CHAPTER XTHE SCIENCE OF NAVIGATION

CHAPTER XTHE SCIENCE OF NAVIGATION

Navigation, I may be permitted to repeat, is the mathematical science of finding ships’ positions at sea and of laying down courses to be followed. For the designation of positions latitude and longitude are used, latitude being measured north and south from the equator to the north and south poles, the equator being zero degrees of latitude, the poles being ninety degrees north and ninety degrees south latitude. Longitude is measured from zero degrees to 180 degrees east and west from the meridian running from the North Pole to the South through Greenwich, England, 180 degrees east longitude marking the same meridian as 180 degrees west longitude. For instance, Three Kings Island, the tiny island which is the northernmost land of the New Zealand group, is located as follows: Latitude 34° South; Longitude 172° East. This means that this island is 34 degrees south of the equator and 172 degrees east of the meridian of Greenwich. Actually navigation is a problem in spherical trigonometry and astronomy, depending principally, nowadays, upon an instrument called a sextant, which is used to measure the altitude above the horizon of a celestial body (sun, moon, or stars), and upon a very accurate timepiece, called a chronometer, which shows the time of a given meridian—generally the meridian of Greenwich, England.

In practice, however, it is necessary to know no mathematics other than arithmetic, for the formulas have been simplified and handbooks have been compiled which eliminateany necessity for the practical navigator to delve into the intricacies of spherical trigonometry, a subject that would frighten most sea captains more than all the other perils of the deep.

There is another but less accurate method, called “dead reckoning,” which is used in connection with the more accurate science, and is used by itself when clouds obscure the sky or fogs hide the horizon. When land is in sight both these methods largely or entirely give way to “piloting,” which makes possible the accurate finding of a ship’s position by reference to known objects ashore.

I shall not attempt to explain all the intricacies of navigation, for even a simplified complete explanation would in itself become a small book. There are many books on navigation. Nathaniel Bowditch’s exhaustive treatises have been revised many times and the whole compilation is kept up to date so that, while Bowditch himself died in 1838, the book bearing his name, and still referred to almost universally as “Bowditch,” is accepted as a peerless authority. But it is a huge tome, and other practical books, such as “Elements of Navigation,” by W. J. Henderson, are available for the person who wishes to profit by a simpler, if less exhaustive, explanation. To these two books, and to a dozen others, I refer the interested reader anxious to learn what, after all, is beyond the range of this outline.

Up to the 15th Century the science of navigation was unknown. Before that time mariners occasionally ventured out of sight of land, for short passages during which, because they had no compasses, they attempted to guide themselves by reference to the sun or stars. When clouds obscured the sky, however, they usually lost their direction, and even when the sky was clear they knew no way of ascertaining anything more than rough approximations of the cardinal points.

It seems just a bit strange that sailors were so backward in developing means of determining their positions at sea by reference to the sun and stars, while even the ancients were fairly accurate in their ability to locate their positions ashore by such methods. This undoubtedly was as much due to the lack of general knowledge among sailors as it was to the unsteadiness of the ships themselves which made it difficult for careful astronomical observations to be made. But whatever the reason, the fact remains that it was not until after the introduction of the compass that navigation began to make its first faltering advances.

USING A CROSS STAFFThis crude instrument was used in an attempt to work out problems in latitude. After holding one end of the staff to the eye and sliding the cross staff along until the observer sighted over one end at the sun and under the other at the horizon, the instrument was placed on a circle marked in degrees, and the angle was determined.

USING A CROSS STAFFThis crude instrument was used in an attempt to work out problems in latitude. After holding one end of the staff to the eye and sliding the cross staff along until the observer sighted over one end at the sun and under the other at the horizon, the instrument was placed on a circle marked in degrees, and the angle was determined.

USING A CROSS STAFF

This crude instrument was used in an attempt to work out problems in latitude. After holding one end of the staff to the eye and sliding the cross staff along until the observer sighted over one end at the sun and under the other at the horizon, the instrument was placed on a circle marked in degrees, and the angle was determined.

This crude instrument was used in an attempt to work out problems in latitude. After holding one end of the staff to the eye and sliding the cross staff along until the observer sighted over one end at the sun and under the other at the horizon, the instrument was placed on a circle marked in degrees, and the angle was determined.

