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William H. Calvin


Leapfrogging Gnomons
A method for surveying a very long
north-south line without modern instruments

William H. Calvin
University of Washington
Seattle WA 98195-1800 USA

Map from Lekson article The archaeologist Stephen H. Lekson has noted that a series of ancient sites lie along a 700-km-long line, the meridian of longitude at 107°57'W. Many similarities have been noted between the pre-Columbian Anasazi cultures of the Four Corners area (a region centered on 37°N and 109°W, where the states of Colorado, New Mexico, Arizona, and Utah meet) and the ruins further south in Mexico. Now Lekson suggests, in an article in Archaeology magazine (from whose website your browser is now borrowing the map by Lynda D’Amico), that three of the largest ancient towns were all constructed to be exactly north-south of one another.
      The misnamed Aztec Ruins are the most northerly, and are connected by an ancient road to Chaco Canyon 88 km to their south, a road that is mostly straight north-south. The meridian1 passes through the northwestern part of Chaco where two large mesa-top sites (Pueblo Alto and Tsin Kletzin) lie on a north-south line that includes, in the valley itself, the great kiva of Casa Rinconada (the two other largest ruins in the valley, Chetro Ketl and Pueblo Bonito, straddle this same north-south line).
      A kilometer east of this meridian is the huge Casas Grandes site, 624 km further to the south in the Mexican state of Chihauhua. Because of some architectural similarities between the sites, it has long been assumed that the Anasazis (who are among the ancestors of the remaining Pueblo Indians) helped to build them all in the centuries spanning AD 900-1500, moving north from Chaco to Aztec Ruins and then far south to Casas Grandes. The Acoma people, Pueblo Indians living 30 km east of this meridian, have a legend of their leaders taking journeys north and far south, as do the Zuni people living somewhat further to the west.
      Long north-south alignments date back even earlier in China. They featured the gnomon, a vertical column whose shortest shadow was used to measure seasonal changes in the elevation of the noontime sun. To quote Krupp (1983):

By A.D. 725 a series of field stations -- each equipped with an 8-foot gnomon and all strung out like widely spaced beads on a single meridian longitude over a span of [more than 2,500 km] -- was set up by a Chinese Buddhist monk, I Hsing [and extended from Indochina to Siberia].
This is a distance equal to extending the Anasazi's line north to the Canadian border, and south to the Pacific Ocean coastline.
      My brief purpose here is to suggest a method for surveying long north-south lines, using several gnomons at a time. Many peoples have used gnomons, such as Borneo tribesmen, Babylonians, and Ionian Greeks. Though I know of no Anasazi use of the gnomon, they did carry long, straight cedar and pine trees for great distances, judging from those remaining as beams in the Chaco ruins.
      I suggest that an experienced team of "utility pole" haulers could stand the pole on end, temporarily holding it in a vertical position with a few guy ropes. Given two such teams2 facilitates an interesting surveying method.

