Of course a sundial that tells the time with any real accuracy is exceedingly rare. The problem is that the earth moves faster along its orbit in January than it does in July, and that the height of the sun's path across the sky changes every day. These difficulties account for the exceptional interest of a sundial constructed recently by Richard M. Sutton, professor of physics at the California Institute of Technology.

"If you leave a tennis ball undisturbed in the closet for a week," writes Sutton, "it turns completely around in space seven times! This simple fact, which ordinarily escapes notice, can be put to good use. Most people would say that the ball has not moved at all, yet they would admit the intellectual fact that the earth turns on its axis. The ball is turned by the earth around an axis parallel to that of the earth, and at just the rate at which the earth turns: 15 degrees per hour.

"If we combine the fact that the ball turns completely around once a day with an equally simple fact, we can convert any globe of the earth into a remarkable universal sundial that tells more about sunlight, the earth's motions in space and the conditions of sunlight in distant lands than might be supposed. The second fact is that the light falling on the earth from the sun comes in a flood of substantially parallel rays. Because of the great distance of the sun (some 93 million miles), even the extremes of a diameter of the earth are struck by rays that diverge by only .005 degree. This means that the angle subtended by a line 8,000 miles long seen at a distance of 93 million miles is about 1/200 of a degree. The significance of this fact will be apparent below.

"The rules for setting up the globe are simple and easily followed. It is rigidly oriented as an exact copy of the earth in space, with its polar axis parallel to the earth's axis, and with your own home town (or state) right 'on the top of the world' (where most of us like to think we belong anyway!). First turn the globe until its axis lies in your local meridian, in the true north and south plane that may be found by observing the shadow of a vertical object at local noon, by observing the pole star on a clear night, or by consulting a magnetic compass (if you know the local variation of the compass). Next turn the globe on its axis until the circle of longitude through your home locality lies in the meridian just found. Finally tilt the axis around an east-west horizontal line until your home town stands at the very top of the world. If you have followed these three steps, then your meridian circle (connecting the poles of your globe) will lie vertically in the north-south plane, and a line drawn from the center of the globe to your own local zenith will pass directly through your home spot on the map. Now lock the globe in this position and let the rotation of the earth do the rest. This takes patience, for in your eagerness to see all that the globe can tell you, you may be tempted to turn it at a rate greater than that of the turning of the earth. But it will take a year for the sun to tell you all it can before it begins to repeat its story.

"When you look at the globe sitting in this proper orientation-'rectified' and immobile-you will of course see half of it lighted by the sun and half of it in shadow. These are the very halves of the earth in light or darkness at that moment. An hour later the circle separating light from shadow has turned westward, its intersections with the Equator having moved 15 degrees to the west. On the side of the circle west of you, the sun is rising; on the side east of you, the sun is setting. You can 'count up the hours' along the Equator between your home meridian and the sunset line and estimate closely how many hours of sunlight still remain for you that day; or you can look to the west of you and see how soon the sun will rise, say, in Japan. As you watch the globe day after day, you will become aware of the slow turning of the circle northward or southward, depending upon the time of year.

"Let us take an imaginative look at the globe as it sits in the sun. Suppose it is during those days in June when the sun stands near the zenith in our new state of Hawaii. The globe dial shows that it is still sunlight at 9:30 p.m. in Iceland, that the midnight sun is shining on the North Cape of Norway. It is between late and early afternoon on the U. S. mainland, being about 6 p.m. in New York and 3 p.m. in San Francisco. The eastern half of South America is already in the darkness of its longer winter nights. The sun has recently risen next day in New Zealand and the eastern half of Australia, and most of China and Siberia are in early-morning light, whereas in Japan the sun is already four hours high in the sky. Alaska is enjoying the middle of a long summer day with the sun as high in the sky as it ever gets. Seattle is in early afternoon about two sun-hours ahead of Honolulu in the midst of a 16-hour day, while Sydney, Australia, is just starting a day with only 10 hours of sunlight.

"Now you don't have to be in Honolulu to see all this happening. Your own globe tells it to you. The same is true for persons who set up their globes in Fairbanks, Honolulu, Tokyo, Caracas, Havana or anywhere else. They will all see exactly the same story at the same time if in each place they have taken the small trouble to set up their globes for their own home towns as directed. If we choose, we can follow the progress of the circle of light and dark through the year.

