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Robert Hamilton


HAMILTON, ROBERT, LL.D., a mathematician and political economist, was born in June, 1743. He was the eighth son of Gavin Hamilton, [Gavin Hamilton, executed an ingenious and accurate model of Edinburgh, which cost him some years’ labour, and was exhibited in a room in the Royal Infirmary in 1753 and 1754; after his death it was neglected and broken up for firewood. It represents a scheme for an access to the High Street, by a sloping road from the West Church; precisely the idea subsequently acted upon in the improvement of the city.] a bookseller and publisher in Edinburgh, whose father was at one time professor of divinity in, and afterwards principal of, the university of Edinburgh. In the life of a retired and unobtrusive student, who has hardly ever left his books to engage even in the little warfares of literary controversy, there is seldom much to attract the attention of the ordinary reader; but where perusing the annals of one of the most feverish periods of the history of the world, posterity may show a wish to know something about the man who discovered the fallacy of the celebrated sinking fund, and checked a nation in the career of extravagance, by displaying to it, in characters not to be mistaken, the unpalliated truth of its situation. Holding this in mind, we will be excused for giving to the world some minutae of this remarkable man, whom neither the events of his life in general, nor his connexion with the literary history of the age, would have rendered an object of much biographical interest.

Like many men who have signalized themselves for the originality or abstractness of their views, Hamilton in his early years suffered much from constitutional debility, an affliction from which his many after years were signally exempt, till his last illness, his only complaint being a frequent recurrence of lumbago, which gave him a characteristic stoop in walking. He is described as having shown, in the progress of his education, an appetite for almost every description of knowledge, and to have added to the species of information for which he has been celebrated, a minute acquaintance with classical and general philosophical subjects: a respected friend, long belonging to the circle of Hamilton’s literary acquaintance, has described his mind as having less quickness in sudden apprehension of his subject, than power in grappling with all its bearings, and comprehending it thoroughly after it had been sometime submitted to his comprehension; it was exactly of that steady, strong, and trustworthy order, on which teachers of sense and zeal love to bestow their labour. He was, in consequence, a general favourite with his instructors, and more especially with the celebrated Matthew Stewart, professor of mathematics in Edinburgh, who looked on the progress and prospects of his future scholar with pride and friendly satisfaction.

The partiality of Mr Hamilton for a literary life he was compelled to yield to circumstances, which rendered it expedient that he should spend some time in the banking establishment of Messrs William Hogg & Son, as a preparatory introduction to a commercial or banking profession; a method of spending his time, less to be regretted than it might have been in the case of most other literary men, as, if it did not give him the first introduction to the species of speculation in which he afterwards indulged, it must have early provided him with that practical information on the general money system of the country, which his works so strikingly exhibit. Soon after this, Mr Hamilton began to form the literary acquaintance of young men of his own standing and pursuits, some of whom gathered themselves into that knot of confidential literary communication, which afterwards expanded into a nursery of orators, statesmen, and philosophers, of the highest grade, now well known by the name of the Speculative Society. The manner in which the young political economist became acquainted with lord Kaimes, has something in it of the simplicity of that literary free masonry, which generally forms a chain of friendly intercourse between the celebrated men of any particular period, and those who are just rising to replace them in the regard and admiration of the world. His lordship’s attention having been attracted by the views on one of his own works, expressed in a criticism which had been anonymously supplied by Mr Hamilton, to one of the periodicals of the day—he conveyed through the same paper a wish that the author of the critique, if already known, might become better known to him, and if a stranger, would communicate to him the pleasure of his acquaintance. The diffident critic was with difficulty prevailed on to accept the flattering offer; the elegant judge expressed considerable surprise at the youth of the writer, when compared with the justness and profundity of his views, and communicated to him by a general invitation to his house, the advantages of an intercourse with his refined and gifted circle of visitors.

