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The Earth Is Not a Cube

by Erhardt Hehn

No, the earth is neither a cube nor a flat sheet nor a disc; rather, it is a globe, a proper aerodynamic design for hurdling through space. For man this ball presents a challenge to man's penchant for measuring time, distance and space.

Once it was accepted that the earth was indeed in the shape of a ball, the concepts of the minds of mariners, cartographers and astrologers coalesced into a system for measuring time and distance. The earth was encircled with imaginary parallel lines progressing from the equator to opposite poles, like rings on a raccoon's tail. The lines, called latitudes, can be viewed as the equivalent of horizontal coordinates on a flat plane.

Visualizing the vertical coordinates as lines at right angle to the horizontal coordinates on a globe presents a problem. These lines, known as longitudes or meridians, must converge on the earth's poles, like the slices of an orange. Thus, the geometric figures formed by the intersection of latitude and longitude lines do not form squares but trapezoids. Trapezoids do not lend themselves as well to a unit of surface measurement as the square. A further complication of this novel imaginary system of coordinates is that the spaces enclosed by the intersecting coordinates become progressively smaller from the equator to the poles as the longitudinal lines converge to a point.

This imaginary network of lines surrounding the earth has indeed been developed as a means of determining a global position on either land, sea or air, and an approximation of time according to 24 longitudinal time zones. As a system for describing land ownership, control and use patterns the system has not been widely applied. In a large measure this is so because the land ownership patterns of the developed areas of the world had been established by a system of metes and bounds before the longitude/latitude grid system and by a recognition of the inherent geometric problems. How widely this grid system was applied to the undeveloped lands of South America, Africa, Australia and New Zealand is not known to me. In 1783 the Congress of the 13 colonies formulated a policy for the disposition of public land and established a permanent method of surveying. I am assuming that the method of surveying was to divide the public lands into blocks one mile square containing 640 acres, more or less. Lines parallel to the latitudes would constitute the bases of the one-mile squares. The problem of the convergence of the longitude lines was resolved by ignoring them. The sides of the squares were simply drawn perpendicular to the bases. Periodically a square mile section was dropped out of a tier to accommodate the convergence of the vertical longitude lines of the grid. Traveling in a north/south direction in an area surveyed in this manner you will note such a correction line approximately every 36 miles by the jog in the otherwise straight road. The Homestead Act of 1862 established one-fourth of a section, 160 acres, as the basic homestead unit often referred to as a "claim." After five years of occupancy the 160 acres could be "claimed" for a small fee. This widely applied method of land survey west of the Appalachian Mountains paid absolutely no attention to the natural features of the land. It was a simple, manageable system of disposition of millions of acres of public domain.

In a sense this insensitive system of land survey was an affront to the very nature of the world as man found it. Nature abhors straight lines and sharp angles. If you are seated next to a port hole, the sky is clear and you are interested, a flight from Bozeman to some point on the North Atlantic Coast will reward you with a mural of the effect of the systems of land survey on the landscape below.

As you climb out of the Gallatin Valley and head East you will see ample evidence of the checkerboard surveying which was done before the arrival of many squatters. In looking across the Bridger Range one can speculate that the gridiron survey may have had something to do with the diaper-like clear-cuts. Neither in the irrigated valley of the Yellowstone River or the grasslands on either side as far as the Badlands do the land-use and ownership patterns bear many marks of a gridiron land survey. The irrigated bottom lands of the Yellowstone River from Billings to its confluence with the Missouri River in North Dakota were subdivided by the Bureau of Reclamation into 40 acre homesteads. In spite of three generations of consolidation the relatively small fields are a remnant of this severe fragmentation. On the eastern Montana and western North Dakota prairies we begin to see an increasing pattern of intersecting north/south and east/west roads at one-mile intervals. Blocks six miles square were organized into townships as political entities. The roads bordering the townships are often recognizable because they are usually the main secondary roads. When flying at right angle to these roads it is interesting to count the seconds it takes to cover an estimated six miles. If you clock less than ten seconds the plane speed is close to the 600 miles per hour sound barrier.

East of the Missouri River our flight takes us across the pot-hole country of North Dakota. We notice the effects of the gridiron survey on the landscape. Many roads which once skirted the potholes and wetlands now run across such areas in a straight line on a high grade. Windbreaks and shelter belts are planted in straight lines along roads and parallel fences and field edges. The only exceptions to the rigid checkerboard pattern are the railroad tracks and power lines that slash their way across the prairie, thanks to being granted eminent domain. Unless a road has been built along a railroad right-of-way you can not get to the next town without making a right angle turn (as is the case in the Gallatin Valley driving between Bozeman and Belgrade).

As we pass into Minnesota and on across Wisconsin and Michigan the unnaturalness of the straight lines and sharp angles resulting from accommodation by users to straight line survey becomes increasingly distasteful. Natural growing wood lots don't end in a straight line. Trees generally grow on both banks of a stream and the entire shore of a lake rather than here or there. It seems likely that the land ownership boundaries determined by metes and bounds would offer a closer harmony between man and the natural world than a rigid gridiron system --- as we fly over and look down on New York, Pennsylvania and the New England states it would appear so from the air. It has been my impression on the ground that the division of land and siting of roads by natural metes and bounds has left the country less impacted by the activities of man than the gridiron system of the West.

George Washington, early in life, had the experience of going with a party that was to survey land west of the Appalachian Mountains for a Lord Fairfax. I have wondered if President Washington may not have had a hand in determining the method with which public lands were to be surveyed. I do hope not because after learning that George may not always have told the truth and that he probably could not have thrown a dollar across the Rappahannock River, I don't think I could tolerate any more hero assassination.

1993 Erhardt R. Hehn

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