WE are so accustomed to maps that it is almost impossible for us to imagine a time when there were no maps, when the notion of travelling according to a map was as foreign to man's conception of ultimate possibilities as the idea of traversing space in the form of a mathematical formula would be to us today.

The ancient Babylonians, who were such excellent geometrists that they could make a cadastral survey of their entire kingdom(that survey was made in 3800 B. C.,or 2400 years before Moses was born),have left us a few clay tablets containing what must have been an outline of their domains, but these were hardly maps in our sense of the word.The Egyptians, in order to get every penny of taxes they could sweat out of their hard-working subjects, also made a survey of their kingdom, which showed that they knew enough about practical mathematics to perform this difficult task.But no maps in the modern sense of the word have so far been found in any of the royal sepulchres.

The Greeks, the most curious-minded and nosey people of the ancient world, wrote endless treatises upon the subject of geography, but we know next to nothing about their maps. Here and there in some great commercial center there seem to have been engraved bronze tablets showing the best route to be followed if a merchant wanted to get from one part of the eastern Mediterranean to another.But none of these tablets has ever been dug up and we have no idea what they looked like.Alexander the Great, who covered greater distances than any other human being before him and very many after him, must have been possessed of a certain“geographical sense”,for he maintained a special body of professional“pacers”—men who went ahead of the army and kept an accurate account of the distances the indefatigable Macedonians wandered on their search for the gold of India.But of regular maps, which would have been understandable to ourselves, not a vestige, not a scrap, not a line.

The Romans, who in quest of plunder(the most marvellously organized“systematic plunderers”of which the world has any account until the beginning of the great colonial epoch in Europe)went everywhere, lived everywhere, built roads everywhere, gathered taxes everywhere, hanged and crucified people everywhere, left the ruins of their temples and swimming-pools everywere, seem to have been able to administer a world-empire without a single map worthy of the name. It is true their writers and orators quite frequently make mention of their maps and assure us that these were of remarkable accuracy and entirely dependable.But the only Roman map that has come down to us(if we except a small and insignificant piece of an ancient plan of Rome in the second century of our era)is something so primitive and clumsy that it is of no earthly value to modern man except as a historical curiosity.

It is known to historians as the Peutinger map because it was a man by the name of Conrad Peutinger, the town clerk to the city of Augsburg, who first conceived the idea of having it broadcasted by means of the recently invented printing-presses of Johann Gutenberg of Strassburg. Unfortunately Peutinger did not have the original to work from.The manuscript map he used was a thirteenth-century copy of a third-century original and during those thousand years, rats and mice had made away with a great many important details.

Even so, the general outline was undoubtedly that of the Roman original and if that was the best the Romans could do, they still had a great deal to learn. I will draw a copy of it here and let you judge for yourself.After a long and patient study of the document you will slowly begin to recognize what was in the mind of the Roman geographers.But you will also recognize that we have made enormous progress since the days when this spaghetti-shaped“world”was the last word in travel literature for a Roman general bound for England or the Black Sea.

As for the maps of the Middle Ages, we can pass them by without any special comment. The Church frowned upon all“useless scientific pursuits”.The road to Heaven was more important than the shortest route from the mouth of the Rhine to the mouth of the Danube, and maps became mere funny pictures, full of headless monsters(the poor Eskimos, huddled in their furs until their heads were no longer visible, were the originals for this fanciful notion)and snorting unicorns and spouting whales and hippogrifs and krakens and mermaids and griffons and all the other denizens of a world bewildered by fear and superstition.Jerusalem was of course shown as the center of the world, and India and Spain were the ultimate limits, beyond which no man could hope to travel, and Scotland was a separate island, and the Tower of Babel was ten times as big as the entire city of Paris.

Compared to these products of the medieval cartographers, the woven maps of the Polynesians(they look for all the world like something done by the children in a kindergarten, but they are exceedingly handy and very accurate)are veritable master pieces of the navigator's ingenuity. Not to mention the work of the contemporary Arabs and Chinese, who however were ruled out as contemptible heathen.Nor was there any real improve ment until the end of the fifteenth century when navigation was at last elevated to the rank of a science.