In 1766, Mr Hamilton, then only twenty-three years of age, was prevailed on by his friends to offer himself as a candidate for the mathematical chair of Marischal college in Aberdeen, then vacant by the death of Mr Stewart, and though unsuccessful, the appointment being in favour of Mr Trail, he left behind him a very high sense of his abilities in the minds of the judges of the competition, one of whom, in a letter to Dr Gregory, states, that "he discovered a remarkable genius for mathematics, and a justness of apprehension and perspicuity, that is rarely to be met with."—"He is," continues the same individual, "an excellent demonstrator; always planned out his demonstration with judgment, and apprised his audience where the stress lay, so that he brought it to a conclusion in a most perspicuous manner, and in such a way that no person of common understanding could raise it." After this unsuccessful attempt to acquire a situation more congenial to his pursuits, Mr Hamilton became a partner in the conducting of a paper mill, which had been established by his father—a concern which, in 1769, he relinquished to the care of a manager, on his appointment to the rectorship of the academy at Perth. In 1771 he married Miss Anne Mitchell of Ladath, whom he had the misfortune of losing seven years afterwards. In 1779, the chair of natural philosophy in Marischal college, in the gift of the crown, was presented to Dr Hamilton. From this chair Dr Copland,—a gentleman whose high scientific knowledge and private worth rendered him, to all who had the means of knowing his attainments, (of which he has unfortunately left behind him no specimen,) as highly respected for his knowledge of natural philosophy and history, as his colleague was for that of the studies he more particularly followed,—had been removed to the mathematical chair in the same university. The natural inclination and studies of each led him to prefer the situation of the other to his own, and after teaching the natural philosophy class for one year, Dr Hamilton effected an exchange with his colleague, satisfactory to both. He was not, however, formally presented to the mathematical chair till several years afterwards.

In short time previously to the period of his life we are now discussing, Dr Hamilton had commenced the series of useful works which have so deservedly raised his name. In 1777, appeared the practical work, so well known by the name of "Hamilton’s Merchandise;"—he published in 1790, a short essay on Peace and War, full of those benevolent doctrines, which even a civilized age so seldom opposes to the progress of licensed destruction. In 1796, Dr Hamilton published his Arithmetic, a work which has been frequently reprinted,—and in 1800, another work of a similar elementary description, called "Heads of a Course of Mathematics," intended for the use of his own students: but the great work so generally attached to his name, did not appear till he had passed his seventieth year. The "Inquiry concerning the Rise and Progress, the Redemption and Present State of the National Debt of Great Britain," was published at Edinburgh in 1813—it created in every quarter, except that which might have best profited by the warning voice, a sudden consciousness of the folly of the system under which the national income was in many respects conducted, but it was not till his discoveries had made their silent progress through the medium of public opinion, that they began gradually to affect the measures of the government. The principal part of this inquiry is devoted to the consideration of the measures which have at different periods been adopted for attempting the reduction of the national debt.

The earliest attempt at a sinking fund was made in the year 1716, under the auspices of Sir Robert Walpole, a measure of which that acute minister may not improbably have seen the inutility, as in the year 1733, he applied five millions of the then sinking fund to the public exigencies; the principal always nominally existed, although it was not maintained with constant regularity and zeal, until the year 1786, when the celebrated sinking fund of Mr Pitt was formed, by the disposal of part of the income of the nation to commissioners for the redemption of the debt, a measure which was modified in 1792, by the assignment of one per cent annually, on the nominal capital of each loan contracted during the war, as a sinking fund appropriated for the redemption of the particular loan to which it was attached. It underwent several other modifications, particularly in 1802 and 1807. The great prophet and propounder of this system, the celebrated Dr Price, unfolded his views on the subject, in his treatise "Of Reversionary Annuities," published in 1771. It is a general opinion, that an application to studies strictly numerical, will abstract the mind from the prejudice and enthusiasm of theory. Dr Price has proved the fallacy of such a principle, by supporting his tables of calculations, with all the virulence and impatience of a vindicator of the authenticity of Ossian’s Poems, or of the honour of queen Mary. Dr Price has given as a glowing example of his theory, the often repeated instance of the state of a penny set aside and allowed to accumulate from the time of Christ:—if allowed to remain at compound interest, it will accumulate to, we forget exactly how many million globes of gold, each the size of our own earth—if it accumulate at simple interest, the golden vision shrinks to the compass of a few shillings—and if not put out at interest at all, it will continue throughout all ages the pitiful penny it was at the commencement. The application of the principle to an easy and cheap method of liquidating the national debt, was so obvious to Dr Price, that he treated the comparative coldness with which his advice was received, as a man who considered that his neighbours are deficient in comprehending the first rules of arithmetic; and it certainly is a singular instance of the indolence of the national mind, and the readiness with which government grasped at any illusive theory, which showed a healing alternative to the extravagance of its measures, that no one appeared to propose the converse of the simile, and to remind the visionary financier, that in applying it to national borrowing, the borrower, by allowing one of the pennies he has borrowed to accumulate in his favour at compound interest, is in just the same situation as if he had deducted the penny from the sum he borrowed, and thus prevented the penny and its compound interest from accumulating against him.

