THOMAS] EXPLANATION OF (SERIES ON PLATES 35 TO 37. 281 



testing the Hues of numei'als in the manner explained. It is appar- 

 ent, therefore, that the following plates form one unbroken series, 

 running from left to right: 29, 30, 31, 33, 33, 34, 35, 36, 37, 38, 39, 40, 

 41, 42, 43, 1, 2; a conclusion which Dr. Forstemann, who has had the 

 opportunity of studying the original, has now reached. 



Having ascertained the object and use of at least one class of black 

 numerals and the relation they bear to the days and day numbers, it 

 may be well to test further the discovery by other examples, in order 

 to see how far it holds good and what new facts it may bring out. 

 In doing this it will be necessary to repeat in part what has already 

 been shown by Dr. Forstemann in his late work; but as these dis- 

 coveries were made independently and before this w^ork came to hand, 

 and as our conclusions differ in some respects from those reached by 

 him, the plan and scope of this paper W(juld be incomplete without 

 these illustrations. 



Commencing with the day column in the middle of Plate 356 and 

 extending through Plates 3Gb and '67b to the right margin of the lat- 

 ter, is a line of alternate red and black numerals, which may be taken 

 as an example of the most common series found in the Dresden and 

 other codices. It is selected because it is short, complete, and has 

 no doubtful symbols or numerals in it. 



Using names and numbers in place of the symbols, it is as foUoAvs: 



I. 

 Caban, 11, Xll: 6, V; 9. I; 4, V; 7, XII; 9, VIII: 6, I. 

 Muluc. 

 Ymix. 

 Been. 

 C'hicchan. 



In this case the red numeral over the day column is I. It is to be 

 observed that the last number of the series is also I, a fact which it 

 will be well to keejj in mind, as it has an important bearing on what 

 is now to be presented. But it is proper to show first that this series 

 is continuous and is connected with the day column. 



Adding the I over the column to the 11, the first black numeral. 

 gives XII, the red numeral following the 11. That this In il . l^ ,<;■(.(" 1 in 

 all cases of this kind will become apparent from the exiuiipli's w hicli 

 will be given in the course of this discussion. Adding together the 

 remaining pairs, as follows: XII-|-G-13=V; V-|-9-13=l; H-4=V; 

 V-|-7=XII; XII-f-0-13=VIII; Vlll-f G- 13=1, we obtain proof that 

 tlie line is one unbroken series. It is apparent that if the black 

 numerals are simply counters used to indicate intervals, as has been 

 suggested, then, by adding them and the red numerals over the col- 

 umn together and casting out the thirteens, we should obtain the last 

 red number of the series. In this case the sum of the numbers 1,11,0, 

 9, 4, 7, 9, 6, is 53; casting out the thirteens the remainder is I, the 

 last of the series. If we take the sum of the black numbers, which 



