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considered. But these analogies, though in my apprehension not inapplicable, would carry me much too far, were I to overpass the precincts of studious, and trench on the sphere of active life. Besides, I have already a good deal transgressed my forethought limits, pretty much as we find gentlemen too often do in their building estimates.

D'ALEMBERT.

The Men of Letters and Science, who flourished in the Times of George III. By HENRY LORD BROUGHAM, Member of the National Institute of France.-D'ALEMBERT.

LORD BROUGHAM introduces the present article with an emphatic eulogy on the study of the mathematics. A higher or more apposite theme of praise could hardly, indeed, we may consonantly affirm, be chosen, for they constitute not only an important branch of the great scientific circle, to every section of which, while quite independent, in their own sphere, of all extraneous support, they are essential auxiliaries, and scarcely less are the arts tributary to their aid, but, again, their pursuit, in its absorbing empire and concentrated mental action, ensures to the devoted aspirant a self-resource and refuge from the world's turmoil. To this mighty influence on human attainments, with which mathematics are so extensively interwoven, and which induced Plato to make their culture an indispensable qualification of admission to his Academy—“Ουδείς αγεωμέτρητος εισίτω, -as it suggested to Pythagoras the axiom, that they were

* Diogenes Laertius, tom. i., edit. Meibomii Amsterd. 1692, 4to.

essential to the well-being of man, as his ruling guide in every art and science, mechanical or philosophicτοὺς ἀριθμους αἰτίους εἶναι τῆς τούσίας-his lordship superadds a scarcely inferior moral effect. "They occupy," he asserts, "the attention entirely, abstracting it from all other considerations. Sir Isaac Newton is said to have forgotten the season of his meals; and greater tranquillity is possessed by none than by mathematicians." This asserted serenity of mind and temper, the retributive homage, we trust, of his lordship's personal experience, in its general application, does not always bear the test of inquiry; but what is related of Sir Isaac, we may state, was exemplified to a much greater extent by the celebrated Vieta, who often spent two or three successive days in immovable devotion to a special study, such as the mathematical analysis, which owes much to him. And Madame Perier, the sister of Pascal, informs us that her father, (one of the originators of the Academy of Sciences, with the Minim, Father Marsenne, Roberval, and others, previous to its royal institution in 1666,) conscious of the predominant passion in himself, had removed from his son's access every volume or object of scientific attraction, lest the early indicated predilection should impede the child's necessary classical tuition. The precaution, however, proved in vain; for we are assured that, as if intuitively, without book or teacher, by a process of his own, which his sister explains, he advanced to the thirty-second problem of Euclid's first book. A similar apprehension had induced Gallileo's father to counteract his son's instinctive astronomical propensities, but with equal failure of success. These illustrations of his views his lordship has not adverted

to, nor, again, to the striking fact of Pascal's relief from, or insensibility to, an excruciating tooth-ache, when engaged intensely in solving the problem of the curve called "La Roulette, or Cycloid;" a salutary effect of science, without example, it would seem, in the time of Shakspere, who makes Leonato say to his brother Antonio, (Much Ado about Nothing, Act v., scene 1,)—

"There never was yet philosopher,

That could endure the tooth-ache patiently."

None of our great dramatist's commentators have referred to this fact, which probably was unknown to them, as little in their course of reading.

But the most signal proof or instance of this engrossment of the mind, also omitted, was that of Archimedes, who, amidst the tumult of a stormed city, and encircled by a soldiery panting for blood and rapine, was found, in total abstraction from the frightful scene, tracing the figures of a geometrical problem-"intentum formis quas in pulvere descripserat," as stated by Livy, (lib. xxv., 31.) Plutarch, however (in Marcello, p. 562, edit. H. Stephani, 1572,) is more explicit. He tells us that, when seized by a soldier, Archimedes earnestly entreated a short respite to conclude his solution, and on the soldier's refusal, while resisting an attempt to drag him to Marcellus, was slain. “ Οὐκ εβουλέτο πρίν ἡ τελέσαι το πρόβλημα, καὶ καταστῆσαι πρός τὴν απόδειξιν.” The event cannot fail to call in recollection the similar request and fate of Lavoisier, in revolutionary France. One hundred and thirtynine years after, (U. C. 540-679.) Cicero, then Questor of Sicily, discovered this wonder-working

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man's tomb, and prided himself that he, "homo Arpinas," should have been so very fortunate, (Quæst. Tuscul. v., 23.) In the last century, (1747) Buffon experimentally proved the power of burning mirrors, such as Archimedes employed for the destruction of the Roman fleet and batteries.* His lordship's introductory pages, we must say, are filled with matter by no means bearing with equal point or interest, as these facts, on his expressed object, which would have been better supported by apposite examples than by general assertion.

Yet this abstraction of thought, here more peculiarly attributed to mathematicians, is not less, we believe, the produced effect of other pursuits, such as metaphysics, which, in their mazes, enfold and entrance the faculties with quite as puissant a grasp. Various passions, enthusiastic excitements, ascetic fervor, or morbid illusions, as we daily witness, hold fully as exclusive possession of the imagination; and so, likewise, do the arts, music, painting, architecture, &c. And if D'Alembert, as his lordship affirms, sought repose in his cherished mathematics, Lagrange assuredly not his inferior as an analyst,† frequently found

* The largest burning glass, probably known, was presented to the Emperor of China in 1792, by Lord Macartney.

† An anecdote demonstrative of this, perhaps the first of analysts' humane sensibilities, derived from the information of the late M. Geoffroi SaintHilaire, to whom a monument has been lately raised at Etampes, his native town, may not be unwelcome to the reader. Witness, on a special invitation, of M. Majendie's experiments on living animals, or vivesection, Lagrange was so affected by the excruciating tortures thus inflicted, that he expressed his determination never again to attend a meeting of the Academy of Sciences during these operations. Existing lusus naturæ, as if prepared by nature for the purpose, exhibited, he contended, the required results, without such outrages on her more perfect creatures. Physical truth could not, he equally affirmed, be more surely discovered in the palpitating fibres, or con

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