be taken that no cruise exceed three years; a term already sufficiently prolonged. In entering a crew, we would not allow them to enter for any particular rank or wages; but would classify them according to their merits when embarked, awarding the stations of petty-officers to those who should possess recommendations for having faithfully filled those stations in other ships, and retaining the power to promote, through all the various gradations of boys, ordinary seamen, seamen, and pettyofficers, according to individual merit and good behavior. We do not think that the boatswain, gunner, carpenter, and sail-maker, should be warrant officers, but entered like the rest of the crew, and equally subject to promotion and degradation. These offices are best filled by individuals temporarily appointed, and liable to removal at the pleasure of the commander; while those who have warrants, having no hope of going higher, and no immediate fear of descending lower, lose all ambition. Moreover, they would furnish to the whole crew, when within their reach, a powerful motive to emulation and excellence. Finally, we would not receive a single individual into our ships who was not a native-born American. But under the present system of discipline, and whilst there is danger of being for ever degraded by the stroke of the lash, American seamen, or, at all events, the better class of them, will not enter the service of their country. That system which deters Americans from serving their country, and forces us to receive a large proportion of foreigners as the only alternative, must be false, cannot be permanent, and, therefore, demands of legislative wisdom (we do not appeal to humanity) an immediate reformation.

Our naval system, as we have already seen, was received from Britain. Her sailors, forced into her navy like slaves, and forming at least one excepted class from the boasted spirit of universal emancipation, could of course only be controlled. by the same bodily compulsion by which they were kidnapped and deprived of their liberty. Though voluntary enrolinent. was at once substituted among us for compulsion, the lash, which was its counterpart, was most inconsistently retained. Hence the more worthy of our seamen were excluded from the public service, except when out of employment in time of war or embargo; and of course it was compelled to supply itself from among the less scrupulous; out of whom and the foreigners, who entered extensively, a class was formed and per

petuated of degraded individuals, who have rendered the name of man-of-war's men a stigma, and who, accustomed to obey no law but that of brute compulsion, are still kept in order only by the means of their degradation.

The navy, in point of ease of labor, quality of food, and the chance which long voyages offer for accumulation (to which sailors, however quickly they may spend their money, are not indifferent, as may be seen by their making long voyages in the merchant service, at reduced wages); the pleasures to be derived in it from a numerous society and stated leisure; its festivities, music, dancing, esprit de corps, pride of ship, and all its multiplied means of enjoyment, holds out strong inducements to seamen; all, however, counteracted among the less corrupt by the terrors of the lash. Take away these terrors, and our best seamen will enter in abundance. Associate with them a large number of youths, alike unimpaired in character and constitution; and these, cherished by their officers, and ambitious to excel, will soon become skilful seamen. Seamanship is incomparably more perfect in the navy, and it will, therefore, be easy to send these young men forth more perfect, than if they had been reared in the merchant service. Hence, then, instead of being indebted to the merchant service for seamen, whom we send back corrupted, and only susceptible of being kept in order by naval discipline, to mutiny, and cause the miscarriage of voyages, we should furnish it with seamen equally distinguished for skill and habits of subordination.

We agree with the author of the Naval Sketches,' in condenning the daily issue of ardent spirits as part of the naval ration. A whole crew, without reference to previous habits or individual constitution, learns to swallow the poisonous dose. We can indeed conceive no idea more shocking, than that grave legislators should have thus set their names to a law, whose sole effect is the promotion of intemperance. There is no truth in the idea that grog is a bounty for enlistment; it is only a bounty to those whom it would be desirable to exclude from the service. In merchant ships, where our best seamen are found, the issue of grog is unusual. Grog, in a man-of-war, is a sufficient source of all discord and of every crime; while grog continues to be drunk there, the sound of the lash and a shriek of the tortured and degraded victims will continue to reverberate through our ships. We agree farther with him in believing that much advantage might be derived from the cul

tivation of the moral character of seamen; and one can, indeed, see no sufficient reason why a ship of war, instead of being a school of ignorance and vice, might not offer a spectacle of intelligence, good order, and morality. We are aware, that in every system of government there will be crimes, and, consequently, that there must be punishments; but what prevents those punishments which are found efficacious ashore, from being equally efficacious afloat? and why might not the hope of reward furnish as strong an excitement to good conduct as the fear of punishment? Be it as it may, substitute whatever punishments you please, even death itself, but let corporal punishments cease henceforth and for ever from among us. With our seamen, as with our children, let us leave them to that nation in which everything is complicated, factitious, unnatural; let it not be said that, while Frenchmen, bowing to the nod of their Emperor, were able to conquer the world by the aid of moral incitements, Americans cannot defend their country but by the impulse of the lash!