Surveying a Long North-South Line

      1. Balance a pole on end, guying it so that observations can be repeated on successive days.
      2. Use a long radial rope, loosely tied around the pole base, to follow the pole tip's shadow throughout the day. Find the shortest shadow length (which occurs at local noon) and stake the spot. Better yet (because maxima and minima are so hard to determine on the fly), find a pair of points in the morning and afternoon where the shadow is the same longer length -- say, the 0900-1500 points when the pole's shadow reaches the rope's end. Stake this pair and then stretch out another rope between the pair (this defines an east-west line); bisect this line by folding the rope to find the midpoint. Stake the center. The noon, 0900-1500 center, and gnomon pole should form a line. If they don't line up, repeat tomorrow with more morning/afternoon pairs, using knots along the radial rope to mark the standard lengths. The result should be a true north-south line.
      3. Send your second team south with the other tall pole. Have them hold it up as far away as a sight line can be maintained, such as atop a ridgeline.
      4. Standing north of the noon stake, the surveyor sights past the center-line stakes and the local pole, ignoring outliers, and judges if the distant pole (or the smoke plume from a signal fire) is in alignment. If not, the surveyor signals the second team to relocate east or west. A good signal for particularly long legs (one ridge line to another could be 20-30 km) would be a blanket tied to the top of the local pole, a rope (in the manner of a flag halyard or a jib sheet) being used to shift this flag from east to west as the surveyor directs.
      5. Once alignment is achieved, the first team bypasses the second to become the third, etc. The second team guys their pole in place and repeats the previous steps to extrapolate another line to the south. Via such leapfrogging gnomons, a long north-south line can be surveyed.
Practical Considerations
      Poles would surely be selected to look straight; otherwise, they will not balance well on end. Without a wind, they ought to have been able to tune the guys for equal (and minimal) tension.
      The pole top should be thick, in the manner of modern utility poles, to produce a sharp shadow. Even with a squared-off top, the shadow will taper to a point at a distance (from the top of the pole) of about a hundred times the pole's width at the top, thanks to the 0.5°-wide sun. For example, for a three-story-high pole of 10 meters and a diameter of 14 cm, the square-tipped noon shadow will become a point when the afternoon sun reaches an elevation of 45°. Fastening a broad object or pennant to the top of the pole would be useful when trying to detect the tip of a long shadow.
      Errors can be either to the east or the west on any given leg but, unless there is some cumulative bias (say, always sighting along the same side of the post, or always folding the east-west rope in the same direction), errors ought to average out and a line will form bracketing a meridian line -- though not necessarily the one that began the series. Shorter legs would keep errors from being amplified. On any one leg, assuming autumn long shadows, the pole-to-noon leg is about 70% longer than the pole, but the surveyor can stand farther back to judge the center-stake alignments, so that's the judgment that governs the error; the farther back, the less the width of the nearby pole will obscure errors in the placement of the distant one.
      The method would not work well in forests, where sightlines can be hard to maintain. But surveyors would tend to leap over valleys3, going from one ridge line to the next, clearing any trees on the ridgeline that interfere with extending the sightline north and south. However, because the land is not approximately flat near ridgelines, there will be errors in using shadow lengths along the ground. An artificial horizontal plane would be useful in most locales.
      Given a vertical pole to rotate about, there is a simple method for generating a horizontal plane. Two radial ropes are used, one rotating about the base of the pole and the other about a higher point, both being defined by pegs or circumferential grooves that keep the respective rope loops from sliding along the pole. The far ends of the two ropes are knotted together, thus fixing their elevation relative to the pegs when held taut, and this would be true along any radial. When the triangle is rotated about the pole, the knot's travels thus define a plane perpendicular to the pole's axis -- and this is horizontal if the pole is indeed vertical. The practicalities of keeping a heavy pole balanced guarantees a vertical alignment, in line with gravity, if they avoided support from the sides of a hole; the pole could be placed on a large slab of stone4 to keep it from holing the ground.
      For the gnomon application, tie a series of N knots in the lower radial rope, then tie the two rope ends together at a comfortable elevation -- say, waist height. As the gnomon shadow rotates, follow it with the ropes5, holding them taut at all times via the end knot. Each of the knots will then be rotating in its own horizontal plane. In the morning, when the shadow shortens enough to reach the rope end, drop a long stake to mark the spot. When the Kth knot is reached, stake that position as well. And so on in the afternoon, as shadows lengthen. When the Kth knot is again reached, use another rope to make a line to its morning partner, bisect it via folding, and drop another center-line stake. Once discovered (and the circular architecture and leveled benches of kivas suggest the Anasazi knew such a rotating rope triangle technique), the rope triangle would surely have been used in preference to clearing and leveling ground around a temporary gnomon.

      Were a leapfrogging gnomon method used along the Lekson meridian, 107°57'W, it seems likely that the poles would have been left somewhere along the line rather than carried back home. Even if they were not permanently erected as gnomons, such valuable timber would likely have been incorporated into structures. Examining tree ring series at the Casas Grande ruins might, for example, discover beams whose decadal weather profiles match those of forests far to the north. Another kind of evidence might come from investigating ridgelines along the Lekson meridian (some of which are on the shoulders of mountains) for archaeological evidence, perhaps equivalents to the Pueblo people's prayer shrines in remote locales6.
      The surveyors might not, of course, have stopped at Casas Grande, continuing south in search of the spot when the pole's shadow disappeared at noon on the summer solstice. The Tropic of Cancer is, alas, offshore in the Pacific Ocean at that meridian, but they could have gotten within a degree by the time that 107°57'W reached the coastline, near the modern city of Culiacán. Given that the pole is tapering, it would be difficult to detect such a shadow at the base of the pole, so the coastline at 107°57'W might well have seemed the right spot, the final destination.


E. C. Krupp, Echos of the Ancient Skies (Harper and Row, NY, 1983). The original length may be somewhat off, and I have substituted additional information in [brackets] from E. C. Krupp (personal communication 1997). He adds that

The most accessible reference for this is Joseph Needham, either his Science & Civilisation in China, Vol. III, page 293, or Needham's article in "The Place of Astronomy in the Ancient World," Transactions of The Royal Society of London, Vol. 276, No. 1257, 1 May 1974, page 74 (his article is "Astronomy in Ancient and Medieval China." Needham was citing a paper by Willy Hartner, and his is the fundamental reference. Even better is

Beer, A.; Ho Ping-Yü; Lu Gwei-Djen; Needham, J., Pulleyblank, E.G., and Thompson, G.I. "An 8th-Century Meridian Line: I-Hsing's Chain of Gnomons and the Pre-history of the Metric System," in Vistas in Astronomy, Vol. 4., (edited by Arthur Beer). Oxford: Pergamon Press, 1961: 1-28.

