HOLMES ANNIVERSARY VOLUME 



Professor Willson of the Department of Astronomy at Harvard Uni- 

 versity suggested to him that these two coefficients might be united 

 to the quantity they modified by addition rather than multiplication, 

 giving the numbers 29 and 30 instead of 180 and 200. This proved 

 to be the correct explanation of the glyph, and immediately indicated 

 its true function as that of the sign for a discriminating lunar month 

 now of 29 days and now of 30 days in length. 



Objective corroboration of this point was soon forthcoming. The 

 writer had long noticed a marked difference in the position of the 

 coefficient in Glyph A as compared with the positions of the coeffi- 

 cients in all other known glyphs, the period, day, and month signs. 

 In the latter the coefficients invariably occur to the left of, or above 

 the element modified. ' In Glyph A, on the other hand, the coefficient, 

 with but three exceptions, is as invariably placed to the right of the 

 moon-sign or below it. (See Nos. 54, 55, and 56.) These exceptions, 

 however, are all found on very late monuments, in fact the three 

 latest at Quirigua. They were erected and inscribed at a period when 

 the Maya had a long and rich experience behind them, and there 

 could have been no longer any doubt in the minds of the priests 

 how the coefficient of the moon-sign was to be joined to it, namely 

 by addition, and not by multiplication as the positions of these three 

 coefficients would appear to indicate. 



Such rare exceptions are relatively unimportant, and it is evident 

 that by placing the coefficients of Glyph A in what were obviously 

 unusual places for coefficients, i.e., behind or below the glyphs modi- 

 fied, the ancient Maya were calling attention by this departure from 

 the regular practice, to the fact that such coefficients were joined to 

 the glyphs they modify by some process other than the usual one of 

 multiplication. If not multiplication, then addition, the simplest of 

 all mathematical processes, would appear to be indicated, and the 

 resultant sums of 29 and 30 — the sine qua non of any lunar count 

 not dealing with fractional days — may be accepted as proof of the 

 point. 



This use of the moon-sign is paralleled in tonalamatls in the 

 codices. Here, when the exigencies of the count required the record 

 of some number in excess of 19, the moon-sign is used with a coefficient 



1 A single exception to this general rule must be noted. On a very early monument (9.3.13.0.0.), 

 discovered by the writer in May, 1916, Stela 6 at Uaxactun, the glyphs on the left-hand side 

 face to the right instead of to the left. These glyphs are the kin, day, and month signs of an 

 Initial Series, and all have their coefficients at the right, i.e. after them. Such a radical departure 

 from an otherwise unvarying rule was due probably to the desire to have the glyphs on both sides 

 of the monument face toward its front, which could be accomplished only by having those on 

 the left side face to the right. 



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