That this beginning was made during the period in whichPortugal expanded her commerce only goes again to show that the application of new minds to old problems results, almost invariably, in progress.

Columbus, of course, did not begin the era of discovery. Prince Henry, the “navigator,” sent out an expedition from Portugal in 1432 which rediscovered the Azores—an astonishing thing for times so early, for the Azores lie 830 miles west of Portugal and are farther from a continental mainland than any other of the islands of the Atlantic. That the islands were known to the ancients, however, is proved by numerous Carthaginian coins found on the island of Corvo, but their location and practically everything else concerning them seems to have been lost until Henry the Navigator attached them to Portugal.

But the rediscovery of the Azores proves only that the sailors put great faith in their compasses, and sailed, despite their fears, out to the west where all of themknew(it was no matter of merebelief) that the sea ended somewhere suddenly, and that their cockleshell ships would, if they but sailed to the edge, fall down the smooth green cataract of an awful, endless waterfall, into limitless space, or, mayhap, to the vast foundations upon which the world was built. To them it was as if a canoe were being paddled downstream to the brink of a cataract to which Niagara itself would be but a raindrop falling from the eaves.

At the time of the rediscovery of the Azores navigation was, with the exception of the compass, without any of the instruments that later came into use. Prince Henry, however, realizing the importance of compiling information useful to mariners, systematized all the information available and erected an observatory to determine more accurately the data in reference to the declination of the sun.

Most navigators use the sun far more than any of the other celestial bodies in order to determine their positions, andthe first thing necessary is to know its declination—that is, its distance north or south of the equator.

During the course of a year the movement of the earth, with its axis inclined at an angle to the plane in which it moves about the sun, brings the sun vertically over every section of the earth from twenty-three and one half degrees north of the equator to twenty-three and one half degrees south and back again.

During the year, then, the sun is twice directly over our equator. Suppose at noon on one of these days a mariner wishes to determine his latitude, that is, his distance in degrees, minutes, and seconds north or south of the equator. He measures, with his sextant, the angle between the sun and the horizon. If he were on the equator that angle would be ninety degrees, for the sun would be directly over his head. He would then subtract the angle shown by his sextant from ninety, the number of degrees between the horizon and the zenith. In this case the answer would be zero. Therefore his latitude would be 0 degrees, and that is on the equator. If he were at the North Pole or the South, the sun would be on the horizon, and his sextant would show an angle of 0 degrees. Subtracting this from ninety he would find his latitude to be ninety degrees, north or south of the equator, as the case might be. At any position between the equator and the poles the problem would be worked in the same manner.

But, except for two days in the year—but for two moments I might almost say—the sun is never directly over the equator, and declination is its distance at any given time north or south of the equator, measured in degrees, minutes, and seconds. This cannot be learned by any observations from a ship at sea. It is comparatively simple, however, to learn it by careful studies made at well-equipped observatories, and the results of these studies are now furnished marinersin carefully compiled form, so that they have merely to turn to their book in order to learn what the sun’s declination is at any given time.

It was this work that Prince Henry began, and modern navigation may, perhaps, be said to have begun with his studies.

But all the tables of declination are of no use without an instrument with which to measure accurately the angle between the sun and the horizon, and such an instrument was slow in coming. The first apparatus used was called a “cross staff.” It was made of two rods, one about thirty-six inches and the other about twenty-six inches long. The shorter staff was arranged so that its centre slid along the other while it remained rigidly at right angles to the longer staff. To work out one’s latitude with this instrument the observer waited until noon was almost upon him. He then took his cross staff and, placing one end of the longer crossbar to his eye and holding the instrument so that the shorter bar stood in a vertical plane, moved the shorter bar back and forth until he could sight over the upper end at the sun and, at the same time, beneath the lower end at the horizon. As the sun continued to mount to its highest point he pulled the cross staff slowly toward him, measuring a greater and a greater angle. When the sun had reached its highest point and the angle between it and the horizon began to lessen, his “sight” was completed, and carefully holding the crossbar where it marked the greatest angle he laid it on a table on which a circle was inscribed. The end that had been at his eye he placed at the centre of the circle, and the segment marked by the lines from the centre past the two ends of the crossbar showed the number of degrees in the angle he had measured between the horizon and the sun.