For then the Turks conquered the bridge-head connecting Europe with Asia, land traffic into the Orient was permanently interrupted, and it suddenly became necessary to find a new way to the Indies by way of the open sea. That meant an end to the old familiar system of sailing by the church-towers of the nearest mainland or sailing by the sound of the dogs barking along the waterfront.And it was this necessity of finding one's way across the ocean without seeing anything at all for weeks at a time except sky and water which brought about the great improvement in the navigating methods of that day.

The Egyptians seem to have ventured as far as Crete but no further, and even then the visits to the big island seem to have been more a matter of having been blown out of one's course than the result of a well-planned voyage of discovery. The Phoenicians and the Greeks were“church-tower sailors”at heart, although a few times they did quite remarkable things and even ventured forth as far as the Congo River and the Scilly Islands.Even then they undoubtedly hugged the shore as much as possible and at night pulled their boats up on dry land to escape being blown towards the open sea.As for the medieval merchants, they stuck to the Mediterranean, to the North Sea and to the Baltic, and were never for more than a few days without a glimpse of some distant mountainrange.

If they found themselves lost in the open, they had only one way in which to discover where the nearest land might be. For that purpose they always carried a few pigeons.They knew that pigeons would take the shortest route to the nearest bit of dry land.When they no longer knew what course to follow, they set one of their pigeons loose and observed the way it flew.Then they steered in that general direction taken by the bird until they saw the mountain tops and could make for the nearest harbor to ask where they might happen to be.

Of course during the Middle Ages even the average person was more familiar with the stars than we are today. He had to be because he lacked all sorts of information which nowadays comes to us in the printed form of almanacs and calendars.The more intelligent skippers therefore could find their way by studying the stars and by setting their course according to the Polar Star and the constellations.But in northern climes, where the sky was usually overcast, the stars were no great help.And navigation would have continued to be a painful and costly business of sailing by God and by guess(mostly the latter)if it had not been for a foreign invention which reached Europe shortly after the first half of the thirteenth century.But the origin and the history of the compass are still shrouded in deep mystery and what I tell you here is a matter of speculation rather than formal knowledge.

Genghis Khan, a little, slant-eyed Mongolian who during the first half of the thirteenth century ruled an empire slightly larger than any other that ever existed(it reached from the Yellow Sea to the Baltic and maintained itself in Russia until 1480)seems to have carried some sort of compass with him when he crossed the vast central Asiatic deserts, bound for the fleshpots of Europe. But it is impossible to say when the sailors of the Mediterranean had their first glimpse of this“blasphemous invention of the Devil”,as the Church people called it, which soon afterwards was to carry their vessels to the ends of the earth.

Inventions of that sort, which are of world-wide importance, all seem to start in the same vague way. Some one returning from Jaffa or Famagusta probably brought a compass with him which he had bought from a merchant in Persia, who had told him that he had got it from some one who had just returned from India.The rumor spread through the ale-houses of the waterfronts.Others wanted to see the funny little needle that had been bewitched by Satan and that would tell you where the north was, no matter where you happened to be.Of course, they did not believe such a thing could be true.Nevertheless, they asked their friend to bring them one too the next time he came back from the East.They even gave him the money, and six months later they had a little compass of their own.The darned thing worked!Then everybody must have a compass.Merchants in Damascus and Smyrna received hurry calls for more compasses.Instrument-makers in Venice and Genoa began to fabricate compasses on their own account.Suddenly we hear of compasses in every part of Europe.And within a few years the little glass-covered metal box had become such a common place sight that no one ever thought it worthwhile to write a book about an instrument that everybody had long since taken for granted.

