My son is bearing, with strained patience, the quasi-hu morous changes being rung upon his last name by his grade,school classmates. My explanation to him that the name "Asimov," properly pronounced, has a noble reso nance like the distant clash of sword on shield in the age of chivalry, leaves him unmoved. The hostile look in his eyes tells me quite plainly that he considers it my duty as a father to change my name to "Smith" forthwith.

Of course, I sympathize with him, for in my time, 1, too, have been victimized in this fashion. The ordinary misspellings of the uninformed I lay to one side. However, there was one time...

It was when I was in the Army and working out my stint in basic training. One of the courses to which we were exposed was map-reading, which had the great advantage of being better than drilling and hiking. And then, like a bolt of lightning, the sergeant in charge pronounced the fatal word "azimuth" and all faces turned toward me.

I stared back at those stalwart soldier-boys in horror, for I realized that behind every pair of beady little eyes, a small brain had suddenly discovered a source of infinite fun.

You're right. For what seemed months, I was Isaac Azimuth to every comic on the post, and every soldier on the post considered himself a comic. But, as I told myself (paraphrasing a great American poet), "This is the army, Mr. Azimuth."

Somehow, I survived.

And, as fitting revenge, what better than to tell all you inoffensive Gentle Readers, in full and leisurely detail, exactly what azimuth is?

It all starts with direction. The first, most primitive, and most useful way of indicating direction is to point. "They went that-a-way." Or, you can make use of some land mark known to one and all, "Let's head them off at the gulch.

This is all right if you are concerned with a small sec tion of the Earth's surface; one with which you and your friends are intimately familiar. Once the horizons widen, however, there is a search for methods of giving directions that do not depend in any way on local terrain, but are the same everywhere on the Earth.

An obvious method is to make use of the direction of the rising Sun and that of the setting Sun. (These direc tions change from day to day, but you can take the average over the period of a year.) These are opposite directions, of course, which we call "east" and "west." Another pair of opposites can be set up perpendicular to these and be called "north" and "south."

If, at any place, north, east, south, and west are deter mined (and this could be done accurately enough, even in prehistoric times, by careful observations of the Sun) there is nothing, in principle, to prevent still finer directions from being established. We can have northeast, north northeast, northeast by north, and so on.

With a compass you can accept directions of this sort, follow them for specified distances or via specified land marks, and go wherever you are told to go. Furthermore, if you want to map the Earth, you can start at some point, travel a known distance in a known direction to another point, and locate that point (to scale) on the map. You can then do the same for a third point, and a fourth, and a fifth, and so on. In principle the entire surface of the planet can be laid out in this manner, as accurately as you wish, upon a globe.

However, the fact that a thing can be done "in prin ciple" is cold comfort if it is unbearably tedious and would take a million men a million years. Besides, the compass was unknown to western man until the thirteenth century, and the Greek geographers, in trying to map the world, had to use other dodges.

One method was to note the position of the Sun at mid day; that is at the moment just halfway between sunrise and sunset. On any particular day there will be some spots on Earth where the Sun will be directly overhead at mid day. The ancient Greeks knew this to be true of southern Egypt in late June, for instance. In Europe, however, the sun at midday always fell short of the overhead point.

This could easily be explained once it was realized that the Earth was a sphere. It could furthermore be shown, without difficulty that all points on Earth at which the Sun, on some particular day, fell equally short of the overhead point at midday, were on a single east-west line. Such a line could be drawn on the map and used as a reference for the location of other points. The first to do so was a Greek geographer named Dicaearchus, who lived about 300 B.c. and was one of Aristotle s pupils.

Such a line is called a line of "latitude," from a Latin word meaning broad or wide, for when making use of the usual convention of putting north at the top of a map, the east-west lines run in the direction of its width.

Naturally, a number of different lines of latitude can be determined. All run east-west and all circle the sphere of the Earth at constant distances from each other, and so are parallel. They are therefore referred to as "parallels of latitude."

The nearer the parallels of latitude to either pole, the smaller the circles they make. (If you have a globe, look at it and see.) The longest parallel is equidistant from the poles and makes the largest circle, taking in the maximum girth of the Earth. Since it divides the Earth into two equal halves, north and south, it is called the "equator" (from a Latin word meaning "equalizer").

If the Earth were cut through at the equator, the section would pass through the center of the Earth. That makes the equator a "great circle." Every sphere has an infinite number of great circles, but the equator is the only parallel of latitude that is one of them.

