh. His father was Gavin Hamilton, an eminent publisher, and distinguished by his loyalty to the House of Hanover during the rebellion in 1745, at which time he acted as chief magistrate of Edinburgh. His mother was Helen Balfour, daughter of James Balfour, Esq. of Pilrig, and the subject of this notice was the eighth child.

Like many other men who have distinguished themselves by the strength and vigour of their mental powers in after life, Dr Hamilton was very delicate in his youth; yet though never robust, he lived to a very advanced age. This may in some degree be attributed to the great regularity of his life, and to his moderation in all things, and not a little to the admirable control under which he had brought every inclination and passion, being thus exempted from those violent emotions which wear out our mortal frames.

His education was entirely conducted in Edinburgh; he was an excellent scholar, and gave complete satisfaction to his teachers, applying himself with diligence and success to the various branches of study usually taught in Scotland. He appears to have had from his earliest years an earnest desire after every sort of learning; and even late in life, when his professional duties and his studies in finance and political economy would have seemed more than enough to occupy all his time, he was able to keep himself acquainted not only with all the discoveries of science, but also with the modern literature of his own and other countries.

His habits and inclinations led him to desire to pass his life in literary pursuits; but the circumstances of his father's numerous family obliged him to devote himself to mercantile business. To prepare himself for this, he spent some time in a banking-house in Edinburgh, a circumstance which he doubtless regretted at the time, but which probably proved of the utmost value to him in after-life; for the accurate habits of business he then acquired were never lost, but were most useful to himself and to others on many occasions, and perhaps even laid the foundation of his work on finance. Whilst a clerk in the banking-house he pursued his studies as far as his leisure permitted. He and some of his companions formed themselves into a literary society, which subsisted for several seasons, and eventually gave rise to the Speculative.

Lord Kames was at that time the leading literary man in Edinburgh, and Dr Hamilton became personally acquainted with him, in a manner equally creditable to both. He had written an anonymous criticism on one of Lord Knimes's works, with which his lordship was so much pleased that he expressed an anxious wish to become acquainted with the author. He was with some difficulty persuaded to reveal himself, and Lord Knimes expressed much surprise at the youth of his able critic. He gave him a general invitation to his house, then the resort of all the literary characters of the day, which proved to him a source both of pleasure and improvement.

The life of a man devoted to literary pursuits rarely furnishes much matter for the biographer, and that of Dr Hamilton is unusually devoid of incident. In the year 1766 the mathematical chair in Marischal College, Aberdeen, became vacant by the death of Professor Stewart. Although only twenty-three years of age, Dr Hamilton's friends were so well aware of his talents and acquirements, that they prevailed upon him, against his own inclination, to become a candidate. He was not successful; but the appearance which he made at the various examinations did him great credit. Two of his rivals were men of great eminence, viz. Dr Trail, who obtained the chair, but after a short period resigned it, and entered the English church (his high attainments in mathematics appear from his life of Simpson); and Professor Playfair, whose name deservedly ranks amongst the greatest of whom Scotland can boast. An account of the comparative trial has been preserved, by which it appears that the questions embraced almost every branch of mathematics; and the sum of the merits of the candidates is thus stated, Trail 126, Hamilton 119, Playfair 90, Fullarton 58, Stewart 47, Douglas 16. The talent he displayed on this occasion was not forgotten, and eventually led to his obtaining the situation of which he was at this time disappointed.

On his return from Aberdeen he entered into partnership with his father in a paper-mill near Edinburgh; but his father died soon afterwards, and as the management of this concern was wholly foreign to his habits and inclinations, he took the first opportunity of placing himself in a more congenial situation, and in 1769 obtained the rectorship of the academy of Perth. In 1771 he married Anne, daughter of Alexander Mitchell, Esq. of Ladath, who died in 1778, leaving him three daughters, who still survive. In 1779 he was appointed by the crown to the chair of Natural Philosophy in Marischal College, Aberdeen. At the same time that Dr Hamilton received this appointment, Dr Copland obtained that of professor of Mathematics. They taught their respective classes for one session; but each feeling the subject allotted to the other to be more congenial to his talents, they agreed to exchange classes; and in future Dr Hamilton taught mathematics, and Dr Copland natural philosophy; an arrangement which was as beneficial to the students, and acceptable to the University, as it was agreeable to the two professors.

In this situation Dr Hamilton remained till the close of his life, although much pressed by some of his friends, at least on one occasion, to remove to what they considered a wider field of usefulness, by accepting a chair in another university. In 1782 he married Jane, daughter of James Morison, Esq. of Elsick. In 1814, finding the duty of teaching his three mathematical classes rather too much for him, he was allowed by the Senatus to employ an assistant. His choice fell on Mr. now Professor Cruickshank, who was soon afterwards appointed by the patrons to be also his successor; Dr Hamilton himself at the same time being regularly inducted into the chair of mathematics, the classes of which he had so long taught. In 1825 he had the misfortune to lose his second wife, by whom he had no family, and from that period he withdrew very much from his active employments and from general society, and spent most of his time at his country house, where he expired on the 14th of July 1829, in the eighty-seventh year of his age.