So much for its career which must forever remain shrouded in mystery. But as for the compass itself, our knowledge about it has made great progress since the first sensitive needle guided the first Venetians from their lagoons to the delta of the Nile.For example, we have discovered that the needle of the compass does not point to the true north except on a few spots on the globe, while at all other places it points either a little to the east or a little to the west—a difference which is technically known as the“variation of the compass”.This is due to the fact that the magnetic north and south poles do not coincide with the north and south poles of our planet but are several hundred miles toward the south and the north of the geographic poles.The northern magnetic pole is located in the island of Boothia Felix, an island to the north of Canada, where Sir James Ross first located it in 1831,and the southern magnetic pole is situated at 73°S.Lat.and 156°E.Long.

It follows therefore that it is not enough for a captain to have merely a compass on board. He must also have charts which show him the variations of his compass in different parts of the world.That however has to do with the science of navigation and the present volume is no handbook on navigation.Navigation is an exceedingly difficult and complicated branch of learning which refuses very positively to let itself be reduced to simple little words of one syllable.For our present purpose it is enough if you will kindly remember that the compass made its entry into Europe during the thirteenth and fourteenth centuries and that it was of tremendous help in making navigation a reliable science, and not merely a matter of fortunate guessing and hopelessly complicated calculations, which were far beyond the mental reach of most people.

But that was only a beginning.

One could now tell whether one were sailing north or north by-east or north-north-east or north-east-by-north or north-east or north-east-by-east or in any of the other thirty-two“general directions”indicated by the compass. But for the rest, the medieval skipper had only two other instruments to help him find out in what part of the ocean he might happen to find himself.

In the first place, there was the lead-line. The lead-line was almost as old as the ships themselves.It would show the depth of the sea at any given point and if one had a chart indicating the different depths of the sea through which one was slowly wending one's way, the lead-line would give some indication of the approximate neighborhood in which one found one's self.

And then there was the log. The log originally was a small log of wood which was thrown overboard from the bow and which was then closely watched to see how long it would take before it passed the stern.As the length of the ship from stern to bow was of course known, one could then figure out how much time the vessel needed to pass a given point and that would show(more or less)how many miles the ship was making per hour.

The log of wood was gradually given up for the log-line, a long and thin but very strong piece of rope with a triangular piece of wood at the end. This rope had been beforehand divided into so many pieces by means of“knots”made at regular intervals and it was heaved overboard at the same time that another sailor started a sand-glass running.When all the sand had run through the glass(one knew of course beforehand how long that would take, two or three minutes)one pulled in the line and counted the knots that had run through one's hands while the sand-glass was emptying its contents from one bulb into the other.After that, a very simple calculation would show how fast the vessel was going, or as sailors used to say,“how many knots”.

But even if the captain knew the speed of his ship and the general direction it was following, there were the currents and the tides and the winds to upset even the most careful of his calculations. As a result an ordinary ocean voyage, even long after the introduction of the compass, remained a most hazardous undertaking.The people who worked on the theoretical end of the problem realized that in order to make it something else, they would have to find a substitute for the old church-tower.

I am not trying to be funny when I say this. The church tower or the tree on top of the high dune or the windmill on the dike or the barking of a watch-dog had been of such tremendous importance in the realm of navigation because it was a fixed point, something that would not change its position, no matter what happened.And given one such“fixed point”,the sailor could then make his own deductions.“I must go further towards the east,”he would say to himself, remembering the last time he had been in that part of the world, or“further towards the west or south or north to arrive where I want to be”.And the mathematicians of that day(brilliant men, by the way, who, considering the scanty information and the faulty instruments at their disposal, did as good work as was ever done in their particular field)knew perfectly well where the crux of the situation lay.They must find a“fixed point”in nature to act as a substitute for the“fixed point”established by man.

They began their search about two centuries before Columbus(I am mentioning his name because 1492 is the one date every man, woman and child seems to know)and they have not finished it even in this day of wireless time-signals and under-water signals and mechanical steering-gears, when the“Iron Mike”has about driven the old helmsman out of his job.

Suppose you find yourself standing on a round ball at the foot of a tower on top of which there waves a flag. That flag will then be right straight over your head and as long as you remain at the foot of your tower it will be right straight over your head.But if you move away from it and try to look at it, you must lift your eyes at an angle, and that angle will depend upon the distance you are away from the tower, as you will see by studying this picture.

