descendants of those who fought at Blore-heath yet remain in Cheshire; while, in Cambridgeshire, a district neither by its situation nor beauties likely to excite any great competition in purchasers, one name only (that of Cotton) remains of the principal families who were returned under the commission of Henry VI!

With respect to the comparative merits of the volumes already published, that of Cambridgeshire is indisputably the best, a distinction for which the authors and their readers are equally indebted to the personal investigations of the present Bishop of Cloyne, when resident in Emanuel College, and of Dr. Charles Mason, of Trinity College, who died rector of Orwell, and Woodwardian Professor, about the year 1770. The account of the University, in which we have detected no errors, but have, as usual, to deplore many omissions, will principally tend to awaken or revive the regret of antiquaries, that no great and authoritative work on so interesting a subject has ever been undertaken under the auspices of that learned body. Will the Musæ Severiores of Cambridge never unbend to the pleasing and grateful task of commemorating, from authentic and original records, their founders and benefactors? And can the overflowings of their wealth be turned into a more delightful channel than that of perpetuating, by the graver, countenances which they now revere on board and canvas, and editices which as yet afford comfort and elegance and devotion to her retirement? We say, as yet afford,' for let it not be forgotten, that in the revolutions of human things, neither the one nor the other are immortal; while, in every event, excepting that of total and overwhelming barbarism, the multiplying power of the press will infallibly preserve the resemblance of both when the originals are no more. What would now be given for contemporary histories, and contemporary drawings, of the religious Houses in their perfect state? Crowland was the mother of Cambridge; and what the parent is, the daughter may become. This inattention is the more to be deplored, or, rather, the less to be excused, because the ice is already broken, and the remaining difficulties are principally modern. Mr. Baker, a nonjuring member of St. John's College in the earlier part of the last century, and a name yet venerated on that very account, by those who will not copy after his example, spent a long life, and a genius capable of better things, in making collections, which yet remain, for a rival work (in his hand it would have been a very superior work) to the Athena Oxonienses, or to the Historia et Antiquitates of the same University by Wood.

With these encouragements to such an undertaking, the succinct, though not inaccurate account of Messrs. Lysons', consisting of fifty-six pages, which, with the exception of some general and very

good

good observations on architecture, professes to inform the world of what deserves to be known of this illustrious seminary, and the ancient town dependent upon it, will certainly oppose a very feeble impediment. Would that no impediment more formidable existed in the incurious spirit of their own institutions! With the same exception, and with the fear of Mr. Bentham before their eyes, our authors prudently dispatch the city of Ely, and its glorious Cathedral, in eight pages: but such an example, the first of any importance which has occurred in their alphabetical career, ought to have instructed them, that elaborate topical works, when they interfere with general and superficial views of a subject, are hinderances instead of helps, and ought, with a respectful reference, to have been wholly declined. Even in these unceremonious days, it is accounted a rudeness to cross the walk of a dignitary in his own cathedral; and we really think, that the merit of having illustrated so fine a subject as Ely in the style of Mr. Bentham, confers a literary dignity entitled to no less attention.

On the whole, considering the laborious work of Messrs. Lyssons as a series of volumes for the purpose of reference, and, more especially, as to the successive descents and alienations of property down to the present day, (an article of information on which they appear to have greatly laboured,) we think it entitled to much and general commendation. The arrangement also is clear, and the style perspicuous and unaffected. These are praises which belong to the authors; the defects of the work arise out of the plan itself -perpetual abridgement where detail was loudly called for, and mortifying transitions, from one subject to another, at the moment when interest and anxiety were beginning to be excited. So far, therefore, as the work before us may, by its sweeping progress, have a tendency to check the spirit of more profound and elaborate inquiry on limited subjects, and, more especially, as it may prevent a great national plan for perfecting a body of English topogra phy, we cannot, without offering violence to our own hopes and feelings, be very cordial in wishing for its success. If, however, (which seems probable enough,) it should, after all, turn out that the vigour of particular understandings is not to be deterred from working the mine because others have already scarified the surface; or if the national energies, in an age when the power of combination is fully understood, should still operate to fill up the great chasms which exist in our antiquarian library, with all the industry of private research, and all the splendour of public munificence, we shall willingly applaud our authors for having shed a previous light upon the subject, if no where powerful, yet no where uncertain, if never dwelling long, or strongly thrown, on any, even on the most interesting object, yet calmly progressive in its course, and pleasingly expansive in its diffusion.

Y 2

ART.

ART. IV. The Principles of Fluxions: designed for the Use of Students in the University. By William Dealtry, M. A. Professor of Mathematics in the East-India College, and Fellow of Trinity College, Cambridge. Royal 8vo. pp. vi. 376. Cambridge, Deighton; London, Rivingtons, 1810.

F

Of all the inventions which have been at once the fruit and the reward of human genius and industry, that of Fluxions is the most brilliant, whether contemplated as the effort of an exuberant imagination, or with a view to the importance of its applications, and the immensity of the subjects which it embraces. Other mathematical inventions apply each to its individual subject, and cannot be brought to bear upon others: but this is an universal instrument, operating upon a variety of problems which could not be touched by any of the methods of the ancient geometers; and, by the generality of its means, bringing under one point of view theories and sciences which had been previously considered as insulated and independent. By it are investigated the laws which hold together the minutest particles of bodies; by it also are developed the grand principles which regulate the motions, and preserve the harmony of the universe; and the rapturous language in which Halley speaks of Newton's discoveries, applies with singular propriety to this the most sublime production of his genius.

