never heard these two chords of the Divine harp struck together. They had heard the solitary note of justice, when amid its thunder, the apostate angels were hurled headlong flaming down to bottomless perdition;' but the chord of mercy had never sent its music through the heavenly halls. They might imagine, as they gazed on these silent strings, that were the fingers of Deity simultaneously to sweep them, the universe would rush into uproar, and lose its harmonic principles amid the reverberations of eternal dissonance. They knew, however, that in the counsels of the past, it had been decreed that these dissimilar chords were to be struck on the stage of this world. Thus informed, with what strange feelings must they have regarded our first parents as they came from the creative hand of the Word, and with what mysterious interest would they gaze upon him, as the Architect, planning and constructing the grand orchestra, whence the wondrous harmony was to burst upon the ear of creation! But the preliminaries are arranged; the universe stands in expectation-Man falls. This is the requisite condition. An appeal is at once made to God as just and as merciful. The guilt of the creature invokes vengeance; his misery, mercy. But these cannot find their object without clashing, as they proceed direct from God. A medium is required; it is found. The Word, the Revealer, and the Glorifier of the Father, is made flesh; he lives on earth, he suffers, he dies; but in dying, as his bleeding head falls on his quivering breast, the divine harp is struck; and while the curtain is darkly descending on Nature and her dying Lord, the chords of justice and of mercy roll forth their blended notes that echo through every circling sphere, to the most distant regions of the peopled universe. Man hears, and hails; heaven hears, and hymns; hell hears, and howls. In that hour an unseen finger inscribed above the Cross, 'He that hath seen me, hath seen the Father."" Notices of Books. POEMS BY ALEXANDER CARLILE. Glasgow: Thomas Murray & Son. London: Arthur Hall, Virtue & Co. GENEVIEVE AND OTHER POEMS. By Andrew James Symington. MANUFACTURES and commerce are not, as many think, opposed to the culture of the faculty of taste. The love of the merely useful which they are said to engender is a safe basis on which to rest the ornamental, and the vices which are laid to their charge are not necessarily inherent in them, but in the spiritless souls that meanly succumb and do not assert the proud prerogative of their nature, and make matter serve them. Limited mental occupation will narrow the scope of any mind, but such an evil is incidental to all departments of labour, and it is in man's own power to counteract this. In these volumns, composed by gentlemen engaged in such pursuits, we have evidence of the truth of what we have said. They have not only cultivated the love of the beautiful, but they have cultured themselves to produce the beautiful in the highest and most difficult walk of art. Mr Carlile is a true lover of nature, and has evidently "from his youth upward" felt its power to awaken and develop the finer feelings of the soul. This is the prevailing consciousness as it were of his compositions, which the spirit, like a will, bends to its own purposes. With such a just relation of the subjective and the objective, true thoughts could hardly fail of being evolved, and that in a style which would not disgrace much more ambitious authors than Mr Carlile. Some of the poems in this volume had the honour of appearing in "Blackwood" in its palmy days, when Christopher North gave its pages an eclat that conserved it to writers of first-rate talent. In "Shadows on the Wall" there is a thoughtful humour, original and racy, which has made us pass by its more dignified compeers: Mr Symington's compositions have been evolved by a conceptive process more subjective than the preceding. He, too, looks upon nature with a true poet's eye, but he rather finds in nature an echo to his thought than his thought prompted by a power in nature. With a keen appreciation of the beautiful he has generally conceived and expressed it in a most artistic manner. We have only space to quote the following verses, which originally appeared in Dickens' "Household Words:" ASPIRATION AND DUTY OH! what is earth to those who long But hush, fond heart! while here below, THE SCIENCE OF ARITHMETIC. A Systematic Course of Numerical THE importance of a sound and well-grounded knowledge of arithmetic, is felt, by all intelligent minds, to be one of the chief items of a liberal education, not only for its advantages in a commercial point of view, but also for the close and pointed reasoning which it is calculated to call forth in the mind of the student. The continuous habit of operating on a given data from the comprehension of certain abstract principles, trains the mind to cautious and correct modes of drawing conclusions. But has arithmetic hitherto been looked upon in this light? have our educators, generally speaking, taken advantage of this art as a means of drawing out the latent reasoning powers of the mind? We are afraid that on inquiry this will be found to have been sadly neglected; what has been so highly lauded in theory has been grossly neglected in practice. We have been informed of the existence of the kernel, but fed with the husk. Although such men as Leslie, Lardner, and De Morgan have turned their attention to this subject-though they have given to the world their investigations, and placed the principles of the science in their truest and clearest light; yet there, in great measure, has the matter rested. We have remained content with knowing the principles without troubling ourselves with the practice of them. The natural inquiry then is, how are these principles to be practically applied? should the rules deduced from these theoretical facts be administered to the minds of pupils under the expectation that they will quicken the mental pulse of the young mind. We assuredly think not. Where the vivifying light of intellect is not brought into play, we can hope for no genuine result. But this science, applied in its true spirit, will be found not only one of the best agents for developing to a high degree the mental powers, but for preparing youths for the more serious business of life. Regarding numerical computation as the result of reasoning, and rules not as abstract principles, but simply reasoning methodised, we apprehend that the following remarks, arising from the conviction that young minds, capable of a power of reasoning according to their several capacities, acquire a greater confidence in themselves in proportion as they are led to think for themselves, embrace the entire theory by which the science of arithmetic may be made a powerful instrument of mental culture. Having proposed a question, endeavour to lead the pupil to consider the sense of it, let him think what he should do in such a case, and, as it were, break it up, see what it really means, and then try to perform the operation accordingly. We feel assured that this method will be found far preferable to cramming him with crude theories and unmeaning rules. Treating a question in this way will enable him to give his own