tried by the assumed test it would be found to want certain quantities. But these are the very quantities which must necessarily go out by the very principle above stated-terms which would add much complication in the reasoning, and have no effect in the conclusion, and have, therefore, by a universal rule of reason, been omitted in a compendious process, which does better without them. Now, one of Berkeley's arguments consists in a calculation by which he makes these quantities appear,-which the ordinary method of fluxions does not exhibit. He thus appears to falsify the ordinary process. But the reply to this objection is, that the omission of certain considerations, for the convenience of an argument, in which it is essentially implied that they are unimportant, is not a fallacy. The equation, in its first form, is a statement of the effective conditions of a question; and all Berkeley's objections could be met by simply adding et cetera. So far relates to the algebraic method: the answer is, however, completed by a consideration which will lead to the other point. The reason why the omission is of no importance is this: that the variables being supposed to pass through all the successive states of magnitude, while the increments, or decrements, diminish to a certain state, in which they cease to exist--the question is, to determine or prove this state. And this is determined by assuming the symbol expressing the increment to be = 0, the equation must then be such as to indicate the sought limit; and the quantities which were involved in the omitted part of the difference, must have ceased to exist. If the question were, what would be the result, supposing the variables to stop half way-all Berkeley's reasoning would be conclusive, so far as it applies. Against the conclusion itself, he offers another curious cavil. But the mathematical reader does not require this exposition; and for the reader unversed in such considerations, we have perhaps gone to the utmost limit of clearness. Berkeley's objection to any conclusion being founded on a ratio, of which the quantities are evanescent, has been anticipated by Newton, in a scholium, contained in the first section of the first book of his Principia. We shall, therefore, here conclude with the observation, that Newton's own statement of the intent of his method should have set Berkeley on a juster course of reasoning. "But because the hypothesis of indivisibles appears more hard, and, therefore, that method has been considered less geometrical, I have thought fit rather to found the demonstrations of the following propositions upon the first and last sums and ratios of nascent and evanescent quantities; that is, to the limits of those sums and ratios."* It is, if just, curious enough, that Berkeley's objection, to what he calls an erroneous equation, might be obviated by the addition of an "&c." If the reader should desire to see Berkeley's powers to advantage, he must look for them in his attacks upon the sophistry of others,-in the Minute Philosopher, and in portions of his Theory of Vision. We have, in this memoir, sufficiently noticed the first of these excellent compositions. *Sed quoniam durior est indivisibilium hypothesis, et propterea minus geometricæ censetur; malui demonstrationes rerum sequentium ad ultimas quantitatum evanescentium summas et rationes, primasque nascentium, id est, ad limites summarum et rationum deducere." His new theory of vision is curious for the mixed evidence it gives of the disposition of his understanding to the illusions of his own subtlety, and the clearness of his apprehension when judging of the fallacies of others. It indeed seems not a little curious how much of the sounder portion of his conclusions appears to be the result of his more unsound reasonings. In his disproof of the external world, he dissipates the erroneous doctrines of abstract ideas. His Theory of Vision, evidently composed for the same purpose, in the same manner draws from him the most admirable details, and the rectification of old fallacies. But the subject occupies much of the attention of the present time, and would lead us too far for any purpose connected with these memoirs. OF MICHAEL CLEARY very little is satisfactorily known, and we should, for this reason, consider ourselves absolved from any notice of him, but for the place which he occupies in the history of our Irish literature. This topic, so far as relates to the commencement of the present division of these memoirs, must be regarded as rather belonging to the antiquarian than to the historical biographer. But it is necessary, as briefly as we may, to account for our neglect of the very numerous poets who lived in the earlier half of the 17th century, and whose writings are yet extant. For this there are sufficient reasons: there are no materials for their personal histories, and their writings are not extant in any published form. The great celebrity of a renowned author of unpublished poetry might impose it upon us to give some account of his works; but great indeed must be the importance of the writings to which such a tribute would be excusable here, and whatever may be the collective worth of the bards and historians of the period included in these remarks, there are, individually, few instances which demand the distinction of a memoir. We might, by the help of some very accessible authorities, easily continue in this period the barren list of unknown poets, which helped to fill the vacuity of our previous period; but, on looking very carefully over those materials, we are unable to perceive what purpose would be served by such a waste of our space, already contracting too fast for the important matter yet before us.* In that portion of the introductory observations allotted to the gene • We should here apprize the reader that the seeming disproportion, between the space which we have given to the ecclesiastics and the literary persons belong. ing to this period, is to be explained by the fact, that the most respectable of our writers hold also a preminent rank among our ecclesiastical dignitaries of the same period. ral consideration of Irish literature, we have endeavoured to give some general notices of the character and importance of this unknown but numerous class of writings, which lie concealed, though not inaccessible, in the archives of colleges, and in public and private libraries. The individual whose name affords us occasion for these remarks, was a native of Ulster, and a Franciscan friar. He was early in life known as learned in the antiquities of his country, and as having a critical acquaintance with the Irish tongue. These qualifications recommended him to Mr Hugh Ward as a fit person to collect information for his projected history of the Irish saints, for which purpose he was sent to the Irish college in Louvain. The materials which he collected in the course of fifteen years passed into the hands of Colgan, by the death of Ward. Cleary at the same time collected materials, which he reduced into three volumes of Irish history, of which the letters are mentioned by Ware. He was one of the compilers of the "Annals of Donegal"—a MS. of the greatest authority in the antiquities of Ireland. His last work was a Dictionary of the obsolete words in the Irish Language, published in 1643, the year of his death. COLGAN was a Franciscan in the Irish convent of St Anthony of Padua, in Louvain, where he was professor of divinity. He collected