Three months later, for example, when the sun has returned close to the celestial equator, and when it passes day by day close to the zenith along our own Equator, we will see the circle between light and dark apparently hinged on the polar axis of our globe. This is the time of the equinoxes, when every spot on earth has 12 hours of light and 12 hours of darkness. On December 21 the sun will have gone to its position farthest south, now failing to light any spot within the Arctic Circle but lighting the region within the Antarctic Circle completely (as you may see by stooping and looking at the lower part of your globe).

"From its position farthest south, the sun starts its way north again at a rate that may seem painfully slow for those in northern latitudes who wait for spring. By March 21 it has again reached the Equator, and we find it at the vernal equinox, the astronomers' principal landmark. Through the centuries this was the time for the beginning of the year. Only as recently as 1752 did December cease to be the 10th month of the year, as its name implies. January 1, 1752, was the first time that the calendar year began in January in England and the American colonies! At the vernal equinox in March there is a sunrise lasting 24 hours at the North Pole, and a sunset lasting 24 hours at the South Pole. Now, as the months advance, we will find that on June 21 this circle of light has advanced to its position farthest north. Sunlight does not enter the Antarctic Circle on the bottom side of your globe at all, but it extends clear over the North Polar region to the Arctic Circle beyond. At noon in your garden on this day you will see how people living on the meridian 180 degrees from your home are enjoying the midnight sun, provided they live within the Arctic Circle. Thus in imagination we have made a complete trip around the earth's orbit and have watched the progress of sunlight during the 365 or 366 intervening days—all right in the garden.

"It is not easy to appreciate the fact that the sun's rays are parallel as they fall on the earth. Let me suggest a simple experiment. On a bright morning take a piece of pipe or a cardboard tube and point it at the sun so that it casts a small, ring-shaped shadow. Now if at the very same moment someone 120 degrees east of you-one third the way around the world-were to perform the same experiment, he would point his tube westward at the afternoon sun. Yet his tube and yours would necessarily be parallel to within a very small fraction of a degree. If you point the tube at the sun in the afternoon, and someone far to the west simultaneously does the same in his morning, his tube will again be automatically parallel to yours. This experiment will help explain how it is that, when our globes are properly set up, people all over the world who are in sunlight will see them illuminated in just the same way.

"How easy it is, with this global dial, to imagine oneself in a distant land, seeing the sun in that sky at that time of day. A pin held at any point on the globe immediately shows the direction of the shadow of a man standing at that spot. Your globe has become a 'terrella,' a little earth that shows what the big earth is doing in space.

"It was from long experimenting with a precision sundial drawn on the floor of my office at Haverford College that I slowly came to the idea of this dial. I had developed that dial to the point where I could tell the time within five seconds. But the global dial is more exciting. When it came to me, I was enthralled by its simplicity and profundity: to be able to see at a glance everything about sunlight all over the world without budging from my own garden or office. However, I had a strong feeling that an idea so simple and universal could not have escaped intelligent people at other times and other places. I have now learned that it was recognized some 300 years ago, when globes were playthings of the wealthy. People were then regarding their world with new understanding, made much richer by the great ' sailing explorations and the increasing recognition of the earth's sphericity. To be sure, the early Greeks had seen that the earth must be a sphere. For example, Archimedes based his great works on floating bodies on a proposition that reads: 'The free surface of any body of liquid at rest is part of a sphere whose center is the center of the earth.' Imagine that for 200 B.C.! There is much evidence in the writings of the Greek mathematicians that they appreciated this fact. Their estimates of the earth's-size were correct in principle and not bad in actual result, but men seem to have ignored their observations and the reasoning behind them until the great age of exploration which we date from Columbus and the discovery of the New World.

"In a book on sundials by Joseph Moxon, first published in 1668, there is a description of 'the English globe, being a stable and immobile one, performing what ordinary globes do, and much more.' Moxon, who was hydrographer to Charles II (and whose book was dedicated to Samuel Pepys, Principal Officer of the Navy), ascribes this globe to the Earl of Castlemaine. It seems certain that the globe existed in London by 1665. In 1756 another global sundial was described by Charles Leadbetter. Consider the delightful title of Leadbetter's book: 'MECHANICK DIALLING, or the New Art of Shadows, freed from the Obscurities, Superfluities, and Errors of former writers upon the Subject-the whole laid down after so plain a method that any person (tho' a Stranger to the Art) with a Pair of Compasses and Common Ruller only, may make a Dial upon any Plane for any place in the World, as well as those who have attained to the greatest Knowledge and Perfection in the Mathematics. A work not only usefull for Artificers but very entertaining for Gentlemen, and those Student at the Universities that would understand Dialling without the Fatigue of going through a Course of Mathematics.' They knew how to make full use of a title page in those days!

