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The calculus of the sines was not known in England till within these few years. Of the method of partial differences, no mention, we believe, is yet to be found in any English author, much less the application of it to any investigation. The general methods of integrating differential or fluxionary equations, the criterion of integrability, the properties of homogeneous'equations, &c. were all of them unknown, and it could hardly be said, that, in the more difficult parts of the doctrine of Fluxions, any improvement had been made beyond those of the inventor. At the moment when we now write, the treatises of Maclaurin and Simpson, are the best which we have on the fluxionary calculus, though such a vast multitude of improvements have been made by the for reign mathematicians, since the time of their first publication. These are facts, which it is impossible to disguise; and they are of such extent, that a man may be perfectly acquainted with every thing on mathematical learning that has been written in this country, and may yet find himself stopped at the first page of the works of Euler or D'Alembert. He will be stopped, not from the difference of the fluxionary notation, (a difficulty easily overcome), nor from the obscurity of these authors, who are both very clear writers, especially the first of them, but from want of knowing the principles and the methods which they take for granted as known to every mathematical reader. If we come to works of still greater difficulty, such as the Méchanique Céleste, we will venture to say, that the number of those in this island, who can read that work with any tolerable facility, is small indeed. If we reckon two or three in London and the military schools in its vicinity, the same number at each of the two English Universities, and perhaps four in Scotland, we shall not hardly exceed a dozen ; and yet we are fully persuaded that our reckoning is beyond the truth.
If any further proof of our inattention to the higher mathematics, and our unconcern about the discoveries of our neighbours were required, we would find it in the commentary on the works of Newton, that so lately appeared. Though that commentary was the work of a man of talents, and one who, in this country, was accounted a geometer, it contains no information about the recent discoveries to which the Newtonian system has given rise; not a word of the problem of the Three Bodies, of the disturbances of the planetary motions, or of the great contrivance by which these disturbances are rendered periodical, and the regularity of the system preserved. The same silence is observed as to all the improvements in the integral calculus, which it was the duty of a commentator on Newton to have traced to their origin, and to have connected with the discoveries of his master. If Dr • VOL. XI. NO. 22.
Horseley has not done so, it could only be because he was unacquainted with these improvements, and had never studied the methods by which they have been investigated, or the language in which they are explained. · At the same time that we state these facts as incontrovertible proofs of the inferiority of the English mathematicians to those of the Continent, in the higher departments; it is but fair to acknowledge, that a certain degree of mathematical science, and indeed no inconsiderable degree, is perhaps more widely diffused in England, than in any other country of the world. The Ladies' Diary, with several other periodical and popular publications of the same kind, are the best proofs of this assertion. In these, many curious problems, not of the highest order indeed, but still having a considerable degree of difficulty, and far beyond the mere elements of science, are often to be met with; and the great nuniber of ingenious men who take a share in proposing and answering these questions, whom one has never heard of any where else, is not a little surprising. Nothing of the same kind, we believe; is to be found in any other country. The Ladies' Diary has now been continued for more than a century; the poetry, enigmas, &c. which it contains, are in the worst taste possible; and the scraps of literature and philosophy are so childish or so old-fashioned, that one is very much at a loss to form a notion of the class of readers to whom they are addressed. The geometrical part, however, has always been conducted in a superior style ; the problems proposed have tended to awaken curiosity, and the solu. tions to convey instruction in a much better manner than is always to be found in more splendid publications. If there is a decline, therefore, or a deficiency in mathematical knowledge in this country, it is not to the genius of the people, but to some other cause that it must be attributed.
An attachment to the synthetical methods of the old geometers, in preference to those that are purely analytical, has often been assigned as the cause of this inferiority of the English mathematicians since the time of Newton. This cause is hinted at by several foreign writers, and we must say that we think it has had no inconsiderable effect. The example of Newton himself may have been hurtful in this respect. That great man, influenced by the prejudices of the times, seems to have thought that algebra and Auxions might be very properly used in the investigation of truth, but that they were to be laid aside when truth was to be communicated, and synthetical demonstrations, if possible, substituto ed in their room. This was to embarrass scientific method with a clumsy and ponderous apparatus, and to render its progress indirect and slow in an incalculable degree. The controversy
that that took place, concerning the invention of the fuxionary and the differential calculus, tended to confirm those prejudices, and to alienate the minds of the British from the foreign mathematicians, and the analytical methods which they pursued. That this reached beyond the minds of ordinary men, is clear from the way in which Robins censures Euler and Bernoulli, chiefly for their love of algebra, while he ought to have seen that in the very works which he criticizes with so much asperity, things are performed which neither he nor any of his countrymen, at that time, could have ventured to undertake.