Stephen H. Lekson, Great Pueblo Architecture of Chaco Canyon. University of New Mexico Press (1984).

Stephen H. Lekson, "Rewriting Southwestern Prehistory," Archaeology 50(1):52-55 (January/February 1997). See story in New Scientist (14 December 1996) and in Salt Lake Tribune (2 December 1996).


1There are actually several north-south lines at somewhat different longitudes. The Great North Road is mostly straight along 107°52' but jogs west, both at its north end (the Aztec Ruins are at about 108°0') and at its south end (where, at Chaco, it meets the prominent north-south alignment of Pueblo Alto, Casa Rinconada, and Tsin Kletzin at 107°57.5').

2Actually, only one gnomon is really needed, as a signal fire would substitute for the second until the first pole could be carried there.

3The meridian can later be extended through the valley, once both ridgelines have a marker pole or signal fire. Two observers stand with a rope stretched out between them; the southern observer maneuvers until the northern marker pole appears above the head of the northern observer. If the northern observer simultaneously sees the southern pole in line with the southern observer, the rope lies along the meridian; otherwise they relocate until both alignments occur at the same time. Note that isolated segments of the meridian can be determined in mid-valley without actually surveying the entire path from ridge to ridge.
      Surveying long lines that are not north-south, such as Chaco's other ancient roads, can use this two-observer method: build large signal fires at each end of the desired path on a still day and then maneuver inbetween. To extend the line, build two signal fires on the existing line and a single observer can maneuver to align them. By using tall smoke plumes, line of sight may not be required to establish alignments.

4One of the Anasazi architectural features, also seen at Casas Grandes, is the practice of burying sandstone disks beneath roof supports -- one way of assuring vertical alignment of a pole balanced atop such a slab (but perhaps just a good way of preventing settling as rainwater undermines a buried pole base).

5Viewing a shadow in midair requires only the broad back of an assistant, bent over beneath the lower rope. Alternatively, tie sticks into the rope (so the knot position can be easily seen on the shadow on the ground) and watch for when the pole tip's shadow reaches a stick shadow.

6Stephen C. McCluskey, "Historical archaeoastronomy: The Hopi example," in Archaeoastronomy in the New World, edited by A.F. Aveni, pp.31-57, Cambridge University Press, Cambridge (1982). Speaking about prayer shrines as solstice sightline markers, the historian notes : "[The] shrines are small, easily disturbed, and bear few of the criteria to give them much credence as distant foresights, except that we are told that they are, and the direction in which they lie confirms this." I discuss this further at pp. 169-170 of How the Shaman Stole the Moon (Bantam 1991).
      In the absence of roads, something similar might mark meridian sightlines where they cross ridgelines with good views to both the north and south. Clearly, some Anasazi sites are critically situated for multiple views: besides marking the winter solstice sunset from Hungo Pavi and the north-south line from Pueblo Alto, Tsin Kletzin (atop Chaco's South Mesa) has a structure (Kiva A, see Lekson 1984, p. 231) with sightlines to six other outlying sites in various directions, some of which are lost by moving 10 m.

"I think they did it all at night, walking backward, watching Polaris."
the architect and illustrator
Mac Wells, 1997


Stephen H. Lekson, editor. The Architecture and Dendrochronology of Chetro Ketl. Reports of the Chaco Center, No. 6, Division of Cultural Research, National Park Service, Santa Fe (1983).

Curtis F. Schaafsma, "The Casas Grandes Interaction Sphere," excerpted from a paper presented at the Durango Conference on Southwest Archaeology (September 16, 1995).

W. J. Judge et al., "The Chaco Canyon Community", Scientific American (July 1988), p. 72.

John Kanter, "An Evaluation of Chaco Anasazi Roadways," webbed research paper and graphics presented to the Society for American Archaeology (1996).

William H. Calvin is neither a surveyor nor an archaeologist. He has written about the Anasazi in two books, The River That Flows Uphill (Sierra Club Books 1987) and How the Shaman Stole the Moon (Bantam 1991). The latter is about prehistoric astronomy, a dozen entry-level methods for predicting eclipses of the sun and moon, and it contains much more on the use of constructed sightlines for making measurements of high accuracy. He is a theoretical neurophysiologist, e.g., How Brains Think (Basic Books 1996) and The Cerebral Code (MIT Press 1996).
Original elements ©1996, 1997 W. H. Calvin

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