began to break in upon our mind, and exhibit to us their sim-. plicity 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 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. The 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not only supplied our own seamen, but has gained an extensive circulation in the English service; and has only been superseded in the latter, within a few years, by Riddle's. The work at the head of this article is very lately from the press, and is the production of a passed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.

Whatever may be the merits of Mr. Maury's book, he deserves credit for the spirit which the attempt evinces. In 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

figure, in which GAB is the quadrant, AB represents the circular brass rim, in which the degrees are marked and numbered. CD is the telescope or eye tube, through which the observer looks at the body, whose altitude he is about to measure, and is made to move on the point at G. EF is a plumb line suspended from E; when the plumb line hangs parallel to the side of the quadrant GB, that side is of course perpendicular to the horizon, and points directly from the centre of the earth to the zenith, and the side GA, being at right angles to GB, is parallel to the horizon. If then the telescope be drawn down till it coincides with GB, it will point directly to the zenith; if it be raised to coincide with AG, it will point to the horizon. The distance from zenith to the horizon being divided by common consent into 90 degrees, the circular plate AB, upon which the end D of the telescope passes while the end C is changing its direction from the horizon to the zenith, is also divided into 90 degrees. If the telescope point at the latter, and in order to observe a star it is necessary to move the end C one 90th part of the whole distance, or one degree toward B, or the horizon, the end D must rise one 90th part, or one degree on the circular plate AB. The number of degrees then that the end D of the telescope is distant from B, shows the star's distance from the zenith. Those intervening between the same end and A exhibit its altitude. The instruments now used for this purpose are far more perfect than the one we have shown here for the mere purpose of exhibiting the principle common to them all. We have not attempted a description of them, having found from experience, that nothing will give a correct idea of a complicated piece of machinery but actual inspection.

The great deficiency in the old instruments, was in the want of some means of determining accurately when the object was in the meridian; as a slight mistake in that respect made a vast difference in the result. That object is now attained by the means of reflectors, which bring the sun's disk down to the verge of the horizon, and thus give the observer a definite line by which to mark it. If it has not yet reached its greatest altitude, but is still rising, after having been brought by the reflectors, to the horizon, it will be seen gradually to lift itself above it. If so, it must be again brought down by lowering the reflector, and the same thing repeated until it cease to rise. When near the meridian, its motion becomes very slow; when the motion ceases, it has reached it, and the observation must be immediately taken. In a few moments, the reflected disk will then sink below the horizon, as fast as it before rose. If then, for instance, the observation show Arcturus to be 20° south of the zenith, that star being 20° north of the equator,

it is evident the observer's latitude must be 40° north, about that of Philadelphia. If he take Capella, whose latitude is 45° north, as the basis of his calculation, and find it to be 5° north of his zenith, he must change the method, since he is now between the equator and the star, having been before north of both. The star being 45° north, and he 5° south of the star, it is evident that he is in latitude 40° north. The same observations apply of course to the sun, when his altitude is taken; except that when he is south of the equator, his latitude must be subtracted from his altitude, and the remainder shows the observer's latitude. This is called finding the latitude by meridian altitudes. When it happens that the sun is so obscured by clouds at mid-day, as to prevent an observation, the navigator must resort to the process of finding it by double altitudes. This is more intricate, and involves much more labour of calculation than the former. The altitude of the sun, for instance, is taken at any period of the day, when he can be seen through the clouds. The time being carefully noted, another opportunity, after about an hour's interval, is seized, and the altitude noted again. Having then represented on paper, the positions of the sun at the two observations, and drawn lines from each to the zenith and the pole, and joined them by another, he has three triangles, each having one side common to another. Of one of them he has given the zenith and polar distance of the sun at the time of observation, making two sides of the triangle, and the time elapsed between the two observations gives him an angle opposite one of them. These enable him to find all the parts, angles or sides of that triangle, one of which latter forms a side of the second. This discovery gives him two sides and an angle of that, and by the same process enables him to find all the parts of the third, one of which is the distance of the pole from the zenith of the observer. That subtracted from 90° leaves the latitude. Though it is not common to resort to this method, when a meridian altitude can be had, a good sailor, if the morning should indicate the prospect of a cloudy noon, will always take an observation of the sun at two points while it can be had, and then if he fails in getting the former, he can work up his latitude by the latter mode at his leisure. We have taken no notice heretofore of the corrections, which must be made to find the sun's true place, which, from several causes, is far from being his apparent one. allowances to be made under all circumstances, are reduced to rule, and may be found in the nautical tables. The most important error arises from the refraction of the sun's rays, coming from a lighter into a denser medium, and making his disk appear much higher than it really is. The parallax arises from the observer's position being upon the surface, instead of