paid to the manner as well as to the matter of elementary mathematical instruction. The Prefaces to two little Pestalozzian manuals, namely, "Lessons on Number," and "Lessons on Form,"* contain some valuable hints on this subject.

"When the true end of intellectual education shall be admitted to be, first, the attainment of mental power, and then the application of it to practical and scientific purposes, that plan of early instruction, which dwells long on first principles, and does not haste to make learned, will be acknowledged as the most economical, because the most effectual. Experience will show, that while superficial teaching may prepare for the mere routine of daily business, whensoever a question, not anticipated in the manual, occurs, none but the pupil whose faculties have been exercised in the investigation of truth, who is the master, not the slave, of rules, will solve the unexpected difficulty, by a novel application of the principles of the science.

"Writers on method have observed, that there is a certain order, in which truths present themselves to minds engaged in the original investigation of a subject; and that when the subject has been investigated, a different arrangement is necessary for the lucid exposition of the truths discovered. These views have been most unhappily applied in the early stages of instruction. For although the artificial order may be best calculated to convey knowledge to a mind already trained for its reception by previous acquaintance with similar subjects, it is by no means suited to the opening faculties of children. . . . . A preparatory course of instruction ought to be arranged, having for its object the training of the mind for the study of the science, rather than the communicating the knowledge of it. In this preparatory course, the order is determined by a consideration of the mind of the pupil; it commences with what is already known to him, and proceeds to the proximate truth; the more easy precedes the more difficult, the individual prepares for the general truth, the example for the rule."-Lessons on Number; (Master's Manual.) Pp. ix.-xi.

The Preface to the "Lessons on Form," asserts and illustrates the same Pestalozzian principle of teaching. Bacon has made an observation to this effect, "that a man really possesses only that knowledge which he in some sort creates for himself. To apply to intellectual instruction the principle implied in these words was the aim of Pestalozzi."

This principle is peculiarly applicable to the teaching of geometry, in consequence of this being a pure science. No science is less dependent on external nature. Every man is born a geometrician. In teaching geometry, therefore,

"The master must not dogmatize, either in his own person, or

* Published by Taylor and Walton.

through the medium of his book; but he must lead his pupils to observe, to determine, to demonstrate, for themselves.

"Aware that clearness of apprehension can take place only when the idea to be formed is proximate to some idea already clearly formed when the step which the mind is required to take, is really the next in succession to the step already taken; he will commence his instruction exactly at that point where his pupils already are, and in that manner which best accords with the measure of their develop

ment. . . .

"The master's next aim must be to cultivate the power of abstract mathematical reasoning. . . . . He will lead his pupils to deduce the necessary consequences from the facts which they know to be true, and then invite them to examine the object, and see whether their reasoning has led to a correct result."-Lessons on Form, pp. iv.-vi.

This gradual development of the power of abstract reasoning is connected, in these "Lessons," with a direct preparation for the study of Euclid's "Elements." Euclid's "Elements," observes Dr. Mayo, "exhibits a series of mathematical reasonings and deductions, arranged in the most perfect logical order; so that the truths demonstrated rest, in necessary sequence, on the smallest possible number of axioms and postulates. But, admirable as it may be in itself, viewed simply in relation to the science, it is not, viewed pedagogically, an elementary work. It is fitted for the matured, and not for the opening mind."-Lessons on Form, p. vii.

The principle, in short, which Dr. Mayo, as a disciple of Pestalozzi, is anxious to bring out, is, that " Every course of scientific instruction should be preceded by a preparatory course, arranged on psychological principles. First form the mind, then furnish it."-Lessons on Form, p. ix.

