sential or highly conducive to the improvements in physical astronomy. 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 foreign 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 Mécanique 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 Horsley 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 department; 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 number 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 solutions 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 fluxions 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, substituted 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 took place, concerning the invention of the fluxionary 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 criticises 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 |