It early became customary to measure off the parallels of latitude in degrees. There are 360 degrees, by coilven 40 tion, into which the full circumference of a sphere can be divided. If you travel from the equator to the North Pole, you cover a quarter of the Earth's circumference and therefore pass over 90 degrees. Consequently, the parallels range from O' at the equator to 90' at the North Pole (the small ' representing "degrees"). .If you continue to move around the Earth past the North Pole so as to travel toward the equator again, you must pass the parallels of latitude (each of which encircles the Earth east-west) in reverse order, traveling from 90' back to O' at the equator (but at a point directly opposite that of the equatorial beginning). Past the equator, you move across a second set of parallels circling the southern half of the globe, up to 90' at the South Pole and then back to O', finally at the starting point on the equator.

To differentiate the O' to 90' stretch from equator to North Pole and the similar stretch from equator to South Pole, we speak of "north latitude" and "south latitude."

Thus, Philadelphia, Pennsylvania is on the 400 north latitude parallel, while Valdivia, Chile is on the 40' south latitude parallel.

Parallels of latitude, though excellent as references about which to build a map, cannot by themselves be used to locate points on the Earth's surface. To say that Quito, Ecuador is on the equator merely tells you that it is some where along a circle 25,000 miles in circumference.

For accurate location one needs a gridwork of lines-a set of north-sbuth lines as well as east-west ones. These north-south lines, running up and down the conventionally oriented map (longways) would naturally be called "longi tude."

Whenever it is midday upon some spot of the Earth it is midday at all spots on the same north-south line, as one can easily show if the Earth is considered to be a rotating sphere. The north-south line is therefore a "meridian" (a corruption of a Latin word for "midday"), and we speak of "meridians of longitude."

Each meridian extends due north and south, reaching the North Pole at one extreme and the South Pole at the other. All the meridians therefore converge at both poles and are spaced most widely apart at the equator, for all the world like the boundary lines of the segments of a tangerine. If one imagines the Earth sliced in two along any meridian, the slice always cuts through the Earth's center, so that all meridians are great circles, and each stretches around the world a distance of approximately 25,000 miles.

By 200 B.C. maps being prepared by Greeks were marked off with both longitude and latitude. However, making the gridwork accurate was another thing. Latitude was all right. That merely required the determination of the average height of the midday sun or, better yet, the average height of the North Star. Such determinations could not be made as accurately in ancient Greek times as in modem times, but they could be made precisely enough to produce reasonably accurate results.

Longitude was another matter. For that you needed the time of day. You had to be able to compare the time at which the Sun, or better still, another star (the sun is a star) was directly above the local meridian, as compared with the time it was directly,above another meridian. If a star passed over the meridian of Athens in Greece at a certain time, and over the meridian of Messina in Sicily 32 minutes later, then Messina was 8 degrees of longitude west of Athens. To determine such matters, accurate time pieces were necessary; timepieces that could be relied on to maintain synchronization to within fractions of a minute over long periods while separated by long distance; and to remain in synchronization with the Earth's rotation, too.

In ancient times, such timepieces simply did not exist and therefore even the best of the ancient geographers managed to get their meridians tangled up. Eratosthenes of Cyrene, who flourished at Alexandria in 200 B.c., thought that the meridian that passed through Alexandria also passed through Byzantium (the modern city of Istanbul, Turkey). That meridian actually passes about 70 miles east of Istanbul. Such discrepancies tended to increase in areas farther removed from home base.

Of course, once the circumference of the earth is known (and Eratosthenes himself calculated it), it is possible to calculate the east-west distance between degrees of longi tude. For instance, at the equator, one degree of longitude is equal to about 69.5 miles, while at a latitude of 40' (either north or south of the equator), it is only about 53.2 miles, and so on. However, accurate measurements of distance over mountainous territory or, worse yet, over stretches -of open ocean, are quite difficult.

In early modem times, when European nations first began to make long ocean voyages, this became a horrible problem. Sea captains never knew certainly where they were, and making port was a matter of praying as well as sailing. In 1598 Spain, then still a major seagoing nation, offered a reward for anyone who would devise a timepiece that could be used on board ship, but the reward went begging.

In 1656 the I)rutch astronomer Christian Huygens in vented the pendulum clock-the first accurate timepiece.

It could be used only on land, however. The pitching, roll ing, and yawing of a ship put the pendulum off its feed at once.

Great Britain was a major maritime nation after 1600, and in 1675 Charles 11 founded the observatory in Green wich (then a London suburb, now Part of Greater Lon don) for the express purpose of carrying through the necessary astronomical observations that would make the accurate determination of longitude possible.

But a good timepiece was still needed, and in 1714 the British Government offered a large fortune (in those days) of 20,000 pounds for anyone who could devise a good clock that would work on shipboard.

The problem was tackled by John Harrison, a Yorkshire mechanics self-trained and gifted with mechanical genius.

