398 BUREAU OF AMERICAN ETHNOLOGY [bull. 28 



the sake of economizing space. He wrote the numerals 7, 2, and 14 

 in black one under the other, and joined to the 14 a red 5, leaving no 

 space between. Now, this 5 neither signifies an independent number 

 nor does it together with the 14 designate 19, but it denotes that 

 besides the 44 a 19 is to be understood. Thus we must read here 

 7, 2, 14, 19, the same group that is found on page 63." This explana- 

 tion is confirmed by the fact that the two other groups on page 31 

 (C, 1 and 0, 17) also occur on pages 02 and (■;3. 



The significance of these groups becomes more apparent if we 

 recognize the fact that the red circles refer not merely to the numerals 

 which they surround, but to the entire group, and that they are 

 attached to only one or two numerals in the group for the sake of 

 economy of space or for calligraphic purposes. Thus each group 

 constitutes one single number, which is to be read according to the 

 rule stated by me on page 5 of my Erlaiiterungen. 



The numbers are as folloAvs: Page 24, 2,200; page 31, 121, 17, 

 51,419; page 43, 352; page 45, 30; page 58, 511; page 02, 456, 121; 

 page 03, 235, 17, 51,419; page 70, 000, 1,046, 80, 208. 



To these sixteen numbers I add four more, which, it is true, have no 

 red circles in the manuscript, but which, according to my firm convic- 

 tion, are without a circle only because the space is limited, their pur- 

 pose being exactly the same as that of the other numbers under dis- 

 cussion. These four numbers are the following: 



1. Page 70, fourth column. 15, 9, 15, 14 (I place the figures side by 

 side, not one under the other) =111,554. 



2. Page 70, fourth column, written in red between the front numerals. 

 14, 2, IG, 12 (here I correct the 10 to 14, as in the penultimate numeral an 

 error of two units is quite natural owing to the Maya system of numera- 

 tion) =101,812. 



3. Page 73, fourth column. 11, 11, 15, 14=83,474. 



4. Page 73, fifth column. 4, 16, 8, 12=34,732. 



To speak briefly, each of these twenty numbers is intended to be 

 subtracted from a large number standing near it, in order that the 

 remainder shall denote a certain da}^ likewise standing near by. I 

 shall at once proceed to explain this matter more in detail. 



The Large Numbers 



On page 30 of my Erlauterungen is to be found a list of many 

 numbers, some of which, it is true, were incorrectly read at the time, 

 but they exhibited the remarkable circumstance that almost all of 

 them lay between a million and a million and a half. I think I have 

 come considerably nearer the solution of the riddle, which has hith- 

 erto seemed absolutely insoluble, by the hj^pothesis that each of these 



« The 5 appears to be a correction by the original scribe. C. T. 