Our notice of the "Educational Magazine" has extended so much further than we at first intended, that we shall cut it abruptly short, by giving one or two passages from a kind of reply to the article on "Learning by Heart," which we have quoted above with general commendation, in which the writer urges an objection against the views there maintained. Considered as an objection, this writer's reasoning appears to us to be foreign to the point at issue; but the principle which he lays down is a valuable one, taken simply by itself. It may also serve as a correction to those incantious passages in Mrs. Tuckfield's "Letters to a Clergyman," to which we have already adverted :

"Does not the notion of explaining beforehand go against what I would call a sort of religious instinct, which may be seen in children? There is to them a kind of mystery in the unintelligibleness of scripture; they feed on a little, a few words and sentences here and there, and, as it were, gaze on the rest. They have a kind of faith, that though what they learn is beyond their understanding, it is all very good, and good for them; it is God's word, and it is about God and His doings.. And is it clear, because they cannot explain words, nay, do not understand many, or most of them,

that they have no just notion of the meaning of what they learn? May they not have deeper thoughts than we can measure, or they express? Thoughts with a freshness and instinctive truth about them, beyond a teacher's power to communicate, by giving them just notions of the sense of words; thoughts such as we have ourselves had in our childhood about passages of scripture, of which we may still retain a little of the fragrance, though we cannot recall them. Indeed, what very deep answers children will make; unconscious, indeed, that they are deep, but prompted by something within that they are true!"-Educational Magazine, vol. i. p. 322.

Our next educational article will treat of Infant Schools. In the mean time, we can recommend the "Model Lessons for Infant Schools," as calculated to afford considerable assistance to Infant School teachers and nursery governesses, by furnishing them with materials for instruction; and the "Letters on Infant Schools," as furnishing a very simple account of Pestalozzi's methods of teaching, which may serve as an introduction to treatises of higher pretension.

Narratives illustrative of the Contests in Ireland in 1641 and 1690. Edited by T. CROFTON CROKER, Esq. Printed for the Camden

Society. London: Nichols & Son. 1841.

CIRCUMSTANCES have prevented our previously noticing this contribution, under the sanction of the Camden Society, towards the illustration of two most interesting periods in Irish history; periods, even now emphatically spoken of, says Mr. Croker, by the Irish peasant, as the times of the troubles.' The Narratives themselves are valuable, as the views of cotemporaries, who were actively engaged in the events described by them.

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The Siege of Ballyally Castle, as the first Narrative is entitled, records the unsuccessful attempt of some followers of the Earl of Thomond, in the winter of 1641, and the spring and summer of the ensuing year, to obtain possession of the castle, which was held by the widow of Maurice Cuffe, a merchant, of English extraction, under lease from Sir Valentine Blake. The demand of the Roman Catholic powers for the surrender of the fortress was treated with disdain by the merchant's widow; nor did her landlord meet with greater respect when he requested his tenant to deliver up Ballyally to the legal authorities. "By the help of God," said the lady, "the castle should be to the hazard of life kept possession of for the king's majesty's use against any that should oppose or besiege it," whilst, at the same time, she coolly asked her landlord for "a help of powder" to assist in the defence thereof, with which counter request Sir Valentine Blake, we are gravely assured, "did not comply.

For thirty-six days the siege went on with varied success; and though the enemy, as the narrator says, "would daily in their sight drae forth there skenes and swordes, flurishing them, showering many dangeroes othes that ear long thaye would drae us forth and hack

us to peeces, terming us Pewritan rogges, and all the base names that might bee," the castle held out in despite of the oaths, the hugh sows, and the leathern piece of cannon. The description and fate of the last weapon of offence deserves insertion :

"The said piece was aboutt 5 foote in length, not bult upon caredge, but fastened in a stocke of timber. This goon thaye planted in the great trench, neere the Castell, to be redy when thaye found accation to discharge har, the diametre being aboutt 5 inches; the lethar thaye made har withall was leetell better than halfe tand.-The next morning thaye made triell of there lethern gun at us, but shee only gave a great report, having 3 of powthar in har, butt let fly backwarde, the bullett remaining within."-Pp. 18-19.

Except as a record of the barbarous manners of the Irish of that day, and the low state of their science of war, this narrative fails in elucidating any important point in the history of the time; unless the following quotation may be taken in evidence either of the reality or the uncertainty of the intentions of the king's friends in Ireland :

"Vowing that shortly Sir Phelim O'Neale, and at least 40,000 souldars, would come in to Thomond and not leve a Protestant living, praing hartely for them, pretending that they then fought for hem; but within a short time after thaye pretended that thaye were wholy the Queenes armey, and that shee and har mother was in the north aiding them, but noe Protestant admitted to luck uppon har. This nott sudenly altard, and then thaye were all for the king, vowing deeply that thaye were his Majesty's Catholic foreces."-P. 16.

