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a building whose ancient name, it is said, was a division into ten,' there is one typifying, or rather positively illustrating, a division into five.
"The coffer, according to the metrological theory, is founded in part on the one ten-millionth of the earth's axis of rotation.
"This is something suspicious of a connection, especially if divided by the pyramidal ten, but not enough; and on looking round the room, an attentive observer may soon perceive a more striking illustration of the division into five, in that the four walls of the room have each four horizontal joint lines, actually dividing the wall's whole surface into five horizontal stripes or courses.
"Hence the chamber is constructed commensurably to the coffer, and the coffer to the chamber, with fifty and five as the ruling numbers. But there exists even more testimony of this sort, identifying the whole pyramid also with the coffer and its chamber, in a quarter, too, where I had certainly never expected to find anything of the kind; viz., the component course of masonry of the entire building."2
From the foregoing observations by Mr. Piazzi Smyth, it is evident that the Egyptians made use of a decimal system derived from their knowledge of the length of the earth's diameter, just as the Mayas did.
Landa tells us that, in archaic ages, before the occurrence of the events which induced them to alter the basis of their chronological computations and adopt as such the number
1 C. Piazzi Smyth, Life and Work at the Great Pyramid, vol. iii., pp.
3 Pio Perez, Cronologia Antigua de Yucatan. Apud Landa, Las Cosas de Yucatan, p. 404. Brasseur's publication.
thirteen, they also made use of the decimal system. "They counted in fives and twenties up to one hundred." "Que su cuenta es de Ven V hasta XX, y de XX en XX hasta C."1
Cogolludo, Lizana, Torquemada, in fact, the majority of the chroniclers who have written on the manners and customs of the ancient Mayas, mention this mode of computation by them until that by thirteenths was adopted. Of all these writers Landa alone hints at the cause of this change.
Many a long and senseless discussion, full of profound learning, has been indulged in; many an eloquently written dissertation, replete with more or less specious reasons to show why the wise men of Mayach adopted the number thirteen as a basis for their computations, has been published by erudite professors, each advocating his private opinion with as much ardor as uselessness. And the conclusion? The same, of course, as that reached by that "scientific society on the Stanislaus," whose debate on a certain jaw-bone, whether it was that of a mule or that of an ass, Bret Harte has recounted. All because they never read the book of Landa, or they disdain to believe the relation of a man who was in an exceptional position to learn much concerning the native traditions.
We need not rely altogether on Landa's testimony regarding the use of a decimal system by the Mayas. We find abundant proofs in the ruins of their temples and palaces.
Had the learned Professor of American Archæology of the Pennsylvania University been less grossly ignorant of all things relating to the Mayas, their religious and cosmogonic notions, their scientific attainments, the meaning of their architecture, and their language, he certainly would not have indited such a paper as his "Maya Measures," nor attributed to eccentri1 Landa, Las Cosas de Yucatan, chap. xxxiv., p. 206.
city my statement that they made use of the metre as a standard of lineal measures.
As to his emphatic assertion that he "does not see from my own measurements that the metre is in any sense a common divisor for them," this is not in the least surprising. He has never personally measured the Maya constructions; he has
never had access to my field notes, or any of the restorations of the buildings made by me from said notes and from the photographs of said edifices made by me in situ. He has only looked superficially at the few plans in my possession when he honored me with his visit; these did not seem to interest him.
The only example of the use of the metre by Maya astron
omers, architects, and mathematicians, ever published from manuscripts written by me, is the protraction of a gnomon which I discovered in the ruined city of Mayapan, situated on the lands of the hacienda X-Canchakan, distant thirty miles from Merida, the capital of Yucatan. This protraction forms part of one of my reports to the "American Antiquarian Society," of Worcester, Mass. (See illustration, p. 212.)
It is not the result of intricate calculations wherein errors may creep. It is a simple drawing constructed from measurements made by me in situ. These must, by force, have been very accurate, or the various parts of the drawing would not fit exactly in their proper places. Such protraction should therefore settle all doubts regarding the true standard of lineal measures used by the Mayas, in very remote times, and even after the destruction of the Land of Mu by earthquakes and submergence.
This report was published in the proceedings of said society under the title of "Mayapan and Maya Inscriptions." It contains various typographical errors. The proof-sheets were not submitted to me before being sent to press (I was then in the forests of Yucatan). Therefore I could not correct them. There is, however, one mistake which is due to a lapsus calami on my part. How did it occur? It was one of those inexplicable oversights that frequently take place in making computations; perhaps a temporary systematic anæsthesia produced by the concentration of the mind on a single point when passing over a number of figures in calculation. At any rate, there is no mistake in the drawing, which is perfect, and in accordance with the measurements made of the gnomon itself.
The diameter of the columns is 0.45 metre. The distance
between their centres is 1.90 metres. In my manuscript, it
seems, I wrote 1.70 metres, or I made the 9 and 7 so as to mislead the printer; and therein consists the grave error that has given ground for Dr. Brinton's criticism of all my measurements. Had he not been looking for an excuse to impugn the conscientious work of an original explorer, thereby seeking his own aggrandizement, he could have seen that the error was merely typographical; and that my statement "that the Mayas, like the Chaldees, did certainly use the metre as a standard of lineal measures," was not eccentricity, but positive knowledge.