The practical results of Dr Price’s theories were, the proposal of a plan, by which a nation might borrow at simple interest, and accumulate at compound interest a fund for its repayment: boldly pushing his theory to its extremities, and maintaining that it is better to borrow at high than at low interest, because the debt will be more speedily repaid; and as a corollary, that a sinking fund during war is more efficient than at any other time, and that to terminate it then, is "the madness of giving it a mortal blow." The supposition maintained by Dr Hamilton, in opposition to these golden visions of eternal borrowing for the purpose of increasing national riches, did not require the aid of much rhetoric for its support - it is, that if a person borrows money, and assigns a part of it to accumulate at compound interest for the repayment of the whole, he is just in the same situation as if he had deducted that part from his loan—and hence the general scope of his argument goes to prove the utter uselessness of a borrowed sinking fund, and the fallacy of continuing its operation during war, or when the expenditure of the nation overbalances the income. The absurdity of setting aside a portion of the sum borrowed for this purpose, (and generally borrowed at more disadvantageous terms as the loan is to any degree increased,) was partially prevented by a suggestion of Mr Fox; but the sinking fund was strictly a borrowed one, in as far as money was laid aside for it, while the nation was obliged to borrow for the support of its expenditure. The evil of the system is found by Dr Hamilton to consist, not only in the fallacy it imposes on the public, but in its positive loss of resources. The loans are raised at a rate more disadvantageous to the borrower than that at which the creditor afterwards receives payment of them, and the management of the system is expensive; if a man who is in debt borrows merely for the purpose of paying his debt, and transacts the business himself, he merely exposes himself to more trouble than he would have encountered by continuing debtor to his former creditor; if he employ an agent to transact the business, he is a loser by the amount of fees paid to that agent. These truths Dr Hamilton is not content with proving argumentatively—he has coupled them with a minute history of the various financial proceedings of the country, and tables of practical calculation, giving, on the one hand, historical information; and, on the others showing the exact sums which the government has at different periods misapplied.

