has been in the mode of their tuition. Twenty years ago, the mathematics were scarcely taught at all in our country. Individuals, indeed, whose natural taste inclined that way, by persevering and almost unaided efforts, made themselves masters of the subject. But they learned, without being taught. The student was carried through the propositions of Euclid, conic sections, spherical trigonometry, fluxions, &c., without the slightest notion, derived either from the professor, or the book placed in his hands, of the practical object of the several propositions, or of the sciences themselves. So that when he had arrived at the end, he knew, for every useful purpose, as much of the path by which he had traveled, or the point he had attained, as if he had been led blindfold through the streets of New York. If blessed with a good memory, he could demonstrate all the problems, and understand the reasoning by which the conclusions were reached. But if asked to apply any portion of it in practice, or to point out the end for which it was all designed, he would have stared at the idea, and most probably have answered, in true schoolboy phrase, that it was not in his book. If, perchance, his attention had been directed to the study of practical surveying, he would have perceived the application to practical purposes of some of the simplest rules of geometry and plane trigonometry, and would have concluded, as we freely confess we did, that the vast science of mathematics, its fearful array of angles, triangles, and rectangles, its sines, its tangents, and its secants, aye, and for all we knew to the contrary, the more awful mysteries of the parabola, the hyperbola, and the ellipse, were designed to measure the width of a river, the height of a church steeple, or the area of a three acre field.

And since this was the only practical purpose we were permitted to see of that which we had expended years in accomplishing, will any one deny the reasonableness of our conclusion? We remember well, after having demonstrated to the satisfaction of the professor, and the admiration of the class, some difficult proposition in spherical trigonometry, the amazement in our private mind, which compelled us to exclaim therein, "what can it all mean!" It was clearly proved to every comprehension, that "the product of radius, and the sign of the middle part" was "equal to the product of the tangents of the extremes conjunct," but why any living creature should care if they were, or how the world was to be benefited by the discovery, was as incomprehensible to us as that most incomprehensible doctrine of the eternity of matter. Baron Napier was no doubt a benefactor to the world. But when we were told that the establishment of the above fact, and another about as intelligible, had made him so, it was truly marvellous in our

eyes. Every boy of fifteen was not taught at that day, that he had a right to understand all he was asked to believe, or we should have been very sceptical upon this subject. It is even doubtful if the professor would have found it easy, had he been put to the trial, to give a reason for his own faith. When some inquisitive youth did venture to enquire, touching the hidden mystery, which he sometimes suspected lay under all this unintelligible jargon, his question was generally treated as an impertinent exhibition of curiosity, unbecoming his years, or would be evaded by the reply, that though old enough to be puzzled with the abstruse theories of the mathematics, he was not yet competent to the far simpler science of its practical application. If he became restless under his bondage, and remonstrated against the propriety of loading his memory with learning it was admitted he could not understand, while so much remained unattained, and within his comprehension, the answer was always at hand. He was told with wonderful gravity of the effect of the study of the mathematics in enlarging the mind, and reminded, that that in itself was an object worth all his labour. Taught, as we were, to believe every thing we were told by such authority, this reasoning produced in us a very unsatisfactory state of conviction. We could not see how stuffing the brain with a mass of undigested confusion would enable it to reason clearly. We concluded that, at all events, it resembled, in offensiveness, certain prescriptions we had swallowed aforetime, and of whose useful influence on our health we had never been convinced. The result was, that the boy received his life's dose of mathematics in college, and, by a most diligent perusal of novels in after life, made every effort to efface its very name from his memory, just as, when somewhat younger, he had devoured sweetmeats, to remove the taste of a cupful of medicine.

In thus retracing our own experience, we hope to be excused from the charge of egotism; since we offer it only as an example under the general rule. Without further apology, we shall carry it a little farther. Some years after our education had received its last polish, according to the fashion of the day, and we had been officially pronounced master of all the arts the college professed to teach, we had the fortune to be embargoed, by a most pitiless storm, in the parlour of a country tavern, with an old magazine for our only companion. Having exhausted its more inviting contents, and accomplished a long dissertation upon political economy, which nothing but the peculiar circumstances of our case would have induced us to touch, we drew courage from despair, and assailed another, then still more formidable, upon the practical application of the principles of mathematics. We had not read far before light VOL. XVIII.-NO. 37.

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began to break in upon our mind, and exhibit to us their simplicity and still more beautiful adaptation to the most magnificent ends. We had admired the ingenious processes by which the square of the hypothenuse of a right angled triangle is demonstrated to be equal to the squares of the other sides, and the sides of any triangle proportional to the sines of their opposite angles, but had never imagined the facts to be of any further use than to aid in the proof of others equally useless when demonstrated. It was with perfect delight that, for the first time, we perceived how, by their aid, we might draw a line across the sun and compute his vast diameter; stretch our compass from planet to planet, and tell their distances. And when, in the further prosecution of the subject, we beheld the mathematician performing wonders which the prophet had ascribed exclusively to Omnipotence; "measuring the waters" of the ocean," comprehending" not only "the dust of the earth in a balance," but estimating the gravity of systems, and meting out the very heavens "with a span," we were prepared to confess the grandeur of a science which, in our ignorance, we had despised; and to appreciate, in some measure, the majesty of that Being who could confer such mighty powers upon his creatures, without diminishing their infinite distance from himself.