and compiled a well-known work of great authority among antiquarians, and of considerable use in some of the earlier memoirs of this work. His writings were numerous; and all, we believe, on the ecclesiastical antiquities of Ireland. His death, in 1658, prevented the publication of many of them. Geoffrey Keating. BORN A.D. DIED A.D. 1650. KEATING, well known as the writer of an antiquarian history of Ireland-of great authority for the general fulness with which it preserves the traditionary accounts of the earliest times, though liable to some rather hasty censures for the indiscriminate combination of the probable and improbable into one digested narrative, and in the language of implicit belief. Such a work is, nevertheless, the most certain and authentic record of the ancient belief of the learned and unlearned of the land; and if the facts be not true in themselves, they evidently characterize the mind of a period, while, generally speaking, there is every reason to give credit to the more important parts of the narrative; and, above all, to the genealogical traditions of the ancient families of chiefs and kings. It is by no means a just inference that they who entertain superstitious notions, and believe the absurdest mythological fables and traditions, are, therefore, to be discredited in their statements of the ordinary facts of history; in the former, both the senses which observe, and the faithfulness which records, are wholly uninvolved the facts belong to a different class of things, and a man may believe a fable, yet speak truth in the concerns of life. When a historian's authority, or the authorities on which he writes, are to be questioned, the question must be,—is the relation honest, and are the facts such as to admit of natural error? Now, in Keating's history, the line of demarcation between truth and error will, in the main, be easily seen. It will be at once observed, that the mere fact of the existence of a large body of ancient literature, with all the extant remains and traditions of Ireland, undeniably prove the existence of some old state of civil order different from anything now existing, and as far removed from the savage state. Such a state of things must needs have left some record stamped with the form, and having at least all the main outlines of the truth; and it may be asked where this record-of which the absence would be more improbable than any part of Irish history-can be found, if not in those very traditions which are the genuine remains of Irish literature, and the authorities of old Keating. The facts are, it is true, often strangely involved with fable; but there is no instance in which the discrimination of an unbiassed intellect cannot at once make the due allowance. Keating studied for twenty-three years in the college of Salamanca. On his return to Ireland he was appointed to the parish of Tybrid, which he soon resigned. He is said to have been driven into concealment by the hostility of a person whose mistress he excommunicated. This person having threatened to murder him, he took refuge in a wood between the Galty mountains and the town of Tipperary; and in this retirement he wrote his history in the Irish language. He was buried in the church of Tybrid, founded by himself and his successor, in 1644. His history was translated into English by a Mr Dermod O'Conor, whose version is considered to have many inaccuracies. Another translation was since commenced by a Mr William Halliday, an Irish scholar of great reputation. His task was cut short by an early death. He had proceeded so far as the Christian era, and published a thin octavo, which has induced much regret among antiquarians that he did not live to complete his undertaking. Keating's other writings are of slight importance—they are a few poems and professional treatises. The Hon. Robert Boyle. BORN A.D. 1626.-died a.D. 1691. THE account of the early infancy of this most illustrious Irishman has been written by himself under the title of Philalethes. This period of his life was subject to more casualties and changes than are often known to occur in the maturer age of the generality of men; and this, indeed, in a manner and to an extent, which the character of our more civilized times can scarcely be conceived to admit of. At the age of three his mother died, and his intellect and moral temper were, at that early age, sufficiently mature to comprehend and feel this irreparable deprivation. The well-known activity of his ambitious father, the first earl of Cork-a man ever on the stretch in the pursuit of fortune and power-left his home often without a master, and his children without a parent. To these sources of casualty may be added the frequent necessity of removal and travelling through a wild and unsettled country, and under the charge of menials. On the road, the robber lurked among the rugged mountain-passes, and in the concealment of the bordering woods; on the British channel the pirate roamed without restraint; and the Turkish galley infested and defied the very coasts, which have now so long been sacred from such insults and dangers. At three years of age he had a narrow escape from being drowned, by the fall of the horse on which he was carried, in crossing a deep and rapid brook which was swollen by the rains. At seven, he tells us that he had a still more remarkable escape from being crushed to death by the fall of the ceiling of the chamber in which he slept. At three years of age he was sent to Eton, of which the provost was then Sir Henry Wotton, an intimate friend of his father's. Here he was placed under the immediate tuition of Mr Harrison, who, it is said, had the sagacity to discover the unusual capacity and the singular moral tendencies of his pupil, even at that early age, as well as the skill to adapt his moral and intellectual treatment to so promising a subject. Perceiving the indications of a mind unusually apprehensive and curious, he was careful that these happy inclinations should not want for exercise; and, as he had a willing mind to deal with, he avoided damping, in any degree, the voluntary spirit, by even the semblance of a constraint, which, in common cases, is of such primary necessity. By this method, so applicable in this peculiar instance, the ardour for information, which seems to have been so providentially implanted in the youthful philosopher's mind, became so intensely kindled, that it became necessary to employ some control, for the purpose of forcing him to those intermissions of rest and needful exercise for which boys are commonly so eager. Harrison meanwhile watched over the extraordinary youth with a zealous, intelligent, and assiduous care, ever ready to answer his questions, and to communicate knowledge in the form of entertaining discourse. The main object of his studies at Eton was the acquisition of classical knowledge, and he soon attained a considerable intimacy with the best writers of antiquity. He himself has mentioned, that the accidental perusal of Quintus Curtius had the effect of awakening his imagination, in an extraordinary degree, and thus. excited in his mind an increased thirst for historical knowledge.* * It is curious to compare the impressions communicated by the same circumstance to different minds. We extract the following from a well-known periodical:— "The effect which the same romantic historian is said to have produced on Charles XII., is, however, more direct and natural. In reading of the feats of |