PRE-COLUMBIAN UNITS OF MEASUREMENT : A Palpa mountain geoglyph may reveal the secret of how the Pre-Incas evolved a scale of measurement.

Introduction. A standard Unit of Measurement was known to exist in some Early Civilisations but the origin of the base unit has always remained obscure. Proposed basic units ,the length of the Kings’ foot, or thumb to elbow, for example, are at best speculative. Other units have been derived by statistical analysis which essentially takes a high number of “averaged unit lengths” which dimensionally fit into a “ high average number of given constructions” - stone circles, for example; this method certainly suggests the possibility of standardisation but is unlikely to reveal the original derivation or the precise magnitude of the basic unit length.

A bi-product of an early 1980’s research programme investigating the relationship between Nascan geoglyphs and astronomical phenomena indicated statistically that the Nasca lines and biomorphic designs were not only constructed using a standard unit of measurement (as suggested by Dr Maria Reiche) but the basic unit might be linked to celestial movements. However, lack of precise survey information precluded further exploratory research . Analysis of a recent aerial photograph of an immense geometric geoglyph found in the Palpa region, 20 kms to the north-west of the small township of Nasca, has given the first clues, not only that the pre-literate indigenous population had access to a standard unit of measurement , but analysis of the geoglyph construction has possibly revealed the principle upon which the unit of length was based.


METHOD OF CONSTRUCTION : The following is a simplified version of the construction used to develop the scale drawing from the geoglyph. aerial photograph.

An x - y axis was drawn to scale length using only dividers , then the horizontals and perpendiculars to form square H-I-J-K. Lengths H-A, A-B, H-U & UV were marked to scale and repeated for each corner. Join horizontals and verticals , adding the diagonals. Through each diagonal bisection, strike off horizontal and vertical grid lines. Complete the whole grid square, H-I-J-K, using the minor grid squares so derived; this will automatically produce the centre cross - shaped box.

It was evident that the geoglyph could be constructed from a series of common lengths directly related in multiples By direct measurement the lengths (units of measurement) could be scaled up in ascending order, one small grid square =13.625 mms, two = 27.25 mms, four = 54.5 mms ........eight = 109 mms, etc.
Diagonal lengths of individual grid squares were 19.3 mms, 27.25 mms, 38.5 mms, 77.2 mms .( i.e. = 2 x,3 x, 4 x 19.3 mms etc)

Square H-I-J-K side lengths equal 8 x 8 major grid squares of 27.25 mms = 218 mms.
Square, H-I-J-K sides equal 16 x 16 minor grid squares of 13.625 mms = 218 mms

Square R-S-T-Q of the geoglyph is turned through 45 ° aligning with the diagonal bisections of square H-I-J-K. Extension of all diagonals forms a second parallel grid .
Square R-S-T-Q sides equal 12 x 12 grid squares of 19.3 mms = 232 mms
Circles.
Outer circle diameter Z-D = 2BF = 2 x 109 = 218 mms. Circumference = 684.8 mms
Inner circle diameter equal to p-q = A-G = 163.5 mms. Circumference = 513.6 mms
Centre circle diameter = g-h = B-F = 109 mms. Circumference = 342.4 mms.

Angular measurements. The outer circle divides into 6 chords of length 109 mms , equal to B-F ,at 60° increments; this gives a naturally divisive circle of 15°, 30°, 45°, 60°, 75° & 90°......360 or 24 divisions of 15°;this could easily be sub-divided into 48 divisions. of 7.5° (in modern terms of degrees.) However, the outer circle appears to have 64 “markers” around the circumference . 360/64 = 5.625° increments ?.

Clockwise from X: OA = 52.5°, OB = 63.5°, OC = 72°, OD = 90°, OE = 108°, OF = 116.5° and OG = 126.9°.

