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cant 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 apprized 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 miss 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. A 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 mea-