The first work which Dr Hamilton gave to the public was his Merchandise, the first edition of which appeared in 1777. It has gone through many editions, the last of which, not long before his death, was, with the author's approbation, edited by Mr E. Johnstone of Edinburgh. In 1790, he printed, for the use of his pupils, a set of mathematical tables, which were reprinted with great accuracy and care in 1807. The labour of preparing and correcting such tables for the press is most irksome, and every student of mathematics can well appreciate their value. In 1796 he published his Arithmetic, which has gone through several editions; and in 1800 he published, for the use of his pupils, Heads of a Course of Mathematics. These are his published works on what may be called professional subjects. It is known that he also prepared a work of considerable extent on Practical Astronomy; but no trace of it was found among his papers after his decease.

In 1790 he published anonymously, an Essay on Peace and War. The object of this work was to show the trifling grounds on which wars are often undertaken, and how seldom, at least comparatively speaking, the avowed object for which they were undertaken has been attained, even by their successful termination; and the inadequacy of the advantages which are obtained to compensate for the expenditure of blood and treasure necessarily incurred. But Dr Hamilton's most important work, the publication of which places him amongst the greatest benefactors to his country, appeared in 1813, under the title of an Inquiry concerning the Rise and Progress, the Redemption and Present State, and the Management, of the National Debt of Great Britain. Up to the period of the appearance of this work, the efficacy of the Sinking Fund system was received by all parties almost as an axiom. It was brought forward for the public advantage by Mr Pitt, with perfect good faith; and it continued to be acted upon by his successors, without being called in question even by political antagonists. Dr Hamilton's work at once showed the unsoundness of the whole system, and that so clearly, that soon after its publication it would have been difficult to find any one who would defend the plans so long pursued. The work immediately attracted notice in all quarters, and though the readers of such books are not very numerous, it passed through three editions in a few years. But to the author the most satisfactory approval was that which he received from the gradual but complete adoption of his principles by the British government. It is not a little remarkable, that no one ever attempted fairly to refute his work, although many able men had every inducement to do so if they could. Everything connected with the fund was so enveloped in technical jargon, that, to all but the initiated, they were an unintelligible mystery. Dr Hamilton divested the subject of this encumbrance; he gave a distinct detail of the progress of our debt, explaining the origin and nature of the different stocks in plain and simple language.

He commences his work by laying down twelve general principles of finance, each of which is so incontrovertible, as hardly to require the support of argument. The second part of it is occupied by the history of our debt, and the different plans proposed or adopted for its discharge, and their operation; and the third part is devoted to the application of the twelve principles to these schemes, and an examination of the different methods adopted in conducting our financial concerns. The scope of the whole work may be summed up in two plain statements: first, that, as with private individuals, so with nations, the only really effectual sinking fund is a surplus of income over expenditure, and therefore that no nation whose finances are managed on opposite principles can avoid ruin in the end, however skilfully its affairs may be conducted; secondly, that to raise money at a low nominal rate of interest, by promising to Hamilton repay a larger sum than is received, is a trifling advantage at first, but incurs a large certain loss on redemption of the debt. These appear so self-evident that it might have been thought a waste of time to prove them, had not long and fatal experience shown that they were neither believed nor acted upon by those men who conducted the finances of the nation. Now, however, they are universally admitted, and no financier of the present day is found bold enough to propose the redemption of our national debt by any other means than keeping the income above the expenditure.

In 1822, Dr Hamilton published a small pamphlet on the Poor Laws; a subject by which he was deeply interested. This pamphlet contains a brief but distinct exposition of the principles on which relief to the poor ought to be afforded in a Christian country. It had probably little circulation beyond the town of Aberdeen, as great part of it is occupied by local details; but the publication of it may fairly be considered as having at least for a number of years delayed the infliction of poor-rates on that city. The last work of Dr Hamilton's which was given to the public is entitled The Progress of Society; this was left by the author ready for the press. He had been occupied in the preparation of it for many years, and continued to correct it till within a few days of his death. It consists of twenty-one essays on different branches of political economy, published at a time (1830) when the minds of all thinking men in this country were directed to those most momentous political changes which absorbed the public attention, to the almost total exclusion of every other subject.