reasons and deduce his own rules, gaining greater satisfaction, and more increasing confidence in himself by one such process, than by the application of all the rules laid down in arithmetic. Although the teaching of this science has been partially misunderstood, or rather, though teachers have not acted according to the information which they possessed or might have possessed; yet this did not arise from the want of manuals capable of supplying many useful hints, for we have treatises by the late Professor Thomson of Glasgow, Davidson, Murray, and others, all of them, by careful study, calculated to advance the interests and improve the understandings of the rising generation. This publication of the Messrs Cornwell and Fitch is, we think, entitled to the first place among those of a similar kind, both for its arrangement, its clear and distinct reasoning, and its collection of useful and appropriate exercises. Neither the labour of thought nor research appears to have been spared in order to render this treatise a valuable acquisition to every student of arithmetic. In respect, however, of its furnishing us with a complete commercial course, as it professes to do, we think it is rather deficient, particularly in the matter of Annuities and Life Insurances, and in the total absence of Foreign Exchange-a feature not to be excluded from a commercial course, considering its great importance in the conducting of our monetary affairs with foreign nations. There is another most important item awanting: the theory and practice of the "chain rule," which is principally applied to compound arbitration of exchange, but which may be applied with advantage to all the varieties of Proportion. The placing of the answers at the end of the book is certainly preferable to having them following the questions; but their arrangement in this case is not only very confused, but many of them are incorrect. Notwithstanding all these deficiencies, however, we sincerely believe, that, in the hands of a judicious teacher, it cannot fail of being productive of much good. THE BRITISH EDUCATOR. JULY, 1856. THE LATE SIR WILLIAM HAMILTON. OUR last issue was in the press at the time of Sir WILLIAM HAMILTON's death, so that we were unable to refer to the melancholy event. We cannot omit some notice of the life and labours-some tribute, however feeble, to the memory of so great a man. For more than twenty years he has been known to the world of letters as one of the most accomplished scholars in Europe, and as the greatest speculative thinker of this century. By his death Scotland has lost the most illustrious of her philosophers, and one of the noblest of her sons. The leading facts of Sir William's life are now generally known. He was born in the City of Glasgow in 1788. Having studied at our University, he went to Oxford on the Snell Foundation, where he obtained first-class honours. He was called to the Scottish Bar in 1813. In 1820 he contested the Chair of Moral Philosophy with the late Professor Wilson. He was appointed, in the same University, Professor of Universal History in 1821, and in 1836 he obtained the Chair of Logic and Metaphysics, which he occupied till the period of his death. He was the lineal representative of the Hamiltons of Preston. Sir William became known to the philosophical world by his contributions to the Edinburgh Review, especially by three of these:that on "the Philosophy of the Unconditioned, in reference to Cousin's Doctrine of the Infinito-absolute," October, 1829; the elaborate defence of the "Philosophy of Perception, against the attack of Dr Thomas Brown," October, 1830; and the article on Logic, April, 1833.* These papers excited the profound attention of all the thinking men in Europe, and at once gained for their author the reputation of being one of the ablest men, and the "first Peripatetic of the age."+ * It was not, therefore, until the age of forty-one, that Sir W. Hamilton wrote anything that he considered worthy of preservation. NO. V. So he was designated by his contemporary, M. Cousin. N For depth and subtlety of argument, for breadth and minuteness of erudition, and for the perfection of philosophical style, it is not too much to say that there is nothing in the English language (excepting some other portions of Sir William's writings) that can be compared to them. They were translated, along with other of his contributions to the Review, into French, German, and Italian. Sir William continued to write for the Edinburgh Review, from 1829 till 1839, on philosophical, literary, and educational subjects, and in 1852 he republished a selection of his articles, under the title of "Discussions," to which are added notes and valuable appendices. The most celebrated of these, besides those to which we have referred, are on Education. His severe exposure and denunciation of the abuses in the English Universities has, we believe, already been attended with beneficial results, especially in Oxford; and his attack on the almost exclusively mathematical training of Cambridge, is supported by such force of argument, and so much learning, as cannot fail to produce a profound impression on all serious men, whether they are more particularly concerned with the education of others, or with their own. In 1846 Sir William published his edition of Reid, and there is a mournful interest now in knowing that it was chiefly on account of the toil and patient thought which he bestowed on this work that his health gave way. He was first struck by paralysis in the July of 1844. The work has never been completed. It is said, indeed, in the advertisement that the sequel of the Dissertations are "either prepared or their materials collected;" but it is difficult to say how much or how little may be implied in this. Even as they stand, however, these notes and dissertations form a monument of matchless critical power and profound learning. It would be here out of place to attempt ought like a formal estimate of the value of Sir William Hamilton's contributions to philosophy. We can do no more than indicate the more obvious results of his labours, and the distinguishing features of his character and intellect. The philosophy of Hamilton is, more than any other, explicitly an evolution of consciousness. This is at once its remarkable and important characteristic. While all have tacitly acknowledged, and none, save sceptics, ever formally disclaimed the authority of consciousness, few philosophers have even in theory, and hardly any in practice, realised that, by the necessity of things, it is the source of all philosophical truth-the last authority on every question touching the intellectual and moral nature of man. This Sir William demonstrated with great precision, and his whole philosophy is a severe protest against the licentious manner in which these ultimate deliverances of our spiritual nature have been so generally, so almost universally dealt with by speculative men. He brought prominently forward the impossibility of all philosophy, if any of the facts of consciousness be disproved. "Falsus in uno, falsus in omnibus." In his own emphatic language, "Consciousness once convicted of falsehood, an unconditioned scepticism in regard to the character of |