But any one who has attempted to sight a gun accurately while standing on an irregularly moving platform will havesome idea of the difficulty these old sailors had in sighting accurately at the horizon and the sun at identically the same time from the deck of a bobbing ship. The glare of the sun, the motion of the ship, and the inaccuracy of the instrument itself could not be expected to give more than approximate results, especially as the several corrections on the angle now known to be necessary (the refraction of the sun’s rays as they enter our atmosphere is one) were either not recognized or were inaccurately known.

USING AN ASTROLABEThis instrument was meant to improve on the cross staff. One man held it, when it was supposed to hang with the horizon line horizontal. Another man sighted at the sun or the stars, and a third read and recorded the angle. Needless to say the instrument was very inaccurate.

USING AN ASTROLABEThis instrument was meant to improve on the cross staff. One man held it, when it was supposed to hang with the horizon line horizontal. Another man sighted at the sun or the stars, and a third read and recorded the angle. Needless to say the instrument was very inaccurate.

USING AN ASTROLABE

This instrument was meant to improve on the cross staff. One man held it, when it was supposed to hang with the horizon line horizontal. Another man sighted at the sun or the stars, and a third read and recorded the angle. Needless to say the instrument was very inaccurate.

This instrument was meant to improve on the cross staff. One man held it, when it was supposed to hang with the horizon line horizontal. Another man sighted at the sun or the stars, and a third read and recorded the angle. Needless to say the instrument was very inaccurate.

Later the “astrolabe,” an instrument almost equally crude, was introduced. It was made of a heavy tin or bronze plate, circular in shape, and pivoted to its centre was a bar running across it from side to side. It was marked in degreesand fractions, and while one man held it, as steadily as he could, a second sighted along the pivoted crossbar and a third read the angles. Vasco da Gama used one of these in 1497 on his voyage around the Cape of Good Hope, but it did not turn out to be much of an improvement on the cross staff.

But up to this time, and even later, the science of navigation consisted almost solely of the approximate determination of latitude and mere guesses, based on the estimated speed and direction of the ship through the water, for longitude. So hopeless did it seem at that time for mariners scientifically to determine their longitude that an old writer on the subject is quoted by the Encyclopædia Britannica as saying, “Now there be some that are very inquisitive to have a way to get the longitude, but that is too tedious for seamen, since it requireth the deep knowledge of astronomy, wherefore I would not have any man think that the longitude is to be found at sea by any instrument; so let no seamen trouble themselves with any such rule, but (according to their accustomed manner) let them keep a perfect account and reckoning of the way of their ship.”

These early sailors learned, of course, that their latitude could be worked out by observing the North Star, and they used that method, crudely, of course, but similarly to the way it is used to-day. For this a contrivance called a “nocturnal” was adopted. With this they could determine what position the North Star was in, in reference to the true pole, for, of course, the North Star does not exactly mark the pole, but revolves about it in a small circle.

While the voyage of Columbus did not actually begin the era of discovery, it did greatly increase interest in exploration, and as most of this exploration necessitated long ocean voyages the interest in navigation grew apace. One of the earliest writers on navigation was a man named John Werner.In 1514 he explained the use of the cross staff, which for many years had been used on shore but had been first utilized at sea not very many years before Werner wrote. A little later one R. Gemma Frisius wrote a book which contained a great deal of information useful to men of the sea. In it he described the sphere with its parallels of latitude and its meridians of longitude much as we use them to-day. Up to this time, however, no agreement had been made upon what meridian to base the measurement of longitude. Nowadays the meridian of Greenwich is used. Frisius, however, suggested the meridian of the Azores. Any meridian, of course, would do, provided that the necessary data be based upon it, but the data available in the early 16th Century were slight indeed.

The necessity for drawing curved lines on flat charts to represent the courses of their ships now began to be understood, for ships do not sail on a flat surface but instead sail on the ever-curving surface of the sea. To the person accustomed, as most of us are, to looking at maps printed on flat pages, this truth becomes evident when he draws a straight line on a flat map, and then transfers the line to a geographical globe, making it pass through the same points.

Mariners were troubled, too, by the difficulty of accurately and easily drawing parallel lines on their charts, but this was overcome in 1584 when “parallel rulers” were first used by one Mordente. “Parallel rulers,” which are nothing more than two rulers hinged together so that whether they touch each other or are separated they remain parallel, are a part of every navigator’s equipment to-day.

