THOMAS] REAL NATl'RE OB^ SO-CALLED TIME PERIODS 261 



If, iiisteail of adding the written names, simiily the figure should 

 be given, the rehxtive positions being maintained and understood, we 

 would have the ^Maya method, and the value would be known as well 

 as by our ordinaiy method of writing numbers horizontally. 



I have given these details of elementary rules and principles iu 

 order to lead up to this point, viz, that symbols may be ixsed to indi- 

 cate orders of units instead of position. In the last example given 

 above, a .symbol may be adopted for the "hundred thousands," 

 another for "ten thousands," another for "thousands," etc. They 

 maj- then be grouped in any regular order inost convenient, and yet 

 be as coi-rectly read as by position. This is precisely what has be(>n 

 done in the inscriptions. Sj-mbols have beeii adopted to indicate the 

 orders of units, as it was inconvenient to do this by means of relative 

 position alone? with the dots and short lines — at any rate it is apparent 

 that the latter method is uot so well adapted to the glyph form iu the 

 inscriptions; but even here we see a strong tendency to maintain the 

 relative position which almost universally obtains and is often the 

 onlj- means of determination. If we take Goodnmn's work and go 

 through it from beginning to end and substitute in every series where 

 they occur "units of the 2nd order" for his chueus, "units of the 3rd 

 order" for his ahaus, "units of the -tth order" for his katuns, "units 

 of the oth order" for his cycles, and "tinits of the 0th order" for 

 his great cycles, the result will be correct in every instance. I am 

 fully aware that this will be true whether we call them real time peri- 

 ods or orders of units. The point, however, for which I am contending 

 is, that as the INIaj'as had a .sy.stem of numeration and must have used 

 it ill expressing numbers in the codices and inscriptions, and this 

 numeral sj'stem corresponds exactly with (xoodman's supposed time 

 periods so far as these are given numerically correct by him, there 

 is no necessity or reason for the theory of a separate Maya chrono- 

 logical .system (identical so far as correctly given w-itli the Maya num- 

 eral system as used in counting time), differing from their calendar 

 sj'stem. 



From the evidence given in the earlier part of this paper and what 

 has been presente(l in mj' preceding pajier, the following conclusions 

 appear to be clearlj- justified: 



That Mr Goodman has dl.scovered independently the sigtiification 

 and numeral values of the symbols found in the inscrii)tious which he 

 designates by the names cycle, katuu, ahau, chuen, and calendar 

 round, though this had been already done in part by others. 



That he has discovered that certain face and other characters are 

 number symbols, and has ascertained theii- values. 



That he has determined the object and use of the numeral series, 

 aud the method of counting by the same .series from the preceding 

 and following dates, as well as to them. 