Along with Mr Pitt’s system of finance, he has given an account of that of lord Henry Petty, established in 1807; a complicated scheme, the operation of which seems not to have been perceived by its inventor, and which, had it continued for any length of time, might have produced effects more ruinous than those of any system which has been devised. The summary of his proofs and discussions on the subject, as expressed in his own words, is not very flattering to the principle which has been in general followed: "The excess of revenue above expenditure is the only real sinking find by which the public debt can be discharged. The increase of the revenue, or the diminution of expense, are the only means by which a sinking fund can be enlarged, and its operations rendered more effectual; and all schemes for discharging the national debt, by sinking funds, operating by compound interest, or in any other manner, unless so far as they are founded upon this principle, are illusory." But it cannot be said that Dr Hamilton has looked with feeling of anything resembling enmity on the object of his attack; he has allowed the sinking fund all that its chief supporters now pretend to arrogate to it, although the admission comes more in the form of palliation than of approbation. "If the nation," he says, "impressed with a conviction of the importance of a system established by a popular minister, has, in order to adhere to it, adopted measures, either of frugality in expenditure, or exertion in raising taxes, which it would not otherwise have done, the sinking fund ought not to be considered inefficient: and its effects may be of great importance."—"The sinking fund," says an illustrious commentator on Dr Hamilton’s work, in the Supplement to the Encyclopeadia Britannica, following up the same train of reasoning, "is therefore useful as an engine of taxation;" and now that the glorious vision of the great financial dreamer has vanished, and left nothing behind it but the operation of the ordinary dull machinery, by which debts are paid off through industry and economy, one can hardly suppose that the great minister who set the engine in motion, was himself ignorant (however much he might have chosen others to remain so) of its real powerlessness. The discovery made by Dr Hamilton was one of those few triumphant achievements, which, founded on the indisputable ground of practical calculation, can never be controverted or doubted: and although a few individuals, from a love of system, while apparently admitting the truths demonstrated by Dr Hamilton, in attempting to vindicate the system on separate grounds, have fallen, mutato nomine, into the same fallacy, [Vide "A Letter to lord Grenville on the sinking fund, by Thomas Peregrine Courtenay, Esq., M.P., London, 1828."] the Edinburgh reviewers, Ricardo, Say, and all the eminent political economists of the age, have supported his doctrine; while the venerable lord Grenville—a member of the administration which devised the sinking fund, and for some time first lord of the treasury—has, in a pamphlet which affords a striking and noble specimen of political candour, admitted that the treatise of Dr Hamilton opened his eyes to the fallacy of his once favourite measure.

A year after the publication of this great work, the laborious services of the venerable philosopher were considered as well entitling him to leave the laborious duties of his three mathematical classes to the care of an assistant, who was at the same time appointed his future successor. The person chosen was Mr John Cruickshank, a gentleman who, whether or not he proved fruitful in the talents which distinguished his predecessor, must be allowed to have been more successful in preserving the discipline of his class, a task for which the absent habits of Dr Hamilton rendered him rather unfit. In 1825, Dr Hamilton’s declining years were saddened by the death of his second wife, a daughter of Mr Morison of Elsick, whom he had married in 1782; and on the 14th day of July, 1829, he died in the bosom of his family, and in that retirement which his unobtrusive mind always courted, and which he had never for any considerable period relinquished. Dr Hamilton left three daughters, of whom the second was married to the late Mr Thomson of Banchory, in Kincardineshire, and the youngest to the Rev. Robert Swan of Abercrombie, in Fife. He had no family by his second wife. Several essays were found among Dr Hamilton’s papers, which were published by his friends in 1830, under the title of "The Progress of Society;" and although the majority of them contain very deep and abstruse remarks well worthy of attention, there are others which may, perhaps, be said to contain too many of the general principles of which the earlier metaphysicians of Scotland were very fond, and too little of the close and practical reasoning which generally distinguishes their author’s mind, to be such as he might have thought fit to have given to the world in their present state. The commercial policy argued by Dr Hamilton in these tracts, is the system which was first inculcated by Dr Adam Smith in 1776, and which, after the lapse of seventy years, was embodied in the great and beneficent free-trade measures of Sir Robert Peel, under the operation of which the nation is developing its resources of trade and manufacture with fresh energy, and all ranks of the community, but more especially the working-classes, enjoy an unexampled degree of prosperity. It is to be hoped that the successful experiment of Great Britain will encourage the other nations, both of the old and new world, to follow so wise and salutary an example, and reciprocate the advantages which they also have derived from it. Dr Hamilton held a peculiar, view on the subject of a metallic currency, believing its value to arise, not from its worth as a commodity, but chiefly from its use as an instrument of exchange. This opinion he maintained with great power and plausibility.