Tables of the tides began to appear in the latter part of the 16th Century, but they were woefully inaccurate, and other information, while increasing, still was liable to be seriously in error.

Even points ashore, where observations could be workedout under the best possible conditions, were thought to be from a few minutes to several degrees from what we now know are their positions, and when one realizes that an error of one minute of latitude means an error of one mile, it will be seen that an error of fifteen or twenty minutes might be enough to put a ship in grave danger while her captain thought her safe, and that a position in which there is an error of several degrees is little more than worthless, for each degree of latitude represents 60 miles, and three or four degrees mean one hundred and eighty or two hundred and forty miles. When it is realized, furthermore, that such errors as these were made ashore, where the observations were much more accurate than they could be at sea, one understands why seamen trusted their navigation but little, for they were often faced, no doubt, with errors of three or four hundred miles. And, if anything, their methods of determining latitude were less inaccurate than those used in determining longitude. Truly, navigation in those days left much to be desired.

Other instruments were invented from time to time in the struggle to master navigation. The “astronomical ring” was one, but it was little less crude than the astrolabe.

A SEXTANT IN USESextants are used to measure the elevation of celestial bodies—the sun, moon, or stars—in working problems in latitude and longitude.

A SEXTANT IN USESextants are used to measure the elevation of celestial bodies—the sun, moon, or stars—in working problems in latitude and longitude.

A SEXTANT IN USE

Sextants are used to measure the elevation of celestial bodies—the sun, moon, or stars—in working problems in latitude and longitude.

Sextants are used to measure the elevation of celestial bodies—the sun, moon, or stars—in working problems in latitude and longitude.

A SHIP’S LOGThe mechanism at the top is fastened on the ship’s rail, and a line with the rotator shown below at its end is allowed to trail in the water astern. The passage of the rotator through the water causes it to turn, the line is twisted, and the log is made to register the miles travelled.

A SHIP’S LOGThe mechanism at the top is fastened on the ship’s rail, and a line with the rotator shown below at its end is allowed to trail in the water astern. The passage of the rotator through the water causes it to turn, the line is twisted, and the log is made to register the miles travelled.

A SHIP’S LOG

The mechanism at the top is fastened on the ship’s rail, and a line with the rotator shown below at its end is allowed to trail in the water astern. The passage of the rotator through the water causes it to turn, the line is twisted, and the log is made to register the miles travelled.

The mechanism at the top is fastened on the ship’s rail, and a line with the rotator shown below at its end is allowed to trail in the water astern. The passage of the rotator through the water causes it to turn, the line is twisted, and the log is made to register the miles travelled.

Now up to the 16th Century navigators were without the one essential instrument necessary to the accurate determination of longitude. That instrument was an accurate timepiece that could be carried to sea. It is not necessary to have a timepiece in order to learn one’s latitude, but longitude is a more difficult problem, andtimeis an element in it. But the watches of the 16th Century were too inaccurate to be of much service, and, as a matter of fact, it was not until 1607 that it was realized that a day is not necessarily made up of twenty-four hours. If one stays in one place it is true that there are twenty-four complete hours from noon to noon, and clocks were designed to register the timeatone place. But suppose, as the sun rises to-morrow morning, you board a very fast airplane and fly it at its fastest speed toward the west. Suppose this airplane flies at the rate of 1,000 miles an hour. In twenty-four hours you have flown around the world, and wherever you have been during that time the sun has been just rising behind you. It has been early morning foryouall the time. Suppose, on the other hand, you had flown east at the same rate of speed. If you started at six o’clock in the morning, in three hours the sun would be overhead—that is, it would be noon foryou. In three more it would be evening. In six more it would be morning again, for you would be halfway around the world. Six hours later evening would cometo you, and in another six hours you would be at your starting point and it would bemorning once more—thesecondmorning you had seen after you started, but only thefirstmorning after for the people you had parted from twenty-four hours before.

Ships, of course, do not travel at 1,000 miles an hour. But they do travel many miles, perhaps several hundred, in twenty-four hours. Therefore, if you start at Guayaquil, Ecuador (I use that, for it is very nearly on the equator), and sail west for twenty-four hours, making 240 miles, your watch will tell you that it is exactly the same time of day that it was when you left Guayaquil. But that is not true. Itisthe same time of dayat Guayaquil, but you are four degrees west of Guayaquil, and the sun must still travel past four degrees of longitude before the time at the spot you have reached will be what your watch suggests. It will take the sun sixteen minutes to cover that distance, and therefore your watch is sixteen minutes fast.