The second narrative is as well more interesting as important than its predecessor. Under the title of "Macariæ Excidium," or the destruction of Cyprus, written originally in Greek by Philotas Philoxypres, translated into Latin by Gratianus Ragallus, and Englished by C. O'K., we have Colonel Kelly's account of the last struggle, between James and William, from the fatal defeat at the Boyne, to the final conquest of Ireland by the troops of William of Orange. Bred in his infancy at St. Omers, an accomplished scholar, a brave soldier, distinguished for his success on behalf of the king in Ireland, for his fidelity to the ill-fated Charles and his banished son, his persecutions during his residence abroad, he returned with his royal master, highly esteemed for his learning, his loyalty, and his great services at home and abroad. In the reign of James he was member for the shire of Roscommon, and a privy counsellor of Ireland; and naturally devoted to that family for whose title to the throne he had fought and suffered, and educated in the Roman Catholic faith, he transferred his devotion to the last of the Stuart kings, and endeavoured to support with his abilities, his piety, and his knowledge, the falling cause. The narrative of one so closely united with the cause of James as Colonel Kelly, even had he allowed his feelings for the unfortunate Stuarts to have biased his account, must have commanded respect from those who might disagree with the views of the author. The extracts which we shall make from this narrative will, we believe, convince our readers that

we are not over-estimating the knowledge and honesty of the writer, when we regard this his short account as most important and trustworthy. The effect of the colonel's testimony is to exonerate the Irish followers of James from the common charge of cowardice and infidelity, and to ascribe the successes of William to the abandonment of the Irish troops by James, their neglect by their French allies, and their betrayal by the treachery of Tyrconnell.

When James returned to Ireland from the court of France, the city of Derry, and a few other places of little importance or strength in the province of Ulster, adhered to the cause of the Prince of Orange. Instead of proceeding with vigour in the prosecution of the siege of Derry, and taking advantage of the fiery spirit of his Irish troops, James began to temporize and vacillate. By his refusal to summon the Roman Catholic bishops to the assembly of the states, or to mitigate the laws of Elizabeth against the Romanists, he threw a cloud over the enthusiasm of his Roman Catholic subjects, whilst his abolition of the act of Charles, by which the Cromwell grants were confirmed, alienated the minds of his Protestant supporters. At the moment that Schomberg was landing in Ireland, and not till then, James sent forth his commissions to raise more troops to resist the invasion. The entire summer, however, was wasted. Schomberg, acting on the defensive, never appeared out of his trenches; whilst James, by neglecting to force the English camp when but slightly manned, lost a fair opportunity of checking if not putting an end to the war, instead of affording to Schomberg the glory of a successful resistance, and cowing the minds of his own soldiers by idleness and delay. The young commanders, however, longed for the winter gaieties of Dublin, and persuaded James to disband his new levies and return to the capital without any advantage, there to spend "the time for serious consultations and necessary preparations, in revels, gaming, and other debauches unfit for a Roman Catholic court."

"The rumour that spread of Theodore's (William's) coming in person to invade Cyprus (Ireland) that summer, encouraged his party there to endure the last extremity, in hopes of seeing now a speedy end to the war. But it did not so much alarm Amasis (James), who seemed resolved, in case Theodore (William) had not come over that season, to make no great effort to expel the Cilicians (English) out of Cyprus (Ireland). This resolution was believed to proceed from a wrong maxim of state, which his evil counsellors prompted him to embrace, that the only way to recover Cilicia (England) was to loose Cyprus (Ireland); for they persuaded him, that Cyprus (Ireland) being once reduced, the Cilicians (English) would immediately recall him, as they formerly brought in his brother Pythagoras (Charles). But this was a favour he could not hope for, whilst he headed a Cyprian (Irish) or a Syrian (French) army. And so, like the dog in the fable, he must let go the substance to snatch at the shadow.However, this grand design, communicated to only a few favourites, must be carried on so cleverly as not to be perceived by Antiochus (Lewis XIV.) or the old Cyprians (Irish); whereupon Amasis (James) made it his business to get Demetrius (Count d'Avaux), the Syrian (French) ambassador, and Rosines (M. de Rosin), a