And once this“fixed spot”had been discovered, the rest would be comparatively easy, for it would all be a matter of angles, and even the Greeks had known how to measure angles, for they had laid the foundation for the science of trigonometry which deals with the relationship between the sides and the angles of the triangle.

This brings us to the most difficult part of this chapter, indeed, I might say of the entire book—the search for what we now call latitude and longitude. The true method to establish one's latitude was discovered hundreds of years before longitude.

Longitude(now that we know how to find it)looks much simpler than latitude. But it offered certain almost insurmountable difficulties to our clockless ancestors.Whereas latitude, being merely a matter of careful observation and even more careful figuring, was something they were able to solve at a comparatively early date.But enough of generalities.Here the problem is, stated as simply as I know how.

You will notice a number of planes and angles. At D you find yourself right beneath the top of the tower, just as you will be standing almost right beneath the sun at 12 o'clock noon if you happen to be on the equator.When you have moved to E the matter becomes a little more complicated.The world on which you stand is round and you need a flat plane if you are to indulge in any figuring of angles.Therefore you draw a line from the imaginary center of the earth, called A, which runs through your own body and loses itself right above you in a spot called Zenith, the official astronomical name for the point of the heavens directly above the observer and which is the opposite of the Nadir, which is the point of the heavens directly under the observer.

Let us try to do this problem so that you can actually see it, for it is rather complicated. Stick a knitting-needle clean through the heart of an apple and imagine yourself on one side of that apple, sitting with your back leaning against the knitting-needle.The top of the knitting-needle is Zenith and the bottom is Nadir.Then imagine a plane that is at right angles with the place you are sitting or standing and the knitting needle.When you are standing at E that plane will be the plane called FGKH and BG will be the line on that plane from which you are making your observation.Furthermore, for the sake of convenience and in order to make the problem a little easier, kindly imagine that your eyes are in your toes, on the exact spot where your feet touch the line BG.Then look up at the top of the flag-pole on your tower and measure the angle top of flag-pole(or L),the spot where you stand(or E),and the end of your imaginary line BC, which is part of the imaginary plane FGKH, which runs at right angles with the imaginary line Zenith-A, which connects the center of the earth with the point of the heavens directly above you, the observer.That angle, if you know anything about trigonometry, will tell you how far you are away from the tower.Move to W and repeat the process.W will become the point where you touch the imaginary line MN, which is part of the imaginary plane OPRQ which runs at right angles with the line connecting the center of the earth A with the new Zenith(the Zenith of course changes every time you move an inch)which I shall call Zenith I.Measure the angle LWM and you know how much further you are away from the tower.

You see, even in the simplest form it is still quite complicated, and that is why I shall only give you a general outline of the basic principles upon which modern navigation is based. If you intend to become a sailor, you will have to go to a special school for a number of years to learn how to make the necessary calculations;and then after you have handled your instruments and your tables and charts for twenty or thirty years, your directors may even make you a captain and trust that you will be able to take a ship from one port to the next.If you have no such ambition, you will never understand all this anyway and so you will pardon me if I make this chapter short and stick to the general idea.

Since navigation was entirely an affair of angles, no possible advance could be made in that science until trigonometry had once more been rediscovered by the people of Europe. The Greeks had laid the foundations for this science a thousand years before, but after the death of Ptolemy(the famous geographer from Alexandria in Egypt)trigonometry had been forgotten or discarded as a superfluous luxury—something a little too clever to be quite safe.But the people of India and after them the Arabs of northern Africa and Spain had no such scruples and they had nobly carried on where the Greeks had left off.These words Zenith and Nadir(both of them pure Arabic)bear witness to the fact that when trigonometry was once more admitted to the curriculum of the European schools(which happened sometime during the thirteenth century)it was a Mohammedan and not a Christian branch of learning.But during the next three hundred years, the Europeans made up for lost time.For although they were once more able to work with angles and triangles, they still found themselves faced by the problem of discovering some definitely fixed point away from the earth to act as a substitute for their church-tower.