The Essays on Rent, and the consequent theory of the incidence of tithes, argued with a modesty which such an author need hardly have adopted, are well worthy the consideration of those who have turned their attention to these abstruse subjects. The author appears to doubt the theory discovered by Dr Anderson, and followed up by Sir Edward West, Malthus, Ricardo, and M’Culloch, which discovers rent to be the surplus of the value of the produce of more fruitful lands of a country, over the produce of the most sterile soil, which the demands of the community requires to be taken into cultivation. "What," says our author, in answer to the assumption of Dr Anderson, "would happen if all the land in an appropriated country were of equal fertility? It would hardly be affirmed that, in that case, all rent would cease." To this the following answer might be made—Were the population insufficient to consume the whole produce of rich fertile land, (which could not long be the case,) certainly there would be no rent. Were the consumption equal to or beyond the produce, the rent would be regulated thus:—If foreign corn could be introduced at a price as low as that at which it could be raised, there would still be no rent—if, either from the state of cultivation of other countries, or the imposition of a duty, corn could only be imported at a price beyond that at which it can be grown, rent would be demanded to such an extent as to raise the price of the home produce to a par with the imported—in the former case the rent being the natural consequence of commerce, in the latter the creature of legislation. The principle maintained by Dr Anderson would here exactly apply, the higher price of importing corn to that of producing it at home, being a parallel to the higher cost of raising produce in sterile than in fruitful soils. But this intricate subject, unsuited to the present work, we gladly relinquish, more especially as the discussion of our author’s ideas on this topic has fallen into other and abler hands. In these Essays we think we can perceive here and there traits of that simplicity and abstraction from the routine of the world, which was on some occasions a characteristic of their author. Men who mingle unobserved with the rest of their species, may be well versant in the lighter and more historical portions of the philosophy of mind and matter; but the illustrious examples of Newton, Locke, Smith, and many others, have shown us, that the limitation of the human faculties calls to the aid of the more abstruse branches of science, a partial, if not total abstraction from all other subjects, for definite periods. Dr Hamilton was remarkable for his absence; not that he mingled subjects with each other, and mistook what he was thinking about, the error of a weak mind, but he was frequently engaged in his mathematical studies, when other persons were differently employed. As with other absent men, numberless are the anecdotes which are preserved of his abstractions—many of them doubtless unfounded, while at the same time it must be allowed, that he frequently afforded amusement to inferior wits. He possessed a singular diffidence of manner, which in a less remarkable man might have been looked upon as humility. Taking advantage of this feeling, and of his frequent abstractions, his class gave him perpetual annoyance, and in the latter days of his tuition, the spirit of mischief and trickery, natural when it can be followed up in classes the greater portion of which consisted of mere boys, created scenes of perfect anarchy and juvenile mischief. The author of this memoir recollects distinctly his stooping shadowy figure as he glided through the rest of his colleagues in the university, with his good-humoured small round face, and his minute but keenly twinkling eyes, surrounded by a thousand wrinkles, having in his manner so little of that pedagogical importance so apt to distinguish the teachers of youth, especially in spots where the assumption of scientific knowledge is not held in curb; by intercourse with an extensive body of men of learning. It is not by any means to be presumed, however, that the subject of our memoir, though retired, and occasionally abstracted in his habits, excluded himself from his due share in the business of the world. He led a generally active life. He maintained a correspondence with various British statesmen on important subjects, and with Say and Fahrenberg, the latter of whom requested permission to translate the work on the national debt into German. He frequently represented his college in the General Assembly. On the bursary funds of the university, and on the decision of a very important prize intrusted to him and his colleagues, he bestowed much time and attention; and he gave assistance in the management of the clergymen’s widows’ fund of Scotland, and in plans for the maintenance of the poor of Aberdeen.

It was once proposed among some influential inhabitants of Aberdeen, that a public monument should be erected to the memory of this, one of the most eminent of its citizens. Strangers have remarked, not much to the credit of that flourishing town, that while it has produced many great men, few have been so fortunate as to procure from its citizens any mark of posthumous respect. We sincerely hope the project may not be deserted, and that such a testimony of respect will yet appear, to a man on whom the city of Aberdeen may with more propriety bestow such an honour than on any stranger, however illustrious.


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