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sical and algebraical abstraction are operations of mind so different, that one cannot well comprehend by what accident they ever were confounded. The objects of metaphysical speculation are the immaterial properties of an immaterial being, intangible even when concrete, demonstrable only as far as probability can reach, and incapable of any emblematic representation. But mathematical inquiries are, for the most part, directed to sensible objects. In geometry, these objects are absolutely tangible. In pure mathematics, they are magnitudes. In mixed mathematics, they are either facts derived from actual experiment, or hypotheses assumed upon analogy, But in every case, even when most disengaged from matter, they cannot just ly be called abstract; for the understanding considers then, in their conventional representatives, a line, an angle, an x, or a y, with as little regard to abstraction, as if the subject, together with its properties, was absolutely submitted to mensuration. To this species of abstraction the French mind is not unapt; and the rigor of mathematical demonstration may form an amusing episode, in the midst of great usual laxity of ratiocination.

The superiority of the French in this science, however, is not ancient; neither do they, at this moment, so far surpass us, as we, in the very long account of a general balance, would be found to have surpassed them. One of the earliest European mathematicians was the venerable Bede. Alcuin gave lessons in this science to Charlemagne. In the 13th century, Sacrobosco, or plain John Holywood, a native of Yorkshire, was professor of mathematics in Paris. Since that time, let the following English mathematicians, and their discoveries— Roger Bacon, Lord Bacon, Lord Napier (logarithms), Briggs (ditto improved), Harris, Harriot, Lord Brounker (continued fractions), Wallis (arithmetic of infinites), J. and D. Gregory, Barrow, Hooke, Hamstead (fixed stars), NEWTON, Bradley (aberration of stars) Hadley, Taylor (increments, his fundamental theorem), Sanderson, M‘Laurin, Simpson, Walmley, Collins, Robins, Landen (residual analysis), Waring, Atwood, Maskelyne, &c. be compared with the following French mathematicians, and their discoveries-Cardan, Victa, Des Cartes, Gassendi, Fermat (de max, et min. theory of numbers), Pascal (probabilities), D. J. and F. Cassini, La Hire, Clairault, N. and D. Bernoulli, La Caille, Bouquet, Jacquiers, Le Seur, Maupertuis, Ricard, Condamine, D'Alembert, &c.—and an immense preponderance will appear in the depth and comprehensiveness of the views and methods discovered in this country, Since the era which may justly be called the mathematical age of Newton, we have rather remained in the inaction into which our admiration of his stupendous mind had plunged us; and the French, particularly when the name of La Grange a Piedmontese is added, could produce a longer list of recent mathematical discoverers than we could. A reproach, indeed, has been made to them, that they have indulged too much in the metaphysics of analysis, and surrounded it with too many difficulties. But this is a dangerous principle in science. Whatever is powerful must be difficult to wield; and if, by bolder methods, new truths are attained, or older systems finally admitted or rejected, the world must not complain of the time or labour which they cost. It must be stated, however, that the methods by which the modern French mathematicians have advanced, are of Newtonian invention, and among the gradual efforts of the mind of man. We are far from admitting 'either that the improvements of La Grange, La Place, &c. bear any thing like the ratio to Newton, which Newton bore to all his predecessors.

Astronomy is so nearly connected with Mathematics, that we have put, under that head, many names which might be inserted here. Beside the greater vigour of reflexion which is a part of our temperament, and a more inquisitive spirit for great' researches, as islanders we have always had the additional stimulus of more extensive navigation, warlike, commercial, social, scientific; and we have always maintained a decided superiority, by wider views of astronomical phenomena and systems, even more than by the detached facts and observations we have added. Much as we excel the French in the long balance of mathematical discovery, we should say, that, in the vast conceptions of the heavenly bodies, we have a still more decided superiority. We are ready to abstract all that Newton has done ; the fact and theory of gravitation; the laws of motion of the heavenly bodies; the mathematical refutation of the vortices of Des Cartes, &c.; and we say, that the French cannot produce any discoveries of theirs comparable to the following—the first which occur to us upon a hasty recollection ;-aberration; the changes of position which have taken place among the stars called fixed; the revolutions of some round others, now well ascertained; the measurement of the diameters of some, not long since deemed impossible; the translation of our solar system through absolute space, demonstrated by observation, after being long suspected, upon one of the great general ideas, entirely English, which elevate the whole human mind~ In a

• system, the parts of which are free to move or to be at rest, • and which are governed by the usual laws of gravitation, the - instant that any one of them is in motion, the others cannot « remain quiescent.' We might add, too, all that relates to double and coloured stars, &c.