That the honour of an invention so diversified in its applications, and so fertile in the production of important results, should have been contested by different persons and nations, is not to be wondered at: yet we cannot but regret that, at the distance of more than a century from the era of the invention, an attempt should be made by a learned foreigner, M. Bossut,* to revive the discussion in such a manner as to involve it in additional obscurity and misrepresentation; and that an English mathematician should be found so insensible to the reputation of his country, as to publish a translation of Bossut's work, unaccompanied by a single word of censure or correction.

As the subject of Fluxions is not likely to come before us very frequently, and as we feel too much for our countrymen to be silent, while we see them stripped of their hard-earned laurels, we shall avail ourselves of the opportunity furnished by Mr. Dealtry, to prove that Newton is not only the inventor but the sole inventor of the Fluxional analysis; and farther, that the French, in endeavouring to rob him of this honour, have acted upon a

* Histoire des Mathematiques. Translated by Bonnycastle.

principle

principle which they have uniformly pursued with regard to English men of science.

We shall not waste the time of our readers in detailing the oft refuted story that Newton, the friend and pupil of Barrow, drew from him the hints which he afterwards worked up into his discoveries;' nor in proving that Newton was the first inventor both of the direct and inverse method of Fluxions; for that is expressly acknowledged by Montucla: but shall content ourselves with inquiring, whether Leibnitz really stole his invention from Newton, while he pretended to have discovered it; and whether the continental philosophers, especially the French, continue to ascribe the invention to Leibnitz, notwithstanding they have sufficient evidence of the contrary?

Now it is beyond dispute that Newton invented the general method of series, and the direct and inverse method of fluxions, in the course of the years 1664, 1665, 1666; that in letters circulated among his friends in those years, he developed the principles and explained the notation of those methods: and it is equally a fact, never called in question by M. Leibnitz or any of his advocates, that the letters containing these discoveries, or at least copies of them, were sent by Collins to Leibnitz in 1672; that Oldenburgh made similar communications early in 1676; and that Newton himself communicated to Leibnitz, first a brief sketch of his method in 1672, and in 1676 an account of his Treatise, in which he described his theory, (not in dark characters, as Bossut insinuates,) and the various kinds of problems to which it would apply. Leibnitz indeed acknowledges that in 1676, being in England, he staid some days in London, where he became acquainted with Collins, who shewed him several letters from Gregory, Newton, and other mathematicians, which turned CHIEFLY on series.' Leibnitz, then, was acquainted with the principles of Newton's methods before the year 1676; and we have evidence that in 1675, he desired Oldenburgh to procure from Mr. Collins, Newton's methods of solving certain problems which he did not understand.

The natural inference from all this, is that Leibnitz borrowed his first, if not his entire notion of the new analysis from the communications of Newton and his friends. Before we decide, however, we must take into account, Leibnitz's reply to Oldenburgh in 1677, in which he says, he has long since treated the subject more generally' than Slusius, in his method of tangents; and look to what Bossut calls the ever-memorable paper' of 1684, which contained the elements of the Calculus Differentialis. This paper, in truth, relates only to a few questions concerning tangents, and to the method of maxima et minima; but its author does

Y 3

does not, even then, meddle with the problems of the higher geometry; though Newton had solved them ten years before. This was Leibnitz's first public essay on the subject, written eight years after he had observed in a letter to Newton- What you seem to say, that almost all difficulties (with regard to fluents) may be reduced to infinite series, I cannot come into; for there are several problems so intricate and perplexed, as not to depend either on equations or quadratures;a remarkable declaration, made, unfortunately for the credit of Leibnitz's veracity, within six months of the time when he affirmed that he had long since treated the subject more generally.

Leibnitz's second essay on the new analysis was given in 1689, when he published as his own the chief propositions of the Principia, (a work which Newton had sent him,) in three different papers, entitled, Epistolæ de lineis opticis; Schediasma de Resistentia medii et motu projectilium gravium in medio resistente; et Tentamen de Motuum Cælestium Causis. In these he pretended that he had discovered all those propositions before the Principia appeared; and the better to appropriate to himself the principal of them, he thought fit to subjoin his own demonstration: here again, unluckily for Leibnitz, his new demonstration, purposely varied from Newton's, was erroneous; he was obliged to retract it himself; and thus proved that at this period he knew not how to work with second fluxions.

Can any one, after the perusal of these facts, believe for a moment that Leibnitz was really the inventor of the new analysis? Is it not the fair inference, that whatever be the merits of Leibnitz in other respects, he owes the invention of the Differential analysis entirely to Newton; and that he merely devised his new notation to disguise its origin?

But we will go still farther, and shew that this adoption of another's discoveries was consistent with the general habits of Leibnitz. In 1669, amongst other series by Newton, one for finding the arc of a circle from the sine-and, in 1671, another by James Gregory for finding the arc from the tangent, were sent to Collins, who, according to his usual custom, communicated them to several persons on the continent. In 1674, Leibnitz mentions, in a letter to Oldenburgh, his being possessed of the first series; and in 1675 both Newton and Gregory's series were sent by Oldenburgh to Leibnitz. But in 1676 Leibnitz dropped his pretensions to the first series, not being able to demonstrate it, and sent to Oldenburgh, as his own, that of Gregory, with a demonstration. Yet, in 1713, papers were discovered which compelled Leibnitz to acknowledge that the series which he formerly pretended to be his own, was stolen from Gregory! In 1676 he asserted