Nominal historical	Azimuths	Geometriglyph
Mid-summer sunrise	65°	63.5°
Mid- winter sunrise	115°	116.5°
Mid-summer sunset	295°	297°
Mid-winter sunset	245°	243.5

The angular measurements taken about centre O replicate within 1.5° average the maximum swing of the solsticial sun for the latitude of the Nasca Lines. Angle BOF = 116.5° - 63.5° = 53°. Length B-F = 109 mms standard unit length. ( the geometriglyph azimuths are extremely close to the actual , bearing in mind they have only been scaled from an aerial photograph).

Similarly, angular measurements taken about centre O for the maximum most northerly /southerly swings of the moon OA and OG replicate closely calculated figures for the latitude of the Nasca Lines. Thus ,angle AOG = 126.9° - 52.5° = 74.4°. Length A-G = 163.5 mms - a standard unit length . ( 12 x 13.625 units).

Angular measurements about centre O for the minimum northerly / minimum southerly lunar swings , OC and OE alignments, have an included angle of 108° - 72° = 36° . Diameter of the outermost circle ZOD = 3 x CE = 3 x 72.66 = 218 mms. Thus 72.66 is another unit of length multiple ( 1/3 rd of 218 mms ) .

Astronomically speaking ,unit length B-F = 109 mms represents the maximum annual solsticial swing of the sun between mid-summer sunrise (or sunset) and mid-winter sunrise (or sunset). Similarly unit length C-E = 72.66 mms represents the swing of the moon at minor standstill . Unit length A-G = 163.5 mms the swing of the moon at major standstill. ( 12 x 13.625 units, or 12 minor grid squares)


Conclusion: Evidence presented briefly in the above resume clearly establishes that UNITS OF MEASUREMENT can be and were derived in Precolumbian Peru utilising astronomical phenomena; the maximum annual solsticial swing of the sun and the maxima/minima swings of the moon at the end of its 18.6 year cycle.

The scale drawing and grids were developed without recourse to mathematics or measuring instruments other than straight edge and dividers except to measure unit lengths in millimetres to test for a datum and existence of a graduated scale. The units of measurement derived by the author matched almost precisely those predicted by the late Dr Maria Reiche .

Reiche: 13.46       32.5     38.2                     82 cms.                       -
Author: 13.625     32.7     38.6 (2 x 19.3)     81.75 (3 x 27.25).     109 ( 13.625 x 8 ) cms..........etc.

Reiche also reported a 11 mm unit .Reducing standard unit 13.625 by a factor of 12 results in an increment of 1.1 mms. (11 mms & 11 cms. factoring by 10).

Comparison with other civilisations. Units of length employed by other Early Civilisations equate very closely to those derived for Precolumbian Peru . Using 109 mms as the Standard Unit of Length, for example -

Peru -

The Temple of the Sun: 93 ft. x 47 ft.
Equivalent to 260 (.05) x 130 (.14) Standard Units .

Egypt -

Obelisk (Cleopatra’s Needle): 68 ft. high.
Equivalent to 190 (.15) Standard Units.

Obelisk (unfinished): 137 ft high.
Equivalent to 383 (.09) Standard Units.

Stonehenge -

Aubrey Circle: 285 ft dia. Equivalent to 797 (796.95) Standard Units.

Sarsen circle : 97 ft dia. Equivalent to 27 (.1 ) Standard Units.

Y hole circle: 126 ft dia Equivalent to 352 (.2 ) Standard Units.
Blue stones circle:78 ft dia. Equivalent to 218 (.1) Standard Units.

These are just a few examples which show a close match to the Precolumbian Units of Length extrapolated from the Palpa geometriglyph .

One final interesting point arising from the investigation; the angular difference between the major and minor moon swing extremes is 72° - 52.5° = 19.5 ° approx. The average annual angular change of the moon’s nodal cycle is 360/18.61 = 19.3°; one standard unit of length = 19.3 mms. Also, 109 mms / 5.625 = 19.3.

This overview does not claim to be complete or try to give an in depth analysis or explanation to what is an extremely complex Precolumbian geoglyph. Neither does it suggest that Old and New World Civilisations got together to agree a Universal Unit of Length. Whilst initial results are encouraging ,only a full site survey can support the hypothesis, but read in conjunction with “ The Rosetta Stones of Nasca “ it provides much food for thought.

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