Beginning in 1728 he built a series of five clocks, each better than the one before. Each was so mounted that it could take the sway of a ship without being affected. Each was more accurate at sea than other clocks of the time were on land. One of them was off by less than a minute after five months at sea. Harrison's first clocks were per haps too large and heavy to be completely practical, but the fifth was no bigger than a large watch.

The British Parliament put on an extraordinary display of meanness in this connection, for it wore Harrison out in its continual delays in paying him the money he had earned and in demanding more and ever more models and tests. (Possibly this was because Harrison was a provincial mechanic and not a gentleman scientist of the Royal So ciety.) However, King George III himself took a personal interest in the case and backed Harrison, who finally re ceived his money in 1765, by which time he was over 70 years old.

It is only -in the last two hundred years, then, that the latitude-longitude gridwork on the earth became really accurate.

Even after precise longitude determinations became pos sible, a problem remained. There is no natural reference base for longitude; nothing like the equator in the case of latitude. Different nations therefore used different systems, usually basing "zero longitude" on the meridian passing through the local capital. The use of different systems was confusing and the risk was run of rescue operations at sea being hampered, to say nothing of war maneuvers among allies being stymied.

To settle matters, the important maritime nations of the world gathered in Washington, D.C. in 1884 and held the "Washington Meridian Conference." The logical de cision was reached to let the Greenwich observatory serve as base since Great Britain was at the very height of its maritime power. The meridian passing through Greenwich is, therefore, the "prime meridian" and has a longitude of 00.

The degrees of longitude are then marked off to the west and east as "west longitirde" and "east longitude."

The two meet again at the opposite side of the world from the prime meridian. There we have the 180' meridian which runs down the middle of the Pacific Ocean.

Every degree of latitude (or longitude) is broken up into 60 minutes ('), every minute into 60 seconds ("), while the seconds can be broken up into tenths, hun dredtbs, and so on. Every point on the earth can be located uniquely by means of latitude and longitude. For instance, an agreed-upon reference point within New York City is at 40' 45' 06" north latitude and 73' 59' 39" west longi tude; while Los Angeles is at 34' 03' 15" north latitude and 118' 14' 28" west longitude.

The North Pole and the South Pole have no longitude, for all the meridians converge there. The North Pole is defined by latitude alone, for 90' north latitude represents one single point-the North Pole. Similarly, 90' south lati tude represents the single point of the South Pole.

It is possible to locate longitude in terms of time rather than in terms of degrees. The complete day of 24 hours is spread around the 360' of longitude. This means that if two places differ by 15' in longitude, they also differ by 1 hour in local time. If it is exactly noon on the prime meridian, it is 1 P.m. at 15' east longitude and 1 1 A.M. at 151 west longitude.

If we decide to call prime meridian 0:00:00 we can assign west longitude positive time readings and east longi tude negative time readings. All points on 15' west longi tude become +1:00:00 and all points on 15' east longi tude become - 1: 00: 00.

Since New York City is at 73' 59' 39" west longitude it is 4 hours 55 minutes 59 seconds earlier than London and can therefore be located at +4:55:59. Similarly, Los Angeles, still farther west, is at +8:04:48.

In short, every point on Earth, except for the poles, can be located by a latitude and a time. The North and South Poles have latitude only and no local times, since they have no meridians. This does not mean, of course, that there is no time at the poles; only that the system for measuring local times, which works elsewhere on Earth, breaks down at the poles. Other systems can be used there; one pole might be assigned Greenwich time, for instance, while the other is assigned the time of the 180' meridian.

In the ordinary mapping of the globe, both latitude and longitude are given in ordinary degrees. However, the time system for longitude is used to establish local time zones over the face of the Earth, and the 180' meridian becomes the "International Date Line" (slightly bent for geographical convenience). AU sorts of interesting para doxes become possible, but that is for another article another day.

And what about mapping the sky? This concerned astronomers even before the problem of the mapping of the Earth, really, for whereas only small portions of the Earth are visible to any one man at any one time, the entire expanse of half a sphere is visible overhead The "celestial sphere" is most easily mapped as an ex tension of the earthly sphere. If the axis of the Earth is imagined extended through space until it cuts the celestial sphere, the intersection would come at the "North Celestial Pole" and the "South Celestial Pole." ("Celestial," by the way, is from a Latin word for "sky.")

The celestial sphere seems to rotate east to west about the Earth's axis as a reflection of the actual rotation of the Earth west to east about that axis. Therefore, the North Celestial Pole and the South Celestial Pole are fixed points that do not partake in the celestial rotation, just as the North Pole and the South Pole do not partake in the earthly rotation.

The near neighborhood of the North Celestial Pole is marked by a bright star, Polaris, also called the "pole star" and the "north star," which is only a degree or so from it and makes a small circle about it each day. The circle is so small that the star seems fixed in position day after day, year after year, and can be used as a,reference point to determine north, and therefore all other directions.