ART. VI.—Elements of Geometry, with Practical Applications for the Use of Schools. By T. WALKER. Second Edition. Boston. Richardson, Lord, & Holbrook. 1830. 12mo. pp. 104.

THE progress of Geometry, from its rude beginnings in Egypt, to its present state of advancement, exhibits one of the most perfect and beautiful developements of human intellect. Starting from a few simple truths, the application of which the necessities of common life first taught that primitive people, it passed, step by step, along its forward path through the Grecian and Alexandrian schools, and from them through the middle ages to modern times, until it has at last entered a region of unerring truth, no less wonderful to the uninitiated eye, than would be the fabled glories of oriental Fairyland. As the science advanced from truth to truth, each more surprising than the last, it is no wonder that the imaginations of its devotees were enkindled to the most dazzling anticipations of the grandeur of future discoveries. The delight, which the mind VOL. XXX.-No. 67.

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naturally experiences from the vivid perception of some hitherto unknown result, must have acted as a continual stimulant to the early cultivators of geometry, prompting them to unwearied efforts in the prosecution of their beautiful studies. Accordingly we learn from history, that the investigations of this science, particularly among the geometers of Greece, aroused an enthusiasm nowise inferior to the divinest inspiration of poetry. The absolute certainty of the truths which it demonstrates, the clear and elegant methods which intellectual ingenuity has devised of arriving at those truths, the regular progress from one portion of the science to another, the beautiful harmony and unerring symmetry of each part with all the others, make it, now that the successive labors of ages have by degrees unfolded the majestic system, one of the most curious and interesting objects of human contemplation; and explain and justify the lofty, and perhaps, at first sight, extravagant admiration with which the ancient mathematicians regarded it.

The study of geometry, to say nothing of other cognate sciences, is not, according to the popular impression, a dry and uninteresting pursuit. There is that in it, which calls out and absorbs the powers of the mightiest intellect, and which, as with the spell of an enchanter, concentrates upon itself the varied energies of the imagination, the reason, and the judgment. No men have obtained a place in the intellectual history of antiquity, who aspired more loftily to eternal fame, who were animated with the impulses of more throbbing anticipations, than the geometers. Their names are not upon our lips, like those of Homer, and Eschylus, and Virgil, because we are less familiar with the prodigious efforts of their minds; they speak not, like the poets, in the seducing tones of passion and sentiment, but in the sterner accents of truth; and he who would hold communion with them, must attune himself, not to the strains of the graceful but Epicurean muse of Horace, but to the severe teachings of unadorned and majestic truth. But though their names are rarely mentioned, except to point a sentence, to give force to an antithesis, or to surround a common thought with the charm of classical allusion, yet among the initiated, who know how to appreciate them, they are reverenced with an intenseness proportioned to their sterling worth; and the more deep and enduring, perhaps, by reason of the narrow limits within which this reverence is confined.

We know but little of Egyptian geometry. Judging from the well-known problem of measuring the height of the pyramids by their shadows, said to have been solved for them by Thales, we should conclude that their theoretical knowledge must have been extremely limited; judging from those stupendous monuments themselves, which thousands of years have not shaken down or perceptibly affected, we cannot resist the conclusion, that, in practical mechanics, they possessed an almost unrivalled skill. We know of nothing more interesting and curious in ancient historical writings, than the minute and apparently accurate sketches of the Egyptians, their national character, their internal economy, their priesthoods and superstitions, their learning, and, most especially, their public works, the pyramids, the labyrinths, and the excavated lakes, given at length in the second book of Herodotus. The same author ascribes the origin of practical geometry to the operation of an Agrarian law,' carried into execution by Sesostris, by which each of his subjects was put in possession of an equal portion of land; but the proximity of some to the Nile, and the exposure of their lands to annual inundation, rendered necessary a remeasurement, and thus gave birth to geometry, or the art of measuring land. But, as we have intimated above, there is no reason to believe the Egyptians ever extended their geometrical discoveries very far, or that any ancient nation, previous to the Greeks, understood geometry as a symmetrical and progressive science. The celebrated and most important theorem, that the square of the hypothenuse of a rectangled triangle is equal to the sum of the squares of the other two sides,' though now understood by every tyro, required for its demonstration the genius of a Pythagoras; and the joy he experienced on discovering and establishing its truth, is, to us, one of the most electrifying passages in the history of the human mind. We can hardly conceive a more befitting occasion of offering a hecatomb to the gods, than when the intellect has just entered triumphantly the citadel of knowledge, and made captive a master-truth, which is destined to bring beneath its sceptre so many subject-domains of science. Of Pythagoras the same thing may be said as of nearly all the Greek geometers, that he was gifted to an extraordinary degree with the power of imagination. In proof of this we have only to adduce his belief and defence of that fanciful doctrine, called metempsychosis, which he had per