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Above forty, three different methods can be used to continue the numeration.

1. We may continue the same employed between 20 and 40, thus:—

and so on.

2. The numeral copulative catac can be used, with the numeral particle tul; as:—

3. We may count upon the next score above, as:

The last mentioned system is that advanced by Father Beltran, and is the only one formally mentioned by him. It has recently been carefully analyzed by Prof. Leon de Rosny, who has shown that it is a consistent vigesimal method.40-1

It might be asked, and the question is pertinent, and is left unanswered by Prof. Leon de Rosny, why hun tu kal means “one to the score,” and hun tu can kal is translated, “one on the fourth score.” This important shade of meaning may be given, I think, by the possessive u which originally belonged in the phrase, but suffered elision. Properly it should be,

Hun tu u can kal.

This seems apparent from other numbers where it has not suffered elision, but merely incorporation, as:—

This system of numeration, advanced by Beltran, appears to have been adopted by all of the later writers, who may have learned the Maya largely from his Grammar. Thus, in the translation of the Gospel of St. John, published by the Baptist Bible Translation Society, chap. II, v. 20; Xupan uactuyoxkal hab utial u mental letile kulnaa, “forty and six years was this temple in building;”41-1 and in that of the Gospel of St. Luke, said to have been the work of Father Joaquin Ruz, the same system is followed.41-2

Nevertheless, Beltran’s method has been severely criticised by Don Juan Pio Perez, who ranks among the ablest Yucatecan linguists of this century. He has pronounced it artificial, not in accordance with either the past or present use of the natives themselves, and built up out of an effort to assimilate the Maya to the Latin numeral system.

I give his words in the original, from his unpublished essay on Maya grammar.42-1

“Los Indios de Yucatan cuentan por veintenas, que llaman kal y en cierto modo tienen diez y nueve unidades hasta completar la primera veintena que es hunkal aunque en el curso de esta solo se encuentran once numeros simples, pues los nombres de los restantes se forman de los de la primera decena.

“Para contar de una à otra veintena los numeros fraccionarios ò las diez y nueve unidades, terminadas por la particula tul ò su sincopa tu,42-2 se juntan antepuestas à la veintena espresada; por exemplo, hunkal, 20; huntukal, 21; catukal, 22; y huntucakal, 41; catucakal, 42; oxtucankal, 83; cantuhokal, 140, etc.

“El Padre Fr. Beltran de Santa Rosa, como puede verse en su Arte de Lengua Maya, formó un sistema distinto à este desde la 2ª veintena hasta la ultima, pues para espresar las unidades entre este y la 3ª veintena pone à esta terminandolas y por consiguiente rebajandole su valor por solo su anteposicion à dichas unidades fraccionarias, y asi para espresar el numero 45 por ejemplo dice ho tu yoxkal, cuando oxkal ò yoxkal significa 60.

“No sé de donde tomó los fundamentos en que se apoya este sistema, quiza en el uso de su tiempo, que no ha llegado hasta este; aunque he visto en varios manuscritos antiguos, que los Indios de entonces como los de ahora, usaban el sistema que indico, y espresaban las unidades integras que numeraban, y para espresar el numero 65 dicen; Oxkal catac hotul ù hotu oxkal, que usa el Padre Beltran por 45.43-1

“Mas el metodo que explico esta apoyado en el uso y aun en el curso que se advierte en la 1ª y 2ª veintena é indican que asi deben continuar las decenas hasta la 20ª y no formar sistemas confusos que por ser mas ô menos análogos à la numeracion romana lo juzgaban mas ô menos perfectos, porque la consideraban como un tipo a que debia arreglarse cualquiera otra lengua, cuando en ellas todo lo que no este conforme con el uso recibido y corriente, es construir castillos en el aire y hacer reformas que por mas ingeniosas que sean, no pasan de inoficiosas.”

In the face of this severe criticism of Father Beltran’s system, I cannot explain how it is that in Pio Perez’s own Dictionary of the Maya, the numerals above 40 are given according to Beltran’s system; and that this was not the work of the editors of that volume (which was published after his death), is shown by an autographic manuscript of his dictionary in my possession, written about 1846,44-1 in which also the numerals appear in Beltran’s form.

Three other manuscript dictionaries in my collection, all composed previous to 1690, affirm the system