Great strides were made during the 16th and 17th centuries and many books were published. Probably the first book entirely about navigation ever published was one entitled “Arte de navigar,” by Pedro de Medina. This appeared in Spain in 1545. The fact, however, that the subject was not really understood is proved by the acceptance at an even later date of the theory that the earth did not move and that the sun revolved about it.

Charts became greatly improved during the latter part of the 16th Century, owing to the studies of Mercator, after whom the “Mercator projection” is named. The Mercator projection is used in the type of map that shows the entire surface of the earth as if it were the unrolled surface of a cylinder, and is the type which is, perhaps, despite its errors, in commonest use to-day.

But despite many improvements it was not until the 18th Century that modern navigation really began. Then, suddenly, both the sextant and the chronometer were inventedin rapid succession—the one in 1731 and the other in 1735. The sextant is the instrument (now greatly perfected) that is used to measure accurately the angles between the horizon and the celestial bodies being observed, and the chronometer is the accurate timepiece (now also greatly perfected) used on practically all sea-going ships to keep a record of the time of the prime meridian of longitude—that is, the meridian numbered zero. Usually, nowadays, that meridian, as I have said, is the meridian of Greenwich, England, for it is at Greenwich that a British observatory is located, and at this observatory the vital data for seamen are compiled.

With the introduction of the sextant and the chronometer the determination of longitude became simple. And latitude, too, because of the sextant, could more accurately be determined.

It is not my purpose to go into detail in explaining the finding of one’s longitude, but I shall attempt to explain, simply, the theory.

The sun, during a day of twenty-four hours, covers the 360 degrees of the circumference of the earth. That is, during every hour it passes 15 degrees. If you have a clock that tells you that it is 9 o’clock in the morning at Greenwich and you know that, according to the sun, it is 8 o’clock in the morning where you are, you know that because of that difference of one hour there is a difference of 15 degrees of longitude, and that you are 15 degrees west of the meridian of Greenwich. If you were 15 degrees east, your time would be 10 o’clock.

Now if you have some accurate way of telling what time it is by the sun where you are, and you have a chronometer telling you the time at Greenwich, all you have to do is to subtract the earlier time from the later and work out how many degrees, minutes, and seconds of longitude are representedby the hours, minutes, and seconds of the difference. If it is later at Greenwich than where you are, you are west of Greenwich; if earlier, you are east.

On the morning of March 7, 1916, I took a sight of the sun when the chronometer showed it was 39 minutes and 1 second past 1. My sextant showed me, after I had made some corrections which I shall not attempt to explain, that the altitude of the sun was 24° 58′. From this, and other data that it is necessary to have, I worked out our timewhen I took the sight. The answer to my problem showed me that the time was 13 minutes and 4 seconds past 8 o’clock. Subtracting this time from the time shown by the chronometer I got 5 hours, 25 minutes, and 57 seconds. Because a difference of one hour of time represents a difference of 15 degrees of longitude, a difference of 5 hours, 25 minutes, and 57 seconds in time represents a difference of 81 degrees, 29 minutes, and 15 seconds in longitude. The Greenwich time was later than ours; therefore, our longitude was 81° 29′ 15″ west of Greenwich.

I have purposely refrained from explaining the working of the problem, for that can only be done with such a reference book as Bowditch at hand, in order that the compiled logarithms may be looked up. Furthermore, the explanation is long, technical, and, to the beginner, tedious, and is beside the purpose of this book. I have given the incomplete explanation only to show that to find longitude one must find one’s “local mean time,” and must have a timepiece showing the “mean time” at Greenwich.

In the foregoing explanation I have left out of consideration several factors vital to accuracy in navigation. For instance, I have not mentioned the fact that the sun is not so accurate in its movements as an accurate chronometer. Sometimes it is a few minutes ahead and sometimes it is a little behind time. From this, two expressions for time havecome into use: “apparent time” and “mean time.” “Apparent time” is the time that is shown by the sun; “mean time” is the time shown by the clock. Because there is this difference there must be a correction made for it, and this correction is to be found in the Nautical Almanac, which is a valuable part of the navigator’s equipment.