The most reliable candidate for this sublime honor was the North Star. The North Star was so far away from us that it never seemed to change its position and besides, it was so easy to locate that even the dumbest shrimp-fisherman could find it, once he had lost sight of land.All he had to do was to draw a straight line through the two stars that were furthest to the right in the Big Dipper, and he couldn't miss it.And, of course, there was always the sun, but its course had never been scientifically mapped out and only the most intelligent mariners could avail themselves of its assistance.

As long as people were forced to believe that the earth was flat, all calculations were bound to be hopelessly at odds with the true state of affairs. Early during the sixteenth century there came an end to these make-shift methods.The“disc”theory was discarded for the“sphere”theory and the geographers at last came into their own.

The first thing they did was to cut the earth into two equal halves which were divided by a plane running at right angles with the line connecting the North and the South Poles. The dividing line was called the equator.The equator therefore was everywhere equally far removed from both the North and the South Pole.Next the distance between the poles and the equator was divided into ninety equal parts.Next ninety parallel lines(circles, of course, for remember the earth was round at last)were drawn between the poles and the equator, each one about sixty-nine miles away from the next, since sixty-nine miles represented one-ninetieth of the supposed distance between the pole and the equator.

Geographers gave these circles numbers, beginning from the equator and going up(or down)to the poles. The equator itself became 0°and the poles 90°.Those lines were called degrees of Latitude(the L's of the picture will make you remember how they run)and a little°placed at the right of the number was used as a convenient symbol for the word“degree”which was too long to be used in mathematical calculations.

All this meant an enormous step forward. But even so, the business of going to sea remained a very dangerous experience.A dozen generations of mathematicians and sailors had to devote themselves to compiling data about the sun, giving its exact position for every day of every year and every clime before the average skipper was able to handle the latitude problem.

Then at last any reasonably intelligent sailor, provided he could read and write, was able to determine within a couple of miles how far away he was from the North Pole and from the equator or in technical terms, in what N. Lat.(degree of latitude north of the equator)or S.Lat.he might find himself.It was not quite so easy once he had crossed the equator, for then he was no longer able to fall back upon the Polar Star which is not visible on the southern hemisphere.But that problem too was eventually solved by science, and after the end of the sixteenth century latitude ceased to be a matter of concern to those who went down to the sea in ships.

There remained however the difficulty of determining one's longitude(longitude to make it easy for you to remember that the longitudinal degrees run in a vertical direction)and it took two whole centuries more before that puzzle had been successfully solved. In trying to establish the different latitudes, the mathematicians had been able to start out with two fixed points—the North Pole and the South Pole.“Here,”so they could say,“stands my church-tower, the North Pole(or the South Pole)and it will remain there until the end of time.”

But there was no East Pole and no West Pole either, because the axis of the earth did not happen to run that way. Of course one could draw an endless number of meridians, circles going around the earth and crossing both poles.But which one of these millions of meridians was the one to choose as“The Meridian”that was to divide the world into halves, so that thereafter the sailor could say,“I am a hundred miles east or west of‘The Meridian'”?The old notion of Jerusalem as the center of the earth was still strong enough to make many people demand that the meridian running through Jerusalem be recognized as Long.°or our vertical equator.But national pride prevented this plan.Every country wanted to have Long.°run through its own capital and even today, when we are supposed to be a little more liberal-minded in this respect, there still are German, French and American maps which show Long.running through Berlin, Paris and Washington.And in the end, as England was the country which happened to do most for the advancement of nautical knowledge during the seventeenth century(when the problem of longitude was finally solved)and as all nautical affairs were then under the supervision of the Royal Observatory, built in Greenwich near London in the year 1675,the meridian of Greenwich was finally adopted as the particular meridian which was to divide the world into longitudinal halves.