We believe, however, that it is chiefly in the public institutions of England that we are to seek for the cause of the deficiency here referred to, and particularly in the two great centres from which knowledge is supposed to radiate over all the rest of the island. In one of these, where the dictates of Aristotle are still listened to as infallible decrees, and where the infancy of science is mistaken for its maturity, the mathematical sciences have never flourished; and the scholar has no means of advancing beyond the mere elements of geometry. In the other seminary, the dominion of prejudice is not equally strong; and the works of Locke and Newton are the text from which the prelections are read. Mathematical learning is there the great object of study; but still we must disapprove of the method in which this object is pursued. A certain portion of the works of Newton, or of some other of the writers who treat of pure or mixt mathematics in the synthetic method, is prescribed to the pupil, which the candidate for academical honours must study day and night. He must study it, not to learn the spirit of geometry, or to acquire the duvapeis eventinn by which the theorems were discovered, but to know them as a child does his chatechism, by heart, so as to answer readily to certain interrogations. In all this, the invention finds no exercise; the student is confined within narrow limits; his curiosity is not roused; the spirit of discovery is not awakened. Suppose that a young man studying mechanics, is compelled to get by heart the whole of the heavy and verbose demonstrations contained in Keil's introduction (which we believe is an exercise sometimes prescribed); what is likely to be the consequence? The exercise afforded to the understanding by those demonstrations, may no doubt be improving to the mind : but as soon as they are well understood, the natural impulse is to go on; to seek for something higher; or to think of the application of the theorems demonstrated. If this natural expansion of the mind is restrained ; if the student is forced to fall back; and to go again and again over the same ground, disgust is likely to ensue; the more likely, indeed, the more he is fitted for a better employment
of his talents ; and the least evil that can be produced, is the loss of the time, and the extinction of the ardour that might have enabled him to attempt investigation himself, and to acquire both the power and the taste of discovery. Confinement to a regular routine, and moving round and round in the same circle, must, of all things, be the most pernicious to the inventive faculty. The laws of periodical revolution, and of returning continually in the same tract, may, as we have seen, be excellently adapted to a planetary system, but are ill calculated to promote the ends of an academical institution. We would wish to see, then, some of those secular accelerations by which improvements go on increasing from one age to another. But this has been rarely the case; and it is melancholy to reflect, how many of the Universities of Europe have been the strongholds where prejudice and error made their last stand-the fastnesses from which they were latest of being dislodged. We do not mean to hint that this is true of the university of which we now speak, where the credit of teaching the doctrines of Locke and Newton is sufficient to cover a multitude of sins. Still, however, we must take the liberty to say, that Newton is taught there in the way least conducive to solid mathematical improvement.
Perhaps, too, we might allege, that another public institution, intended for the advancement of science, the Royal Society, has not held out, in the course of the greater part of the last century, sufficient encouragement for mathematical learning. But this would lead to a long disquisition; and we shall put an end to the present digression, with remarking, that though the mathematicians of England have taken no share in the deeper researches of physical astronomy, the observers of that country have discharged their duty better. The observations of Bradley and Maskelyne have been of the 'utmost importance in this theory; their accuracy, their number, and their uninterrupted series, have rendered them a fund of immense astronomical riches. Taken in conjunction with the · observations made at Paris, they have furnished La Place with the data for fixing the numerical values of the constant quantities in his different series; without which, his investigations eould have had no practical application. We may add, that no man has so materially contributed to render the formulas of the mathematician useful to the art of the navigator, as the present Astronomer-Royal. He has been the main instrument of bringing down this philosophy from the heavens to the earth; of adapting it to the uses of the unlearned ; and of making the problem of the Three Bodies the surest guide of the mariner in his journey acarss the ocean.
ART. II. Hours of Idleness: A Series of Poems, Original and
Translated. By George Gordon, Lord Byron, a Minor. 8vo. pp. 200. Newark. 1807.
The poesy of this young lord belongs to the class which neither
1 gods nor men are said to permit. Indeed, we do not recol. ject to have seen a quantity of verse with fo few deviations in either direction from that exact standard. His effusions are spread over a dead flat, and can no more get above or below the level, than if they were so much stagnant water. As an extenuation of this offence, the noble author is peculiarly forward in pleading minority. We have it in the title-page, and on the very back of the volume ; it follows his name like a favourite part of his style. Much stress is laid upon it in the preface, and the poems are connected with this general statement of his case, by particular dates, substantiating the age at which each was written. Now, the law upon the point of minority, we hold to be perfectly clear. It is a plea available only to the defendant; no plaintiff can offer it as a supplementary ground of action. Thus, if any suit could be brought against Lord Byron, for the purpose of compelling him to put into court a certain quantity of poetry; and if judgement were given against him; it is highly probable that an exception would be taken, were he to deliver for poetry, the contents of this volume. To this he might plead minority ; but, as he now makes voluntary tender of the article, he hath no right to sue, on that ground, for the price in good current praise, should the goods be unmarketable. This is our view of the law on the point, and we dare to say, so will it be ruled. Perhaps however, in reality, all that he tells us about his youth, is rather with a view to increase our wonder, than to soften our censures. He' possibly means to say, 'See how a minor can write! This poem was actually composed by a young man of eighteen, and this by one of only sixteen!'- But, alas, we all remember the poetry of Cowley at ten, and Pope at twelve ; and so far from hearing, with any degree of surprise, that very poor verses were written by a youth from his leaving school to his leaving college, inclusive, we really believe this to be the most common of all occurrences ; that it happens in the life of nine men in ten who are educated in E:gland, and that the tenth man writes better verse than Lord Byron.
His other plea of privilege, our author rather brings forward in order to wave it. He certainly, however, does allude frequently to his family and ancestors-sometimes in poetry, sometimes in notes; and while giving up his clain on the score of rank, ke takes care to remember us of Dr Johnson's saying, that when a