Again, the navigator takes the angle of the sun from the bridge or some other elevated part of his ship. The angle he gets from such a height is slightly different from the one he would get if he were at the water level. Therefore he must make a correction for the difference. This he finds by knowing his elevation above the water and looking up the correction.

USING A PELORUSThis apparatus consists of a movable plate marked with compass bearings, set in a stand. The observer sets the plate to correspond to the standard compass, and then sights across it in determining the compass bearings of points ashore from which he wishes to learn his exact position.

USING A PELORUSThis apparatus consists of a movable plate marked with compass bearings, set in a stand. The observer sets the plate to correspond to the standard compass, and then sights across it in determining the compass bearings of points ashore from which he wishes to learn his exact position.

USING A PELORUS

This apparatus consists of a movable plate marked with compass bearings, set in a stand. The observer sets the plate to correspond to the standard compass, and then sights across it in determining the compass bearings of points ashore from which he wishes to learn his exact position.

This apparatus consists of a movable plate marked with compass bearings, set in a stand. The observer sets the plate to correspond to the standard compass, and then sights across it in determining the compass bearings of points ashore from which he wishes to learn his exact position.

There are other corrections still, applying to the sextant angle, to the sun itself, and to time. All of these are necessaryif one wishes to be accurate, and a navigator should always be as accurate as his science permits.

But often it is impossible to learn the angle between the horizon and any of the celestial bodies, for clouds and fog sometimes shut off the sky and the horizon. Sometimes one is clear while the other is obscured; sometimes both are hidden. But still it is necessary to know the position of the ship. As a matter of fact, the heavier the clouds or the thicker the fog the more desirable it is to know one’s position accurately. Until recently, however, seamen have had to depend only upon dead reckoning which often is anything but accurate. But now the radio direction finder and the method of learning one’s position by asking radio stations ashore to supply it by plotting the directions from which one’s radio message reaches two or more of them are coming into more and more common use.

Dead reckoning however, is still highly important, and is used by every careful navigator. It requires considerable experience for a navigator accurately to place his ship by dead reckoning alone. As a matter of fact, if the voyage is long and the sky has been obscured, the navigator expects to find himself somewhat wrong in his estimation of his position and is correspondingly careful. He has had to depend upon his log, which, as I explained in the last chapter, is a kind of nautical speedometer. As a check against this he often keeps a record of the revolutions of his propeller, for he knows, from experience, how far he will sail in an hour with his propeller running at any given speed. This is advisable because seaweed may foul the rotator of his log, or driftwood tear it away or bend it.

In addition to the distance he has sailed he must know accurately the direction he has sailed, and if he has changed his direction he must know when and how much. Furthermore, he must study his charts carefully in order to learnwhether or not he is sailing in a part of the ocean in which there are currents, and if so he must figure out very carefully what effect the current has on his ship.

Suppose a ship was sailing by dead reckoning across the Gulf Stream directly east of Cape Hatteras. The Stream, let us say, is 100 miles wide, and he is ten hours in crossing it. The current flows at the rate of three miles an hour. Therefore, if he has headed straight across, the current has carried him thirty miles to the northeast, and unless he knows how wide the stream is, which direction and how fast it flows, and how long he has been in it, he cannot possibly know just where he is. It is as if you tried to cross a river in a rowboat and pointed its bow at right angles to the shore all the way. The current would certainly carry you downstream, so that you would not land on the opposite side directly across from where you started.

When it is necessary, then, for seamen to sail their ships entirely by “dead reckoning” they are always anxious to check up their positions by any outside aids that are available. It was for this reason that our captain, on the imaginary voyage we took from Philadelphia to Havana in the last chapter, sailed so close to Diamond Shoal Lightship instead of crossing the Gulf Stream and heading out to sea.

I shall add but one more thing before I end this brief and incomplete explanation of navigation and its related subjects. Navigation and dead reckoning we have touched upon. Piloting still remains untouched.

This branch of navigation, if branch it really is, shows the navigator the position of his ship by reference to objects ashore. Let us suppose that a ship has crossed the ocean and is approaching a harbour entrance. While at sea an error of half a mile or so meant little, but as he approaches shore he wants to knowexactlywhere he is.