Then at last the sailor had his longitudinal church-tower, but he was still faced with another difficulty. How was he to discover how many miles he was either east or west of that Greenwich meridian, once he was out on the high seas?To settle this matter for good and all, the English government in the year 1713 appointed a special“Commission for the Discovery of Longitude at Sea”which was to solve the problem by the practical expedient of offering large rewards for the best method of“determining longitude on the high seas”.A hundred thousand dollars was a lot of money, two centuries ago, and everybody set to work with a will.When the commission was finally disbanded during the first half of the nineteenth century it had spent more than$500,000 in the form of rewards for deserving inventions.

Most of their labors have long since been forgotten and the work they did has been dropped as obsolete. But two inventions, following in the wake of these generous monetary rewards, have proved to be of lasting benefit.The first of these was the sextant.

The sextant is a complicated instrument(a sort of miniature nautical observatory which one can carry under one's arm)which allows the sailor to measure all sorts of angular distances. It was direct heir to the clumsy medieval astrolabe and cross-staff and the quadrant of the sixteenth century, and, as so often happens when the whole world is looking for the same thing at the same moment, three men claimed to be the original inventors and fought bitterly for the honor.

But the excitement caused in nautical circles by the appearance of the first sextants was mild compared to the interest shown in the chronometer when that faithful and reliable time-piece made its appearance four years later, in 1735. The chronometer, invented by John Harrison, an horological genius(he was a carpenter until he became a watch-maker),was a clock which worked so accurately that it made it possible to carry Greenwich time to any part of the world in any clime and in any form, sort or mode of conveyance.This John Harrison had been able to do by providing his clock with something he called a“compensation curve”.It altered the length of the balance-spring in proportion to the expansion or contraction caused by changes in temperature in such a way that his chronometer was practically weather-proof.

After endless and unseemly quarrels about the reward, Harrison received his hundred thousand dollars(in 1773,three years before his death). And today, no matter where a ship happens to be, provided it carries a chronometer, it will always know what time it is in Greenwich.And since the sun revolves around the earth in twenty-four hours(it is the other way around, but I am using the expression for the sake of convenience)and passes through fifteen degrees of longitude in one hour, all we need to do in order to determine just how far we have travelled east or west of The Meridian is to first determine what time it is on the spot where we ourselves happen to be and then compare our local time with Greenwich time and note the difference.

For example, if we find(after careful calculations which every ship's officer can make)that it is twelve o'clock where we are, but two o'clock by our chronometer(which gives us the exact Greenwich time),then we know that since the sun travels through fifteen degrees in one hour(which means four minutes for every single degree)and since there is a difference of two hours between our time and that of Greenwich, that we must have travelled exactly 2×15°=30°. And we write down in the log-book(a little book so-called because before the general introduction of paper it used to be a piece of wood on which all such figures were written down with chalk)that on such and such a day at noon our ship found itself at Long 30°West.

Today that startling invention of the year 1735 has lost a great deal of its importance. Every day at noon the Greenwich Observatory broadcasts the correct time all over the world.Chronometers are rapidly becoming superfluous luxuries.Indeed, if we are to believe our navigators, wireless telegraphy will eventually do away with all our complicated tables and our diligent calculations and computations.Then that lengthy chapter of finding one's way across those uncharted seas, where one wave looked so hopelessly much like the next that even the best of sailors could lose himself in less time than it takes to write down this sentence—then that marvellous chapter of courage and endurance and high intelligence will also have come to an end.The imposing man with the sextant will disappear from the bridge.He will sit in his cabin with a telephone clasped to his ear and he will ask,“Hello, Nantucket!(or Hello Cherbourg!)Where am I?”And Nantucket or Cherbourg will tell him.And that will be that.

But these twenty centuries of effort to make man's progress across the face of the earth safe and pleasant and profitable will not have been in vain. For they were one of the first successful experiments in international cooperation.Chinese, Arabs, Indians, Phoenicians, Greeks, Englishmen, Frenchmen, Dutchmen, Spaniards, Portuguese, Italians, Norwegians, Swedes, Danes, Germans, they all of them did their share to help the good work along.

That particular chapter in the history of cooperation has now been closed. But there remain enough others to keep us busy for quite a long time.