In Optics we have a like superiority. One of the earliest works published on this science, since the revival of letters, was by.Peccam, archbishop of Canterbury, contemporary of Roger Bacon. The first notable French optician was Des Cartes, lo whom it belongs to have explained the laws of refraction, upon plain mechanical principles ; to have brought Dioptrics into the form of a science; and to have added much to the speculations of A. de Dominis on the rainbow. This philosopher, however, was not satisfied with what really belonged to him, but took possession of the discoveries of Snellius, whose papers, as Huy-. ghens solemnly declares, upon his own positive knowledge, Des Cartes had rummaged ; and whose law of reflexion and refraction having fallen into one of the Frenchman's vortices, he brought to light again, in somewhat an altered form, as the result of his own researches. From Des Cartes till Malus, the French made no leading discovery in Optics; yet that period includes the most remarkable progress of this science. They do, indeed, claim Mr Dolland as a Frenchman. This requires a few observations: and we must again sav, that we wish some general law were fixed, about this kind of national property; and a treaty made to assign discoveries and inventions to the countries either where their authors were born, or where they reside. In the present anarchy, the French rest their claims upon both of these grounds, and carry it down to generation after generation. Now John Dolland, of achromatic memory, was born January 10th, 1706, in Spitalfields, of Norman Protestant refugee parents; consequently, as he would have been liable to be hanged, and that without the privilege of a jury de medietate lingua, had he been taken in arms against England, we cannot give him up to any claim from France. He was a true-born Briton; and we are proud of him. But, let us suppose that he was born in France; we assert that the most disastrous principle-unless reciprocity be excluded—which the French could advance, would be the very one now in question; though it certainly is the true and fair principle upon which justice should be distributed; for, of the persons already named in this article, they would lose Cardani, Dom. Cassini, the Bernoullis, La Grange, and Berthollet; while, of our much longer lists, the only names about which a doubt could be raised are,

Herschel, a subject of the King of Great Britain, though not a Briton born; and Black, whose father was a British winemerchant, resident at Bourdeaux, where his son was born indeed, but where he did not end the years of his childhood, being sent to his father's native town, Belfast, for the purpose of receiving a British education. Dom. Cassini was not naturalized in France till he had attained the age of 48. We have looked over the names of persons celebrated at different times in both countries, and in various departments of intellect; and we have found, that the number of foreigners who have contributed to the glory of France, and who have, in consequence thereof, been received into the bosom of that country, and claimed as its own, is about five times as great as that of such foreigners in England. In this calculation are included two Frenchmen, to whom our country is at this moment indebted, Mons. Didot, who has established a manufactory of paper of indefinite length; and, much more, Mons. Brunel, whose block machinery is one of the wonders of our naval arsenals. We know the French will attribute this to their amenity to strangers; but we could refute this argument by our much more extensive and enlightened hospitality and benevolence, so often and so largely exercised, without hope of benefit or return.

The discovery of Malus is certainly very meritorious; but what he has termed polarization, was at least suspected by Huyghens long since; and Dr Higgins, in his Essay on Light, maintains that the polarity of all parts of matter varies in the different arcs of each atom. To Malus we can oppose Dr Herschel; and to the French corps de reserve we can bring up Brewster, Dalton, Leslie, Wollaston, Young, &c. over whom it would not be easy for the world combined to obtain a victory at this moment.

The accusation brought against Des Cartes by Huyghens relative to the papers of Snellius, reminds us of another instance of plagiarism in the same philosopher. Sir Charles Cavendish showed Roberval Harriot's algebra, from which Des Cartes had stolen the method of placing all the terms of an equation on one side, and making them = 0; and, upon further examination, it was found, that he owed many of his discoveries in algebra to the same source.

The names which could be brought forward, in France, as having contributed to the advancement of the sciences, comprised under the general title of Natural Philosophy, are wonderfully few; and the discoverics made by French philosophers,

in this branch, are rare, and not very generally in the first order of importance. Des Cartes, Pascal, Réaumur, are no doubt brilliant exceptions: But what a host of overpowering names and facts might we not oppose to them !_Gilbert, two Bacons, Boyle, Hooke, Newtori, Halley, Gray, Hawkesbee, Dolland, Hutton, Priestley, &c.

In Natural History, the French possess a host in the name of Buffon, who, with considerable defects as a philosopher, yet ranks very high as a poctical thinker, and an eloquent discourser upon the works of Nature. But when he came to generalities, he showed the usual failings of his country intellect; and drew most rash and hasty conclusions from limited premises. His works, however, will always be a favourite study of those who take delight in adequate representations of the wonders of the universe.

A branch of natural history which the French have altogether raised to the rank of a mathematical science, and which, in this point of view, is in a great measure their own, is Mineralogy; or, in a more restricted sense, Crystallography. They were not indee: the first who discovered the tendency of certain minerals, always to assume regular forms; but Romé de Lisle, and infinitely more the Abbé Haiy, have deciuced from this property such an admirable series of laws, so beautiful a system of nature, that any previous knowledge which others may have had of the mere leading fact, does not in the least diminish their glory. In England, we have not achieved any thing comparable to the immense crystallographic labours of the Abbé Haüy; but, notwithstanding the pompous establishments for diffiising mineralogical knowledge in France, and the very magnificent cabinet at the King's garden in Paris, with many other public collections, an acquaintance with minerals is much more common in Britain. We defy the French, in all their mineralogical annals, to produce such an example of zeal, talent, and public spirit, as the single geological society of London has evinced, during the few years it has existed and such a mass of facts and observations as it has communicated to the world within so short a period. If we were inclined to follow the example of the French, we should claim the labours of the Count de Bournon as ours, for they were performed and published in London.

Is it because Botany is one of the sciences which demands the smallest range of intellect, that the French have made themselves more conspicuous in it than in most others– and may absolutely claim a superiority over England! Though Ray in

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