The

The deficiency in the old mode of tuition originated with the books then placed in the learner's hands. Their authors had been contented to display the theory of their subject, and leave all practical applications to the teacher. They forgot to calculate the chances in favour of that individual being either. incompetent to his duty or too indolent to perform it. more modern books assume the whole duty, and enable an intelligent student to do nearly as well without, as with the aid of an instructer. Those on that particular branch, or rather application, of the mathematics with which we have to do, have been few and far between. Bowditch's Navigation has, since its first appearance, not only supplied our own seamen, but has gained an extensive circulation in the English service; and has only been superseded in the latter, within a few years, by Riddle's. The work at the head of this article is very lately from the press, and is the production of a passed midshipman in our navy. Though the world has ceased to wonder at every first instance of literature in a seaman, we think they will be surprised at the announcement of a scientific treatise from the pen of a midshipman.

In

Whatever may be the merits of Mr. Maury's book, he deserves credit for the spirit which the attempt evinces. itself it presupposes an amount of information, which, with all reverence for that branch of our national defence, is not common

to others of his rank, and an amount of industry, still less their characteristic. He has, however, the greater merit of having ventured with success. Having mastered the difficulties, which, in the absence of competent teachers, and competent books, assume so formidable an aspect to the beginner; having borne his own share of discouragement, and witnessed the despair of his less persevering companions, he is peculiarly fitted for the task he has assumed. He knows exactly where to find the difficulties, and how to remove them, and comes to the aid of his fellows, with the feeling of a knight of the olden time, to the rescue of his companions in arms.

The majority of mankind know less of navigation than of any other of the practical sciences. By common consent, the dwellers on terra firma have left the exclusive knowledge of its simplest principles to that portion of the species whose business is on the great deep. It is hoped, then, that a brief account of the modes in use, for tracing a ship's course, and finding her position, will not prove entirely uninstructive to some of our readers.

The position of a vessel is of course her latitude and longitude, or the point at which any line drawn parallel to the equator, intersects her meridian. The former indicates her distance from the equator, the latter from the prime meridian from which, by general consent, the degrees of longitude are counted. Unfortunately, the world has not been able to agree upon a prime meridian. Four nations, with ridiculous vanity, claim in this respect to give law to the world. England long since fixed on the meridian of Greenwich, and Spain on that of Cadiz. France, spurning the idea of vassalage to either of her then rivals, erected one of her own at Paris, and republican America, with less reason than either, counts her longitude from Washington. We shall, for the purposes of this article, consider Greenwich as our prime meridian. The latitude is easily deduced from astronomical observations. As early as the days of Prince Henry of Portugal, this mode of finding the latitude was practised, though with comparative inaccuracy. He invented an instrument, something like the quadrant of the present day, which he used to find the elevation of the north star. Supposing that star to be at the pole, it would appear to an observer, on the equator, to be precisely upon his 'horizon. If he advanced one degree north, the star would be that much elevated, and would continue to rise as he progressed, until having reached the pole, it would stand directly over his head. It followed, therefore, that the number of degrees the polar star was elevated above the horizon of any observer, indicated his latitude. The basis of this calculation being untrue, inasmuch as the north star is not precisely at the pole,

the conclusion founded upon it was of course inaccurate; and though the error of a few degrees was then considered a trifle, that mode of determining latitude has long been abandoned. It was manifest, that any other of the principal fixed stars offered equal advantages for the purpose. The altitude of a heavenly body is measured on a line supposed to be drawn through the zenith point of the observer, and the body itself to the horizon. The distance of the body from the horizon, measured on that line, is its altitude, and its distance from the zenith, its zenith distance. As the whole space from the zenith to the horizon is the quarter of a circle, and therefore measures 90°, if either zenith distance or altitude be known, the other is found by subtracting the known part from 90°. The altitude of a body, may be taken at any point after its rising, and when the latitude is to be found by what are called double altitudes, it is immaterial where. But it is evident that the distance of a star from the horizon, until it reaches the meridian, is changing every moment, and if the calculation be made at any number of intermediate points, the result would vary each time. But its altitude when on the meridian is always the same, at the same point on the earth. The sun affords the best opportunity for accurate calculation, and is always used for that purpose, when his disk can be seen. A star is in itself comparatively indistinct, and being visible only at night, when the verge of the horizon is undefined, it becomes very difficult to take a correct observation of its position. The sun, indeed, unlike the fixed stars, changes his latitude daily, but as it is known for every day in the year, the process is not more complicated. At half past eleven, on board our vessels of war, it is the rule to call the officers on deck to be prepared for the observation. This precaution is necessary, lest an error of the time-pieces, arising from the change of longitude, should cause a loss of the opportunity. In order to make the operation entirely intelligible to the uninitiated, we append the following