Its importance to travel in the days before the compass was incalculable.

The imaginary reference lines on the Earth can all be transferred by projection to the sky, so that the sky, like the Earth, can be covered with a gridwork of ghost nes.

There would be the "celestial equator," making up a great circle equidistant from the celestial poles; and "celestial latitude" and "celestial longitude" also.

The celestial latitude is called "declination," and is measured in degrees. The northern half of the celestial sphere ("north celestial latitude") has its declination given as a positive value; the southern half ("south celestial latitude") as a negative value. Thus, Polaris has a declina tion of roughly +89'; Pollux one of about +30'; Sirius one of about -15'; and Acrux (the brightest star of the Southern Cross) a declination of about -60'.

The celestial longitude is called "right ascension" and the sky has a prime meridian of its own that is less arbitrary than the one on Earth, one which could therefore be set and agreed upon quite early in the game.

I The plane of the Earth's orbit about the Sun cuts the celestial sphere in a great circle called the "ecliptic" (see Chapter 4). The Sun seems to move exactly along the line of the ecliptic, in other words.

Because the Earth's axis is tipped to the plane of Earth's orbit by 23.5', the two great circles of the ecliptic and the celestial equator are angled to one another by that same 23.50.

The ecliptic crosses the celestial equator at two points.

When the Sun is at either point, the day and night are equal in length (twelve hours each) all over the Earth.

Those points are therefore the "equinoxes," from Latin words meaning "equal nights."

At one of these points the Sun is moving from negative to positive declination, and that is the "vernal equinox" because it occurs on March 20 and marks the beginning of spring in the Northern Hemisphere, where most of man kind lives. At the other point the Sun is moving from positive to negative declination and that is the autumnal equinox, falling on September 23, the beginning of the northern autumn.

The point of the vernal equinox falls on a celestial meridian which is assigned a value of O' right ascension.

The celestial longitude is then measured eastward only (either in degrees or in hours) all the way around, until it returns to itself as 360' right ascension.

By locating a star through declination and right ascension one does precisely the same thing as locating a point on Earth through latitude and longitude.

An odd difference is this, though. The Earth's prime meridian is fixed through time, so that a point on the Earth's surface does not change its longitude from day to day. However, the Earth's axis makes a slow revolution once in 25,800 years, and because of this the celestial equator slowly shifts, and the points at which it crosses the ecliptic move slowly westward.

The vernal equinox moves westward, then, circling the sky every 25,800 years, so that each year the moment in time of the vernal equinox comes just a trifle sooner than it otherwise would, The moment precedes the theoretical time and the phenomenon is therefore called "the preces sion of the equinoxes."

As the vernal equinox moves westward, every point on the celestial sphere has its right ascension (measured from that vernal equinox) increase. It moves up about 1/7 of a second of arc each day, if my calculations are correct.

This system of locating points in the sky is'ealled the "Equatorial System" because it is based on the location of - the celestial equator and the celestial poles.

A second system may be established based on the observer himself. Instead of a "North Celestial Pole" based on a rotating Earth, we can establish a point directly overhead, each person on Earth having his own overhead point-although for people over a restricted area, say that of New York City, the different overhead points are practically identical.

The overhead point is the "zenith," which is a medieval misspelling of part of an Arabic phrase meaning "over head." The point directly opposite in that part of the celestial sphere which lies under the Earth is the 'nadir," a medieval misspelling of an Arabic word meaning "op posite."

The great circle that runs around the celestial sphere, equidistant from the zenith and nadir, is the "horizon," from a Greek word meaning "boundary," because to us it seems the boundary between sky and Earth (if the Earth were perfectly level, as it is at sea). This system of locating points in the sky is therefore called the "Horizon System."

The north-south great circle traveling from horizon to horizon through the zenith is the meridian. The cast-west great circle traveling from horizon to horizon through the zenith, and making a right angle with the meridian, is the 14 prime vertical."

A point in the sky can then be said to be so I many degrees (positive) above the horizon or so many degrees (negative) below the horizon, this being the "altitude."

Once that is determined, the exact point in the sky can be located by measuring on that altitude the number of degrees westward from the southern half of the meridian.

At least astronomers do that. Navigators and surveyors measure the number of -degrees eastward from the north end of the meridian. (In both cases the direction of meas ure is clockwise.)

The number of degrees west of the southern edge of the meridian (or east of the northern edce, depending on the system used) is the azimuth. The word is a less corrupt form of the Arabic expression from which "zenith" also comes.

If you set north as having an azimuth of O', then east has an azimuth of 90', south an azimuth of 180', and west an azimuth of 270'. Instead of boxing the compass with outlandish names you can plot direction by degrees.

And as for myseff?

Why, I have an azimuth of isaac. Naturally.

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