This work attracted less attention than his National Debt. It is written in his usual plain and perspicuous style, and his deductions from admitted facts appear to be in general incontrovertible, though they lead at times to conclusions widely different indeed from those of most modern writers on political economy. But when the time shall come that a greater number of fixed principles on political economy shall be established, and the subject shall thus be brought in truth to be a science, then it is expected that this work will be found to contain more sound doctrine than most of its precursors. Much of the author's benevolence appears in its pages, and of his desire for the general good, and not that of particular classes of society. The whole is pervaded by his favourite doctrine, that the object of government should be the moral good, and not the wealth or the grandeur, of a people. In 1831 Dr Hamilton's family reprinted privately his Essay on Peace and War, which had become very scarce, as well as that on the Poor Laws, omitting the local details; and to these were added an unfinished fragment of an essay on Government. It cannot now be ascertained at what time it was written; but probably it was during the progress of the French Revolution, of which Dr Hamilton always spoke in terms of the strongest reprobation. In 1814 Dr Hamilton was elected one of the three judges for awarding the Burnet prize, for the best essay on the Being of a God. The large amount of the prizes (£1,200 and £400) attracted many competitors, and rendered the duty of the judges laborious. Dr Hamilton applied himself to the work with his wonted care, and wrote out a full abstract of each of the fifty treatises, to enable him to come to a right decision on their respective merits; a labour which occupied many hours a day for several months.

His work of finance brought him into correspondence with several of the leading members of both houses of parliament, and also with some foreign economists who were interested in the subject, particularly J. B. Say, who notices the Inquiry in terms of strong commendation, in his Traité de l'Economie Politique (vol. ii. p. 351).

He was also frequently consulted on mathematical questions by his former pupils; and as he never ceased to feel an interest in their progress through life, so he had much pleasure in assisting them when in his power, as many still remember with gratitude. In like manner, his advice was sought and obtained as to the various schemes for equalizing weights and measures, for supplying the town of Aberdeen with water, for calculating the invaluable fund for the widows of the clergy of the church of Scotland, and a similar institution for the widows of advocates in Aberdeen. To the management of the poor's funds, and the various charitable institutions in Aberdeen, and of the funds of the college of which he was a member, much of his time and attention were devoted. He was never idle, and all his talents were ever ready to be employed for the service of those who required them.

Dr Hamilton's personal appearance was striking: he was naturally tall and thin, but with a considerable stoop, which increased with his years: his countenance was mild and very intelligent, often with a certain air of abstraction; but when animated, as it often was, particularly in conversation, it was remarkably expressive. His habits and pleasures were completely domestic, and he enjoyed the society of his friends with the keenest relish. For many years he made annually a tour to some part or other of Britain, and at the age of seventy-eight visited the Low Countries and the north of France. From these tours he acquired much information of immediate use to his studies on political economy, and he was in the habit of noting down every day whatever came before him worthy of remembrance.

In pursuing his studies he followed a similar plan, rarely reading a work of importance without committing to writing his remarks upon it; and the result was, that he possessed a fund of solid information rarely to be met with. His natural diffidence prevented his displaying his resources in general society, where he was more anxious to hear than to speak; but in the circle of his intimate friends his conversation was in the highest degree pleasing and instructive. His favourite relaxation was the cultivation of flowers, a taste in perfect unison with the simplicity of his whole character. Dr Hamilton was no party man, although he was often unjustly regarded as such. He used his strong powers of mind to judge of public measures by their own merits, without regard to party; and it is pleasing to remark the gentleness and candour with which in his works he amends on those from whose opinions and principles he dissents.

It is not necessary to add much on his private character; he was full of benevolence, active as well as speculative. Amongst his papers were found "Regulations for his future conduct," drawn up at the early age of twenty-two; and on reviewing the long course of his subsequent life, it is clear that he never lost sight of the high standard which he had then proposed for himself. His piety was always sincere, though unostentatious; it became more and more fervent as his earthly career approached its termination; and for some time previous to his decease, it was his practice to retire to his closet three times a day for private devotion. His faculties continued unimpaired to the last, and his end was perfect peace. Soon after his death a subscription was proposed, to erect a monument to his memory; and so general was the respect entertained for him, that a large sum was immediately raised. The monument has been lately erected in the burying-ground of St Nicholas, Aberdeen, not far from his grave. It consists of a solid basement, six feet high, on which are placed four fluted Doric columns, each of one block of granite, supporting an entablature of the same order, above which rises a low roof. Under this roof stands an urn, and on the last side of the basement is a tablet with the following inscription:

Memoriae Sacrum Roberti Hamilton, LL.D. In Academia Mariscallana Mathesis Professoris, Qui XIV. die Julii A. D. MDCCCXXIX. et aetatis sue LXXXVII. obit. Cives, Amici, et Discipuli, Hoc Monumentum posuerunt.

The height of the whole structure is twenty-one feet six inches. The design is correctly classical, and the execution of it is the best specimen we have seen of any modern work in granite.