Foii.sTK.MAXN] THE LARGE NUMBERS 401 



The last two remainders are both meant for the day VIII 17. 

 Now, directly in the middle of the page the day X 17 is recorded, 

 but over the X an VIII is written quite fine as a correction. 



Without being set down a second time, these last two large num- 

 bers are the minuends in the two final cases; but the subtrahends, 

 which should reall}' be encircled, do not stand here, but on page 73, 

 at the top of the fourth and fifth columns, at the farther end of the 

 series of numbers ^^■hicll extends from pages 70 to 73, since there was 

 no room for them on page 70. Thus we read : 



Page 70. 1,507,332— (page 73) 34,732=1,532,«J00, again=VIII 17. 

 Page 70. 1,520.654— (page 73) 83,474^-1.437.180, again=VIII 17, as we 

 read page 70 corrected. 



Thus it is proved by twenty-one large and as many smaller numbers 

 surrounded by circles and bv applying but few" and insignificant con- 

 jectures, in the first place, that the circles in a w^ay signified the minus 

 sign ( — ) with the Mayas and, in the second, that the large numbers 

 alw^ays denoted pai'ticular days. As a rule, then, the large number 

 is the minuend and the encircled number the subtrahend, while the 

 remainder is recorded in the manuscript, not by a number, but by 

 its corresponding day. 



But there are found on pages 51 and 52 six more large numbers 

 without such encircled subtrahends; unfortunate!}', these are in parts 

 very indistinct and probably spoiled. First, on page 51, the numer- 

 als 8, 16, 4, 11, occur. If an 8 is read here instead of the 11, 

 the result is the number 1 ,268,800 ; that is, the most important of all 

 days, IV 17, which likewise seems to be recorded above. Numerals 

 in red, 10, 19, 6, 0, 8, are crowded in between these numbers. If 

 we substitute a 1 here for the 0, we have 1,578,988, the day XII 5, 

 therefore, and this date is set down below. 



The following page, 52, at the right near the top, contains four 

 large numbers, again two black ones with two reel ones written in 

 among them, tAvo in the fifth and two in the sixth column. The two 

 occurring in the sixth present no difficulty; they are 1,412,848 and 

 1,412,863, and below the days XII 5 and I 20 are specified, which, in 

 fact, correspond to the numbers. "Jlie difference between the numbers, 

 as between the days, is 15. On the other hand, the numbers in the 

 fifth column can not be made to agree. The manuscript reads 9, 16, 

 4, 10, 18, and 9, 19, 8, 7, 8. I propose in the first number to read 11 

 instead of 10 and in the second 5 instead of the first 8 ; then the num- 

 bers will denote 1,412,878 and 1,434,748, and these actually correspond 

 to the days III 15 and ^^11 5, which are recorded below. In fact, the 

 first of the two numbers is distant by a difference of 15 from the num- 

 ber 1,412,863, as well as the first of the two days, from the day I 20 



7238— No. 28—05 26 