"Leadbetter tells how to erect an immobile stone sphere and inscribe a map on it. He says: 'According to their true latitudes and longitudes ( for various spots on earth) you may discover any moment when the Sun shines upon the same, by the illuminated parts thereof, what Places on Earth are enlightened, and what Places are in darkness... The Extremity of the Shadow shows likewise what Places the Sun is Rising or Setting at; and what Places have long Days; these with many more curious Problems are seen at one View, too many to be enumerated in this place. The dial is the most natural of all others because it resembles the Earth itself, and the exact manner of the Sun's shining thereon.' Leadbetter suggests that a pin be placed at each pole in order to use the global sundial to tell time. Around each pin are 24 marks-one every 15 degrees- corresponding to the hours; the time is read by noting the position of the pin's shadow with respect to the marks. I, too, have used this system. Leadbetter adds: 'As you see, that [pin] at the North Pole will give the hour in summer, that at the South Pole the hour in Winter.'

"There is no spot on earth with which we do not at some time during the year share the light from the sun. One might object that surely the nadir, that spot directly beneath our feet on the other side of the earth, has no sunlight while we ourselves have it, but atmospheric refraction keeps the sun in the sky longer than geometry alone predicts, making every sunrise about two minutes early and every sunset about two minutes late.

"It is easy to tell from the global sundial just how many hours of sunlight any latitude (including your own) will enjoy on any particular day. All you need to do is to count the number of 15-degree longitudinal divisions that lie within the lighted circle at the desired latitude. Thus at 40 degrees north latitude in summer the circle may cover 225 degrees of longitude along the 40th parallel, representing 15 divisions or 15 hours of sunlight. But in winter the circle may cover only 135 degrees, representing nine divisions or nine hours. As soon as the lighted circle passes beyond either pole, that pole has 24 hours of sunlight a day, and the opposite pole is in darkness.

"One or two other concepts may make the dial even more useful. First, we can answer the question: Where is the sun in the zenith right now? Can we find the spot on earth where men find their shadows right at their feet? Easily. Hold the end of a pencil at the surface of the globe and move it until its shadow is reduced to its own cross section. When the pencil points from the center of the sun to the center of the globe, the spot on the map where its end rests corresponds to the point immediately beneath the sun. Better still, if you use a small tube instead of a pencil, you can let the sunlight pass down the tube to cast a ring-shaped shadow at the point beneath the sun. This point is important, because it gives the latitude and longitude of the sun at that moment and locates the center of the great circle of daylight. Ninety degrees around the globe in any direction from that point is a point where the sun appears on the horizon, either rising or setting. At the north and south extremes of the circle between light and darkness are 'the points where sunrise and sunset meet.' In June, for example, the southern point shows where the sun barely rises and then promptly sets in Antarctica, and the northern point (beyond the North Pole ) shows where the midnight sun dips to the horizon and immediately rises again.

"To find the point directly beneath the sun still more accurately, you can construct a simple cardboard tripod. Just cut three identical pieces of cardboard and fasten them together with gummed paper as shown in the accompanying illustration [above]. When the tripod stands on a level table, the line joining the three vanes is vertical. When the tripod rests on the surface of your globe, the line extends outward along a radius of the globe. If you move the tripod about until the shadow of its three vanes disappears into three lines, you find the subsolar point at the junction of these lines. Once you have found the subsolar point, and hence the exact location of the sun in our system of coordinates, it is a simple matter to count off the hours since or until your local noon, to tell your local sun-time, to forecast the time until sunset and to tell how long it is since sunrise. You can also determine these things for locations other than your own.

"Perhaps this little sundial, so simply set up, will clarify the apparent motions of the sun, caused of course by the earth's daily rotation on its axis and its annual revolution around the sun. Surely it is fun to bring so much of the system of the world into your garden. The global dial can give one a fuller appreciation of the sunlight on which all men depend. If it thereby strengthens your feeling of kinship for people far-away, the instrument will have served you well."

Bibliography

EVERYBODY S WATCHES. Arthur Tremayne. N. A. G. Press, 1942.

HOW TIME IS MEASURED. Peter Hood. Oxford University Press, 1955.

Suppliers and Organizations

The Society for Amateur Scientists
5600 Post Road, #114-341
East Greenwich, RI 02818
Phone: 1-401-823-7800

Internet: http://www.sas.org/