260 MAYAN CALENDAR SYSTEMS [eth. axx. 22 



ami numeral systems, should Ix' accepted ratlier than a tlieory which 

 introduces new and hitherto unknown featui'es. 



If we use ordinary numbers in place of tlie numeral syml)ols, and 

 keep them in the relative pctsitions given above, the result will be as 

 follows : 



If we assume these to be successive orders of units indicated by 

 relative position, increasing upward, the day being counted as the 

 primary unit and the vigesimal system being used, except in passing 

 from the second to the third order, where the multiple is 18, all the 

 requirements of the series will be met. Thus, in the first, or right- 

 hand, column, we have IS units of the 1st order and 3 of the second, 

 or 3x20 = 00, making together G0+1S = 7S; and in the second column 

 •Ki of the 1st order and 7 of the 2ud order, or 7x20=140, making 

 together 140+16 = 156, and so on to the fifth column, where we find 

 10 of the 1st order, 1 of the second, or 1x20=20, and 1 of the 3rd 

 order, or 18 x 20=360, making together 360+20+ 1(J=300. Thesenum- 

 bers give correct results, as, counting 78 days from 13 Muluc, we reach 

 13 Manik; counting 150 from the same initial date, we reach 13 Chic- 

 chan, or counting 390 days, we reach 13 Cauac. It is clear, therefore, 

 that if we take these numerals to indicate the number of different 

 orders of units, the orders being indicated by relative position, all 

 re(iuirements of tlie series are satisfied and the proper results are 

 obtained. 



If we take one of the high series we find that preciselj^ the same lule 

 obtains, as, for example, one of those on plate LXii, Dresden code.x 

 (see plate Lxxix): 



4 of the tith order of units 4 



6 (if the .jth order of units ■- 6 



9 of the 4tli order of units ._ • • --^ 9 



1.") of the 3rd order of units __ ^^^^ 15 



13 of the 3nd order of units . ' • • 12 



19 of the 1st order of units " ' ' ' 19 



This is upon precisely the same principle as oui; metliod of expressing 

 numbers, except that it is according to the vigesimal system, while 

 we use the decimal. Take the number 643,527, where the relative 

 positions express the relative values, it becomes possible to represent 

 the number thus : 



6 hundred thousands 



4 ten thousands 

 3 thousands 



5 hundreds 

 2 tens 



7 units 