On each side of the harbour entrance let us suppose thatthere is a lighthouse. The navigator gets out his large-scale chart of the vicinity and lays it on his chart table. This chart shows the harbour entrance and shows the positions of the lighthouses. Then he determines the direction of these two lighthouses according to his compass. Let us suppose one lies exactly northwest and the other exactly southwest. On the chart, then, he draws two lines, one through the point marking each of the lighthouses. From the lighthouse to the northwest he draws a line extending southeast (the opposite direction) out to sea. From the lighthouse to the southwest he draws a line to the northeast. These two lines cross, and he knows that his ship was exactly at the intersection when he took his bearings. As this can be done in a minute or two the position is very accurate, unless his ship is sailing very rapidly, which it probably would not be. This is known as the “cross bearing” method of learning one’s position, and is one of the simplest problems in piloting.

Suppose, however, that a ship is sailing along the shore, and but one prominent object can be seen on the land. The navigator watches until the object (a lighthouse, perhaps) is “four points off his bow”—that is, until the angle between his course and the direction of the object is 45 degrees. From that moment the log is watched carefully, until the object is directly at right angles to the ship’s course. The distance sailed during that time is the same as the distance from the ship to the object ashore at the time the second bearing is secured, and if a compass bearing is taken when the ninety-degree bearing has been taken, a line drawn on the chart from the position of the object ashore can be marked with the distance in miles, and the navigator will know exactly the position of his ship at that moment. This is known as “bow and beam bearings.” There are other similar methods of obtaining the desired result.

In foggy weather when ships are “on soundings”—that is, where the water is shallow enough to permit of the easy use of a line with a weight attached for measuring its depth—careful navigators invariably use the “lead line” constantly.

SOUNDING BY MACHINEA glass tube with the upper end closed and the lower end open is lowered in a special case to the sea bottom, and then brought to the surface. As the tube descends, the water compresses the air in the tube, and gradually creeps up inside. The inside of the tube being of ground glass the water leaves a mark showing how far it has entered the tube. By laying the tube on a special scale the depth to which the glass was carried can be gauged. There are other methods not greatly dissimilar from this.

SOUNDING BY MACHINEA glass tube with the upper end closed and the lower end open is lowered in a special case to the sea bottom, and then brought to the surface. As the tube descends, the water compresses the air in the tube, and gradually creeps up inside. The inside of the tube being of ground glass the water leaves a mark showing how far it has entered the tube. By laying the tube on a special scale the depth to which the glass was carried can be gauged. There are other methods not greatly dissimilar from this.

SOUNDING BY MACHINE

A glass tube with the upper end closed and the lower end open is lowered in a special case to the sea bottom, and then brought to the surface. As the tube descends, the water compresses the air in the tube, and gradually creeps up inside. The inside of the tube being of ground glass the water leaves a mark showing how far it has entered the tube. By laying the tube on a special scale the depth to which the glass was carried can be gauged. There are other methods not greatly dissimilar from this.

A glass tube with the upper end closed and the lower end open is lowered in a special case to the sea bottom, and then brought to the surface. As the tube descends, the water compresses the air in the tube, and gradually creeps up inside. The inside of the tube being of ground glass the water leaves a mark showing how far it has entered the tube. By laying the tube on a special scale the depth to which the glass was carried can be gauged. There are other methods not greatly dissimilar from this.

This tells them not only how deep the water is, but by putting tallow or soap on the bottom of the lead weight they bring up sand or mud or shells from the bottom. With this and the depth, a line is drawn on tracing paper on the same scale as the chart. Along this line these soundings and the kind of mud or sand the lead brings up are marked, at intervals corresponding to the distance the ship has sailed between soundings. The chart is printed with the depth of the water in fathoms and with the kind of bottom that will be found. After the navigator has compiled his data for afew miles the tracing paper with the line on it can be moved about over the chart, and if care has been taken in sounding and watching the speed and direction of the ship, the navigator will find the place on the chart where his series of soundings will match the printed soundings. Then he will know very accurately where he is, even if it be a fog-enshrouded night.

Many, many important aspects of these three vital subjects have been completely passed over in this short chapter. If, however, I have been able to explain a little of the subjects, and if, particularly, I have quickened the interest of any of my readers in them, my purpose has been served. Going to sea is not so difficult as many people ashore are prone to think. But becoming a thorough seaman and a thorough navigator is not so simple, perhaps, as to become adept at much of the work that occupies men ashore.


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