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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,

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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 lalitude 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. The 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 the centre of the earth, for which the rational horizon is calculated. This operates to sink the sun's apparent place lower than its real, though not enough to counterbalance the contrary effect of refraction. When the proper corrections are made of these errors, and others of less consequence arising from the aberration of light, &c. the true altitude is found, and the true latitude follows.

It still remains to find the ship's longitude. Having found thus much, the navigator may point out the parallel of latitude upon which he is, but for all he can tell from celestial observations, he may be any where between Nova Scotia and the mouth of Oregon. In former days, not far removed, the entire dependence for longitude was upon “dead reckoning,” the whole mystery of which consisted in a careful record of the ship's bearings, and rate of sailing, from which her course was traced and her present position ascertained. By these means latitude was found at the same time as longitude, but as the means of ascertaining the former, from the bearing of the heavenly bodies, was introduced into general use before the more complicated methods of finding the latter, “dead reckoning” continued to be relied on for that purpose, long after it had ceased to be used for the former, except in cloudy weather, when it still is the navigator's sole reliance. Upon leaving the land, the ship's course is carefully noted, both from the shore and the compass, and thus the “departure" taken. After this, every thing depends for “ dead reckoning" upon the compass, and the log; the former to ascertain the course, the latter the distance sailed. The log is a long line fastened to a piece of wood, something like a buoy, which being loaded at one end stands upright in the water. The cord is divided into a number of equal parts, by knots, which are termed knots, and half-knots, each knot being the 120th part of a mile. When every thing is ready to throw the log, an officer stands ready with the logglass, which is emptied of its sand in 30 seconds, or the 120th part of an hour. After the log is in the water the glass is turned, and the number of knots noted, which run out as the vessel passes on her course in the 30 seconds. Each knot bearing the same proportion to a mile, which the time does to an hour, of course the number of knots sailed in that time indicate the number of miles the ship is going by the hour. This process is repeated hourly, and, for a few days together, affords the data for a pretty good guess at the true position of the vessel, though on long voyages it is far from satisfactory. The navigator having started from the point A in the annexed figure, finds by his compass that his bearing is in the direction AB, and by his log that the distance AB is twenty miles. In order to find his longitude at B, he must ascertain the difference between that of A, (which having been his starting point he knows,) and B. The line AC is the parallel of latitude which passes through A; BC, the meridian, or parallel of longitude of B, and of course perpendicular to AC; AC, is then the difference of longitude, and BC of latitude, between A and B. ACB being a right angled triangle, if he has found his latitude at B, by astronomical observation, and consequently the length of the side BC, he may find the side AC by the 47th proposition of the first book of Euclid: which proves the square of AB to be equal to the sum of the squares of AC and BC, and consequently the square of AC to be equal to the difference between the square of AB and that of BC. But if, as is generally the case, the navigator, has recourse to his dead reckoning, for want of an opportunity for observation, and knows no more of his latitude than of his longitude, he has no data, but the length of the side AB and the angle at C, which being the point at which the meridian BC intersects the parallel of latitude AC is a right angle, and therefore 90 degrees, and the angle at A, which he has found by calculating the difference between the ship's course AB and a due east course AC. He has therefore two angles and the side of a. triangle, and easily finds the other sides, one of which is the side AC the difference of longitude, and BC the difference of latitude, between A and B. That difference, added to the latitude and longitude of A, makes those of B. The veteran Commodore Rogers is said to have been singularly skilful in this kind of navigation, and to have made his famous cruise during the last war, in the President, without other help, and, what is the more remarkable, without miscalculation.

At this day, longitude is found whenever observations can be had from the lunar distances, and from the chronometer, the one being used to test the accuracy of the other. The moon, as every one knows, has a rapid motion among the fixed stars, and other heavenly bodies. Upon this, the whole system of lunar observations depends. The almanac contains the data from which the precise time the moon at Greenwich

appears at a certain distance from the sun, can be deduced. By noting, then, the time at which they assume the same relative position to the observer, he has the difference between his time and that of Greenwich. That difference will give the difference of longitude between the two places. The time of any place depends upon the sun's passage over its meridian. When that takes place, it is twelve o'clock, noon, and the other hours are counted from that period. The sun, rising in the east, and progressing westwardly, reaches the meridian of the more eastward of two places, before that of the other; and the time of the former will be faster than that of the latter, by precisely the time it takes the sun to travel from the former meridian to that of the latter. If, then, it be ascertained that the sun and moon have assumed to the observer, on shipboard, a relative position, two hours after the former passed his meridian, or at two o'clock, which they held at Greenwich at noon, his time is two hours behind that of his prime meridian, and he is evidently west of it. He knows that the sun passes over 15° of space in an hour of time, and that he must consequently be twice that many.degrees west from Greenwich.

The method of finding longitude by chronometer, is only another mode of finding the difference of time between the ship's position, and the prime meridian. After that is accomplished, the process is the same as in the last described mode. The time, at the ship's position, having been carefully ascertained, as described in our account of the mode of finding lati-tude, from the sun's passage over the meridian, it only remains to fix the time at the prime meridian. For this purpose, modern ingenuity has constructed the chronometer, a kind of watch, of peculiarly accurate workmanship. Before leaving port, it is carefully regulated, and set to the true time of the prime meridian, found by astronomical observations. During the whole course of the voyage, it therefore preserves that time, and enables the navigator, whenever he can find his own true time, to tell with great accuracy his longitude. For the sake of greater certainty, it is usual to take at least three chronometers. Two are worse than one, since, if they differ, neither will be trusted. With three, there must always be a majority, unless, like the vanes on our court-houses, they make a point of no two ever agreeing. Even if this should be the case, the moon may be brought in as umpire, to decide upon their veracity, though it be something new under the sun, to make her the standard of truth. The use of these instruments has become universal in the merchant service. Our government is the only shipowner who refuses them to her vessels. The smaller of our national ships are not considered worth a chronometer. What particular amount of tonnage, or

VOL. XVIII.-NO. 37. 13

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